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Jordan Brand Extend their Flight Utility Collection with the Air Latitude 720

Air Jordan.

Jordan Brand’s lifestyle-focused Flight Utility Collection has opened up an entirely new market for the Jumpman Brand. While their retro department is now whole-heartedly lifestyle-focused, demand has shifted to the use of modern designs and tech — and that’s exactly what Jordan has achieved with this new range. Joining the already-intriguing Protro-Max, Protro-React, and Apex-Utility is the Air Latitude, which draws clear inspiration from the Air Unlimited and Air Jordan 8. But while Jumpman has looked to the past, their focus is still on the future. The use of sleek lines, ultra-light woven uppers, and other new materials, as well as Nike’s biggest and comfiest Air unit to date, has set this, and the entire Flight Utility Range, in a class of its own.

The two debut colorways – a triple black and a women’s Aqua influenced palette (similar to the recently previewed Air Jordan 8) – are set to drop on June 6th.

Tune in to our Release Calendar to stay up to date with Jordan release dates, add reminders directly to your calendar and find direct links for each drop!



Lowest layer of Earth's atmosphere

Atmospheric Circulation:the Three Cell Modelof the circulationof the planetary atmosphere of the Earth, of which the troposphere is the lowest layer.

The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur.[1] From the planetary surface of the Earth, the average height of the troposphere is 18 km (11 mi; 59,000 ft) in the tropics; 17 km (11 mi; 56,000 ft) in the middle latitudes; and 6 km (3.7 mi; 20,000 ft) in the high latitudes of the polar regions in winter; thus the average height of the troposphere is 13 km (8.1 mi; 43,000 ft).

The term troposphere derives from the Greek words tropos (rotating) and sphaira (sphere) indicating that rotational turbulence mixes the layers of air and so determines the structure and the phenomena of the troposphere.[2] The rotational friction of the troposphere against the planetary surface affects the flow of the air, and so forms the planetary boundary layer (PBL) that varies in height from hundreds of meters up to 2 km (1.2 mi; 6,600 ft). The measures of the PBL vary according to the latitude, the landform, and the time of day when the meteorological measurement is realized. Atop the troposphere is the tropopause, which is the functional atmospheric border that demarcates the troposphere from the stratosphere. As such, because the tropopause is an inversion layer in which air-temperature increases with altitude, the temperature of the troposphere remains constant.[2]

The atmosphere of the Earth is in five layers:
(i) the exosphereat 600+ km;
(ii) the thermosphereat 600 km;
(iii) the mesosphereat 95–120 km;
(iv) the stratosphereat 50–60 km; and
(v) the troposphere at 8–15 km.
The scale indicates that the layers’ distances from the planetary surface to the edge of the stratosphere is ±50 km, less than 1.0% of the radius of the Earth.

Structure of the troposphere[edit]


In the Earth’s planetary atmosphere, a volume of dry air is composed of 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide, trace gases, and variable amounts of water vapor. The sources of atmospheric water vapor are the bodies of water (oceans, seas, lakes, rivers) on the planetary surface, which humidify the troposphere through the process of evaporation, which influences the occurrence of weather phenomena; the greatest proportion of water vapor is in the atmosphere nearest the surface of the Earth. The temperature of the troposphere decreases at high altitude by way of the inversion layers that occur in the tropopause, which is the atmospheric boundary that demarcates the troposphere from the stratosphere. At higher altitudes, the low air-temperature consequently decreases the saturation vapor pressure, the amount of atmospheric water vapor in the upper troposphere.


The maximum air pressure (weight of the atmosphere) is at sea level and decreases at high altitude because the atmosphere is in hydrostatic equilibrium, wherein the air pressure is equal to the weight of the air above a given point on the planetary surface. The relation between decreased air pressure and high altitude can be equated to the density of a fluid, by way of the following hydrostatic equation:

{\displaystyle {\frac {dP}{dz}}=-\rho g_{n}=-{\frac {mPg_{n}}{RT}}}



The planetary surface of the Earth heats the troposphere by means of latent heat, thermal radiation, and sensible heat. The gas layers of the troposphere are less dense at the geographic poles and denser at the equator, where the average height of the tropical troposphere is 13 km, approximately 7.0 km greater than the 6.0 km average height of the polar troposphere at the geographic poles; therefore, surplus heating and vertical expansion of the troposphere occur in the tropical latitudes. At the middle latitudes, tropospheric temperatures decrease from an average temperature of 15°C (59°F) at sea level to approximately −55°C (−67°F) at the tropopause. At the equator, the tropospheric temperatures decrease from an average temperature of 20°C (68°F) at sea level to approximately −70°C to −75°C (−94 to −103°F) at the tropopause. At the geographical poles, the Arctic and the Antarctic regions, the tropospheric temperature decreases from an average temperature of 0°C (32°F) at sea level to approximately −45°C (−49°F) at the tropopause.[4]


The temperature of the troposphere decreases with increased altitude, and the rate of decrease in air temperature is measured with the Environmental Lapse Rate (-dT/dz) which is the numeric difference between the temperature of the planetary surface and the temperature of the tropopause divided by the altitude. Functionally, the ELR equation assumes that the planetary atmosphere is static, that there is no mixing of the layers of air, either by vertical atmospheric convection or winds that could create turbulence.

The difference in temperature derives from the planetary surface absorbing most of the energy from the sun, which then radiates outwards and heats the troposphere (the first layer of the atmosphere of Earth) while the radiation of surface heat to the upper atmosphere results in the cooling of that layer of the atmosphere. The ELR equation also assumes that the atmosphere is static, but heated air becomes buoyant, expands, and rises. The dry adiabatic lapse rate (DALR) accounts for the effect of the expansion of dry air as it rises in the atmosphere, and the wet adiabatic lapse rate (WALR) includes the effect of the condensation-rate of water vapor upon the environmental lapse rate.

Altitude Region Lapse rate Lapse Rate
(m) (°C / km) (°F / 1000 ft)
     0.0   – 11,000  6.50  3.57
11,000 – 20,000  0.0   0.0   
20,000 – 32,000−1.0−0.55
32,000 – 47,000−2.8−1.54
47,000 – 51,000  0.0    0.0    
51,000 – 71,000  2.80  1.54
71,000 – 85,000  2.00  1.09
Compression and Expansion

A parcel of air rises and expands because of the lower atmospheric pressure at high altitudes. The expansion of the air parcel pushes outwards against the surrounding air, and transfers energy (as work) from the parcel of air to the atmosphere. Transferring energy to a parcel of air by way of heat is a slow and inefficient exchange of energy with the environment, which is an adiabatic process (no energy transfer by way of heat). As the rising parcel of air loses energy while it acts upon the surrounding atmosphere, no heat energy is transferred from the atmosphere to the air parcel to compensate for the heat loss. The parcel of air loses energy as it reaches greater altitude, which is manifested as a decrease in the temperature of the air mass. Analogously, the reverse process occurs within a cold parcel of air that is being compressed and is sinking to the planetary surface.[2]

The compression and the expansion of an air parcel are reversible phenomena in which energy is not transferred into or out of the air parcel; atmospheric compression and expansion are measured as an Isentropic Process ({\displaystyle dS=0}) wherein there occurs no change in entropy as the air parcel rises or falls within the atmosphere. Because the heat exchanged ({\displaystyle dQ=0}) is related to the change in entropy (dS by {\displaystyle dQ=TdS}) the equation governing the air temperature as a function of altitude for a mixed atmosphere is: {\displaystyle {\frac {\,dS\,}{dz}}=0} where S is the entropy. The isentropic equation states that atmospheric entropy does not change with altitude; the adiabatic lapse rate measures the rate at which temperature decreases with altitude under such conditions.


If the air contains water vapor, then cooling of the air can cause the water to condense, and the air no longer functions as an ideal gas. If the air is at the saturation vapor pressure, then the rate at which temperature decreases with altitude is called the saturated adiabatic lapse rate. The actual rate at which the temperature decreases with altitude is the environmental lapse rate. In the troposphere, the average environmental lapse rate is a decrease of about 6.5°C for every 1.o km (1,000m) of increased altitude.[2] For dry air, an approximately ideal gas, the adiabatic equation is: {\displaystyle p(z){\Bigl [}T(z){\Bigr ]}^{-{\frac {\gamma }{\,\gamma \,-\,1\,}}}={\text{constant}}} wherein \gamma is the heat capacity ratio ({\displaystyle \gamma \approx \,}7⁄5) for air. The combination of the equation for the air pressure yields the dry adiabatic lapse rate:{\displaystyle {\frac {\,dT\,}{dz}}=-{\frac {\;mg\;}{R}}{\frac {\;\gamma \,-\,1\;}{\gamma }}=-9.8^{\circ }\mathrm {C/km} }.[5][6]


The environmental lapse rate (dT/dz), at which temperature decreases with altitude, usually is unequal to the adiabatic lapse rate (dS/dz\neq 0). If the upper air is warmer than predicted by the adiabatic lapse rate (dS/dz>0), then a rising and expanding parcel of air will arrive at the new altitude at a lower temperature than the surrounding air. In which case, the air parcel is denser than the surrounding air, and so falls back to its original altitude as an air mass that is stable against being lifted. If the upper air is cooler than predicted by the adiabatic lapse rate, then, when the air parcel rises to a new altitude, the air mass will have a higher temperature and a lower density than the surrounding air and will continue to accelerate and rise.[2][3]


Main article: Tropopause

The tropopause is the atmospheric boundary layer between the troposphere and the stratosphere, and is located by measuring the changes in temperature relative to increased altitude in the troposphere and in the stratosphere. In the troposphere, the temperature of the air decreases at high altitude, however, in the stratosphere the air temperature initially is constant, and then increases with altitude. The increase of air temperature at stratospheric altitudes results from the Ozone layer’s absorption and retention of the ultraviolet (UV) radiation that Earth receives from the Sun.[7] The coldest layer of the atmosphere, where the temperature lapse rate changes from a positive rate (in the troposphere) to a negative rate (in the stratosphere) locates and identifies the tropopause as an inversion layer in which limited mixing of air layers occurs between the troposphere and the stratosphere.[2]

Atmospheric flow[edit]

The general flow of the atmosphere is from west to east, which, however, can be interrupted by polar flows, either north-to-south flow or a south-to-north flow, which meteorology describes as a zonal flow and as a meridional flow. The terms are used to describe localized areas of the atmosphere at a synoptic scale; the three-cell model more fully explains the zonal and meridional flows of the planetary atmosphere of the Earth.

Three Cell Model[edit]

Zonal Flow:a zonal flow regimeindicates the dominant west-to-east flow of the atmosphere in the 500 hPa height pattern.
Meridional Flow:The meridional flow pattern of 23 October 2003 shows amplified troughs and ridges in the 500 hPa height pattern.

Main article: Atmospheric circulation

The three-cell model of the atmosphere of the Earth describes the actual flow of the atmosphere with the tropical-latitude Hadley cell, the mid-latitude Ferrel cell, and the polar cell to describe the flow of energy and the circulation of the planetary atmosphere. Balance is the fundamental principle of the model — that the solar energy absorbed by the Earth in a year is equal to the energy radiated (lost) into outer space. That Earth’s energy balance does not equally apply to each latitude because of the varying strength of the sunlight that strikes each of the three atmospheric cells, consequent to the inclination of the axis of planet Earth within its orbit of the Sun. The resultant atmospheric circulation transports warm tropical air to the geographic poles and cold polar air to the tropics. The effect of the three cells is the tendency to the equilibrium of heat and moisture in the planetary atmosphere of Earth.[8]

Zonal flow[edit]

A zonal flow regime is the meteorological term meaning that the general flow pattern is west to east along the Earth's latitude lines, with weak shortwaves embedded in the flow.[9] The use of the word "zone" refers to the flow being along the Earth's latitudinal "zones". This pattern can buckle and thus become a meridional flow.

Meridional flow[edit]

When the zonal flow buckles, the atmosphere can flow in a more longitudinal (or meridional) direction, and thus the term "meridional flow" arises. Meridional flow patterns feature strong, amplified troughs of low pressure and ridges of high pressure, with more north–south flow in the general pattern than west-to-east flow.[10]

See also[edit]


External links[edit]

Look up troposphere in Wiktionary, the free dictionary.
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Dell has refreshed its Latitude Rugged laptops portfolio by bringing two new models — Dell Latitude 5430 Rugged and Dell Latitude 7330 Rugged Extreme. The latest Dell Latitude Rugged models come with 11th-generation Intel Core processors and run Windows 11 out-of-the-box. Dell has offered optional 5G support on both Latitude 5430 Rugged and Latitude 7330 Rugged Extreme. The laptops are also claimed to deliver an improved battery life of up to 25 hours, along with fast charging support and dual hot-swappable batteries. Dell's latest Latitude Rugged models will compete against durable laptops offered by companies including Panasonic Toughbook and Getac.

Dell Latitude 5430 Rugged, Dell Latitude 7330 Rugged Extreme availability

The new Dell Latitude 5430 Rugged and Dell Latitude 7330 Rugged Extreme will be available for orders in global markets starting December 9. Pricing details are yet to be revealed.

Dell Latitude 5430 Rugged, Dell Latitude 7330 Rugged Extreme specifications

Dell Latitude 5430 Rugged and Dell Latitude 7330 Rugged Extreme both run on Windows 11 and come with daylight-readable displays, with up to 1,400 nits of brightness and glove-touch support. The laptops are powered by 11th-generation Intel Core processors, along with an optional vPro integrated platform. There is also TPM 2.0 ControlVault for advanced security. On the connectivity front, the new machines have Wi-Fi 6E as well as optional 5G support.

Dell has provided dual hot-swappable batteries on both Latitude 5430 Rugged and Latitude 7330 Rugged Extreme that are rated to deliver up to 25 hours of power on a single charge. You will also get Express Charge Boost that is touted to offer up to 35 percent of charge in 20 minutes.

In terms of differences, Dell Latitude 5430 Rugged carries a 14-inch screen, while Dell Latitude 7330 Rugged Extreme carries a 13-inch display. The Latitude 5430 Rugged also comes with an IP53-rated build and is claimed to be drop-tested from up to three feet. It comes with an optional discrete graphics card and its weight starts at 1.97 kilograms.

dell latitude 5430 rugged image Dell Latitude 5430 Rugged

Dell Latitude 5430 Rugged comes with a 14-inch display
Photo Credit: Dell


Dell compares the Latitude 5430 Rugged with Panasonic Toughbook 55 and Getac S410, claiming that it is the lightest model in the 14-inch semi-rugged laptop series.

The Latitude 7330 Rugged Extreme, on the other hand, comes with a more tough build that is IP65 certified and drop tested from up to six feet. It also includes the optional 1,400-nit display that has gloved multi-touch capability.

On the basis of an internal comparison with Panasonic Toughbook CF31 and Getac B360, Dell claims that the Latitude 7330 Rugged Extreme is the smallest 5G-capable 13-inch fully-rugged laptop.

Both new Latitude Rugged models come with Dell Optimizer software that is claimed to use artificial intelligence and machine learning to optimise system performance based on usage. The laptops are targeted at customers working in industries including oil and gas, first responders, as well as government and law enforcement.

Windows 11 has been unveiled, but do you need it? We discussed this on Orbital, the Gadgets 360 podcast. Orbital is available on Apple Podcasts, Google Podcasts, Spotify, Amazon Music and wherever you get your podcasts.

For the latest tech news and reviews, follow Gadgets 360 on Twitter, Facebook, and Google News. For the latest videos on gadgets and tech, subscribe to our YouTube channel.

Further reading: Dell Latitude 5430 Rugged Specifications, Dell Latitude 5430 Rugged, Dell Latitude 7330 Rugged Extreme Specifications, Dell Latitude 7330 Rugged Extreme, Dell Latitude Rugged, Dell, Windows 11

Jagmeet SinghEmail Jagmeet

Jagmeet Singh writes about consumer technology for Gadgets 360, out of New Delhi. Jagmeet is a senior reporter for Gadgets 360, and has frequently written about apps, computer security, Internet services, and telecom developments. Jagmeet is available on Twitter at @JagmeetS13 or Email at [email protected] Please send in your leads and tips. More
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How to cancel a booking

Please remember to cancel your booking via your original point of purchase as each partner has a unique booking system that we are unable to access, and they are better equipped to assist you.

If you booked directly through Air Canada, you may cancel your booking online by visiting My Bookings and following the instructions.

You may cancel your booking online if:

  • You originally booked your flight on or via the Air Canada mobile app
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For cancellations outside of 24 hours, refundability will depend on the fare type you purchased.

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I submitted a refund request (before the July 12 deadline) for a cancelled flight during the COVID-19 Goodwill period, but I haven’t received it yet?

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A change or cancellation fee may apply based on the type of ticket you purchased. Please note that Air Canada has never charged a refund processing fee to customers or travel agencies. If you purchased your ticket with a travel agency and have a question about a fee, please contact your travel agency for more information.

Are taxes, fees and additional charges associated with my ticket refundable?

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Examples for completely unused tickets:

Taxes, fees and additional chargesRefundable ticketNon-refundable ticket
CA– Air Travellers Security Charge – Canada Refundable, within 24 months of ticket issuance if no Canadian departure has occurred

The following taxes are also refundable if they were applied to the Air Travellers Security Charge:
  • Quebec Sales Tax (XQ)
  • Goods and Services Tax (XG)
  • Harmonized Sales Tax (RC)
Refundable, within 24 months of ticket issuance if no Canadian departure has occurred.

The following taxes are also refundable if they were applied to the Air Travellers Security Charge:
  • Quebec Sales Tax (XQ)
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  • Harmonized Sales Tax (RC)
Notwithstanding, the refundability rules mentioned above, Air Canada will exceptionally refund the Air Travellers Security Charge outside the 24 months limitation for eligible tickets only (ticket with travel dates on or after February 1, 2020 and purchased before April 13, 2021).
SQ – Airport Improvement Fee – CanadaRefundable

The following taxes are also refundable if they were applied to the Airport Improvement Fee:
  • Quebec Sales Tax (XQ)
  • Goods and Services Tax (XG)
  • Harmonized Sales Tax (RC)

The following taxes are also refundable if they were applied to the Airport Improvement Fee:
  • Quebec Sales Tax (XQ)
  • Goods and Services Tax (XG)
  • Harmonized Sales Tax (RC)
RC – Harmonized Sales Tax – CanadaRefundableRefundable only if they were applied to the Air Travellers Security Charge (CA) and Airport Improvement Fee (SQ), and the CA and SQ are refunded.
XG – Goods and Services Tax – CanadaRefundableRefundable only if they were applied to the Air Travellers Security Charge (CA) and Airport Improvement Fee (SQ), and the CA and SQ are refunded.
XQ – Quebec Sales Tax – CanadaRefundableRefundable only if they were applied to the Air Travellers Security Charge (CA) and Airport Improvement Fee (SQ), and the CA and SQ are refunded.
US – Transportation Tax – U.SRefundableNon-refundable
XF – Passenger Facility Charge – U.S.RefundableNon-refundable
ZP – Flight Segment Tax – U.SRefundableNon-refundable
AY – Passenger Security Fee – U.S.RefundableRefundable
XY – Immigration Fee – U.SRefundableRefundable
YC – Customs Fee – U.S.RefundableRefundable
XA – Animal and Plant Health Inspection Service (APHIS) User Fee – U.S.RefundableRefundable
FR – Civil Aviation Tax – FranceRefundableRefundable
O4 – Air Passenger Solidarity Tax Surplus - FranceRefundableRefundable
QW – Passenger Service Charge (domestic flights) – FranceRefundableRefundable
QX – Passenger Service Charge (international flights) – FranceRefundableRefundable
IZ – Solidarity Tax – FranceRefundableRefundable

Examples of non-refundable rules for international taxes, fees and charges:

Taxes, fees and additional charges
CR – Transportation Tax – Costa Ricarefundable by customer’s request to the Costa Rican Tourism Institute, as Air Canada is not allowed to refund it directly due to country regulations.
DO – Transportation Tax – Dominican Republic Refundable on the unutilized portion of service, if within 30 days of ticket issuance. Not refundable on forfeited amounts.
L8 – Tourism Tax - Dominican Republic Only refundable by customer’s request to the Dominican Republic authority, as Air Canada is not allowed to refund it directly due to country regulations.
E2 – Infrastructure Tax - EcuadorNot refundable.
ED – International Tourism Fee – EcuadorNot refundable.
EC – Government Transportation Tax - EcuadorRefundable on fully unused tickets. Not refundable if ticket is partially used or on forfeited amounts.
PA – Value Added Tax - PanamaRefundable on the unutilized portion of service, if within 180 days of ticket issuance. Not refundable on forfeited amounts.
PE – Sales Tax - PeruRefundable on fully unused tickets, if within 30 days of ticket issuance. Not refundable if ticket is partially used or on forfeited amounts.
K3 – Goods and Services Tax - IndiaRefundable on the unutilized portion of service, but only until the following August 31st of the India government financial year* in which the ticket was issued. Not refundable on forfeited amounts.
*India government financial year is from April 1 to March 31. Please contact Air Canada Reservations for assistance.

I cancelled the credit card used at the time of booking, or it expired. How do I receive my refund?

Air Canada will refund the money to the credit card you used at the time of purchase.

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  • If the original financial institution no longer exists, you will still need to request a refund. Air Canada will be notified of the financial institution’s closure and will contact you directly to finalize payment details. If you have not heard back from us within 2 months of your original request submission, please contact us at 1 888 247-2262.
  • Should we become aware of the fact that your bank, credit union or other financial institution has rejected a refund, we will contact you.

I am a travel agent unable to process the refund in my GDS. What can I do?

If you are unable to process the refund because you can’t display the eTicket or process an adjustment refund because the coupons are not available, please fill out our application form and your request will be reviewed by an Air Canada agent.

I am an OAL partner and require Air Canada's assistance with a refund request. How should I proceed?

Please fill out our application form and your request will be reviewed by an Air Canada agent.

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Latitude air

This past weekend, the US Navy’s Blue Angels and a variety of aircraft blazed across the sky over San Francisco Bay for the 2021 Fleet Week Air Show. We mentioned in last Wednesday’s ‘Lectronic Latitude that we were excited about the air show, and the actual event did not disappoint. Here are a few photos that were sent to us by Jörg Bashir, who was aboard Call of the Sea’s schooner Seaward with his two kids for Saturday’s air show. Jörg would ordinarily be sailing his own boat Kipu Kai, a Pacific Seacraft Orion 27, which is berthed at Marina Village Yacht Harbor in Alameda. But clearly for such an occasion, it’s by far better to have someone else take the helm and keep a lookout for other boats, and keep your own eyes free to enjoy the show, and take great photos.

Jet planes

Although there was often less than a minute between the various ‘performances’, there were plenty of sailboats to admire between shows.

Bay Area sailor Jeff Berman was also on the Bay and sent us the following shots.

A big “Thank you” to Jörg Bashir and Jeff Berman for sharing their photos.

And an extra big “Thank you” to all the sailors, power boaters, ferry captains, kayakers, jet ski drivers … As far as we’re aware, there were no unfortunate or unpleasant incidents over the weekend on the Bay in relation to the air show. Except for that one boat that we understand had hit a rock and was taking on water — we hope that all worked out OK. Oh, and there was “that one person” who decided to cut through the no-go zone in a great hurry. As expected, the Coast Guard hurried right after them. Wouldn’t like to have been in that driver’s seat when they all reached the dock.

Stay tuned to ‘Lectronic Latitude — if we can, we might slip in a few more photos in future editions. And if you have any photos to share, you can send them to us at: [email protected] or for Sailagram, send to:  [email protected]

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Celestial navigation

Navigation using astronomical objects to determine position

For other uses, see Celestial navigation (disambiguation).

A diagram of a typical nautical sextant, a tool used in celestial navigation to measure the angle between two objects viewed by means of its optical sight.

Celestial navigation, also known as astronavigation, is the ancient and continuing modern practice of position fixing using stars and other celestial bodies that enables a navigator to accurately determine his or her actual current physical position in space (or on the surface of the earth) without having to rely solely on estimated positional calculations, commonly known as "dead reckoning", made in the absence of GPS or other similar modern electronic or digital means.

Celestial navigation uses "sights", or timed angular measurements, taken typically between a celestial body (e.g. the Sun, the Moon, a planet, or a star) and the visible horizon. Celestial navigation can also take advantage of measurements between celestial bodies without reference to the earth horizon, such as when the moon and other selected bodies are utilized in the practice called "Lunars" or lunar distance method, used for determining precise time when time is unknown.

Celestial navigation using the Sun and the horizon whilst on the surface of the earth is commonly used, providing various methods of determining position, one of which is the popular and simple method called "noon sight navigation"—being a single observation of the exact altitude of the sun and the exact time of that altitude (known as "local noon")—the highest point of the sun above the horizon from the position of the observer in any single day. This angular observation combined with knowing its simultaneous precise time referred to the time at the prime meridian directly renders a latitude and longitude fix at the time and place of the observation by simple mathematical reduction. The Moon, a planet, Polaris, or one of the 57 other navigational stars whose coordinates are tabulated in any of the published nautical almanac or air almanacs can also accomplish this same goal.

Celestial navigation accomplishes its purpose by use of angular measurements (sights) between celestial bodies and the visible horizon to locate one's position on the world, whether on land, in the air or at sea. In addition, observations between stars and other celestial bodies accomplished the same results whilst in space - and was use extensively in the Apollo space program as well as currently on many contemporary satellites. Equally celestial navigation may be used whilst on other planetary bodies to determine position on their surface, using their local horizon and suitable celestial bodies with matching reduction tables and knowledge of local time.

For navigation by celestial means when on the surface of the earth for any given instant in time a celestial body is located directly over a single point on the Earth's surface. The latitude and longitude of that point is known as the celestial body's geographic position (GP), the location of which can be determined from tables in the nautical or air almanac for that year. The measured angle between the celestial body and the visible horizon is directly related to the distance between the celestial body's GP and the observer's position. After some computations, referred to as sight reduction, this measurement is used to plot a line of position (LOP) on a navigational chart or plotting worksheet, the observer's position being somewhere on that line. (The LOP is actually a short segment of a very large circle on Earth that surrounds the GP of the observed celestial body. An observer located anywhere on the circumference of this circle on Earth, measuring the angle of the same celestial body above the horizon at that instant of time, would observe that body to be at the same angle above the horizon.) Sights on two celestial bodies give two such lines on the chart, intersecting at the observer's position (actually, the two circles would result in two points of intersection arising from sights on two stars described above, but one can be discarded since it will be far from the estimated position—see the figure at example below). Most navigators will use sights of three to five stars, if available, since that will result in only one common intersection and minimizes the chance of error. That premise is the basis for the most commonly used method of celestial navigation, referred to as the 'altitude-intercept method'. At least three points must be plotted. The plot intersection will usually provide a triangle where the exact position is inside of it. Accuracy of the sights is indicated by the size of the triangle.

Joshua Slocum used both noon sight and star sight navigation to determine his current position during his voyage. In addition he used the lunar distance method (or "Lunar's") to determine and maintain known time at Greenwich (the prime meridian), there by keeping his "tin clock" reasonably accurate, and therefor his position fixes accurate during the first recorded single-handed circumnavigation of the world.

Celestial navigation can only determine longitude when time at the prime meridian is accurately known, and the more accurately known the more accurate the fix - as for every four seconds that the time source (commonly a chronometer or, in aircraft, an accurate "hack watch") is in error, the position may be off by one nautical mile. When time is unknown or not trusted, the lunar distance method can be applied so long as there is at least a functioning time piece with a second hand or digit. From no knowledge of time at all, a lunar calculation (given an observable moon of respectable altitude) can provide time accurate to close to a second with about 15 to 30 minutes of observations and work.


Sun Moon (annotated).gif

An example illustrating the concept behind the intercept method for determining one's position is shown to the right. (Two other common methods for determining one's position using celestial navigation are the longitude by chronometer and ex-meridian methods.) In the adjacent image, the two circles on the map represent lines of position for the Sun and Moon at 1200 GMT on October 29, 2005. At this time, a navigator on a ship at sea measured the Moon to be 56 degrees above the horizon using a sextant. Ten minutes later, the Sun was observed to be 40 degrees above the horizon. Lines of position were then calculated and plotted for each of these observations. Since both the Sun and Moon were observed at their respective angles from the same location, the navigator would have to be located at one of the two locations where the circles cross.

In this case the navigator is either located on the Atlantic Ocean, about 350 nautical miles (650 km) west of Madeira, or in South America, about 90 nautical miles (170 km) southwest of Asunción, Paraguay. In most cases, determining which of the two intersections is the correct one is obvious to the observer because they are often thousands of miles apart. As it is unlikely that the ship is sailing across South America, the position in the Atlantic is the correct one. Note that the lines of position in the figure are distorted because of the map's projection; they would be circular if plotted on a globe.

An observer at the Gran Chaco point would see the Moon at the left of the Sun, and an observer in the Madeira point would see the Moon at the right of the Sun.

Angular measurement[edit]

Using a marine sextant to measure the altitude of the sun above the horizon

Accurate angle measurement evolved over the years. One simple method is to hold the hand above the horizon with one's arm stretched out. The width of the little finger is an angle just over 1.5 degrees elevation at extended arm's length and can be used to estimate the elevation of the sun from the horizon plane and therefore estimate the time until sunset. The need for more accurate measurements led to the development of a number of increasingly accurate instruments, including the kamal, astrolabe, octant and sextant. The sextant and octant are most accurate because they measure angles from the horizon, eliminating errors caused by the placement of an instrument's pointers, and because their dual mirror system cancels relative motions of the instrument, showing a steady view of the object and horizon.

Navigators measure distance on the globe in degrees, arcminutes and arcseconds. A nautical mile is defined as 1852 meters, but is also (not accidentally) one minute of angle along a meridian on the Earth. Sextants can be read accurately to within 0.2 arcminutes, so the observer's position can be determined within (theoretically) 0.2 nautical miles (370 m), or about 400 yards. Most ocean navigators, shooting from a moving platform, can achieve a practical accuracy of 1.5 nautical miles (2.8 km), enough to navigate safely when out of sight of land.[citation needed]

Practical navigation[edit]

Ships Marine Chronometer giving an accuracy of less than ± 5 seconds per year, French Navy issued, 1983

Celestial navigation instruments

Practical celestial navigation usually requires a marine chronometer to measure time, a sextant to measure the angles, an almanac giving schedules of the coordinates of celestial objects, a set of sight reduction tables to help perform the height and azimuth computations, and a chart of the region. With sight reduction tables, the only calculations required are addition and subtraction. Small handheld computers, laptops and even scientific calculators enable modern navigators to "reduce" sextant sights in minutes, by automating all the calculation and/or data lookup steps. Most people can master simpler celestial navigation procedures after a day or two of instruction and practice, even using manual calculation methods.

Modern practical navigators usually use celestial navigation in combination with satellite navigation to correct a dead reckoning track, that is, a course estimated from a vessel's position, course and speed. Using multiple methods helps the navigator detect errors, and simplifies procedures. When used this way, a navigator will from time to time measure the sun's altitude with a sextant, then compare that with a precalculated altitude based on the exact time and estimated position of the observation. On the chart, one will use the straight edge of a plotter to mark each position line. If the position line indicates a location more than a few miles from the estimated position, more observations can be taken to restart the dead-reckoning track.

In the event of equipment or electrical failure, taking sun lines a few times a day and advancing them by dead reckoning allows a vessel to get a crude running fix sufficient to return to port. One can also use the Moon, a planet, Polaris, or one of 57 other navigational stars to track celestial positioning.


Main article: Meridian altitude

See also: Latitude determination

Two nautical ship officers "shoot" in one morning with the sextant, the sun altitude (1963)

Latitude was measured in the past either by measuring the altitude of the Sun at noon (the "noon sight"), or by measuring the altitudes of any other celestial body when crossing the meridian (reaching its maximum altitude when due north or south), and frequently by measuring the altitude of Polaris, the north star (assuming it is sufficiently visible above the horizon, which it is not in the Southern Hemisphere). Polaris always stays within 1 degree of the celestial north pole. If a navigator measures the angle to Polaris and finds it to be 10 degrees from the horizon, then he is about 10 degrees north of the equator. This approximate latitude is then corrected using simple tables or almanac corrections to determine a latitude theoretically accurate to within a fraction of a mile. Angles are measured from the horizon because locating the point directly overhead, the zenith, is not normally possible. When haze obscures the horizon, navigators use artificial horizons, which are horizontal mirrors or pans of reflective fluid, especially mercury historically. In the latter case, the angle between the reflected image in the mirror and the actual image of the object in the sky is exactly twice the required altitude.


See also: Longitude determination

The relative longitude to a position (for example Greenwich) can be calculated with the position of the sun and the reference time (for example UTC/GMT).

If the angle to Polaris can be accurately measured, a similar measurement to a star near the eastern or western horizons would provide the longitude. The problem is that the Earth turns 15 degrees per hour, making such measurements dependent on time. A measure a few minutes before or after the same measure the day before creates serious navigation errors. Before good chronometers were available, longitude measurements were based on the transit of the moon, or the positions of the moons of Jupiter. For the most part, these were too difficult to be used by anyone except professional astronomers. The invention of the modern chronometer by John Harrison in 1761 vastly simplified longitudinal calculation.

The longitude problem took centuries to solve and was dependent on the construction of a non-pendulum clock (as pendulum clocks cannot function accurately on a tilting ship, or indeed a moving vehicle of any kind). Two useful methods evolved during the 18th century and are still practiced today: lunar distance, which does not involve the use of a chronometer, and use of an accurate timepiece or chronometer.

Presently, lay-person calculations of longitude can be made by noting the exact local time (leaving out any reference for Daylight Saving Time) when the sun is at its highest point in the sky. The calculation of noon can be made more easily and accurately with a small, exactly vertical rod driven into level ground—take the time reading when the shadow is pointing due north (in the northern hemisphere). Then take your local time reading and subtract it from GMT (Greenwich Mean Time) or the time in London, England. For example, a noon reading (1200 hours) near central Canada or the US would occur at approximately 6 pm (1800 hours) in London. The six-hour differential is one quarter of a 24-hour day, or 90 degrees of a 360-degree circle (the Earth). The calculation can also be made by taking the number of hours (use decimals for fractions of an hour) multiplied by 15, the number of degrees in one hour. Either way, it can be demonstrated that much of central North America is at or near 90 degrees west longitude. Eastern longitudes can be determined by adding the local time to GMT, with similar calculations.

Lunar distance[edit]

Main article: Lunar distance

An older but still useful and practical method of determining accurate time at sea before the advent of precise timekeeping and satellite based time systems is called "lunar distances", or "Lunars" which was used extensively for a short period and refined for daily use on board ships in the 18th century. Use declined through the middle of the 19th century as better and better timepieces (chronometers) became available to the average vessel at sea. Although most recently only used by sextant hobbyists and historians, it is now becoming more common in celestial navigation courses to reduce total dependence on GNSS systems as potentially the only accurate time source aboard a vessel. The method is theoretically sound, and now with several bureau re-publishing lunar tables for this purpose on an annual basis there is an uptick in use—albeit we hope mainly for practice! Destined for use when an accurate timepiece is not available or timepiece accuracy is suspect during a long sea voyage, the navigator precisely measures the angle between the moon and the sun, or between the moon and one of several stars near the ecliptic. The observed angle must be corrected for the effects of refraction and parallax, like any celestial sight. To make this correction the navigator measures the altitudes of the moon and sun (or star) at about the same time as the lunar distance angle. Only rough values for the altitudes are required. A calculation with suitable published tables (or longhand with logarithms and graphical tables) requires about 10 to 15 minutes' work converting the observed angle(s) to a geocentric lunar distance. The navigator then compare the corrected angle against those listed against the appropriate almanac pages for every three hours of Greenwich time, using interpolation tables to derive intermediate values. The result is a difference time between the time source (it being of unknown time) used for the observations, and the actual prime meridian time (that of the "Zero Meridian" at Greenwich also known as UTC or GMT). Now knowing UTC/GMT, a further set of sights can be taken and reduced by the navigator to calculate his or her exact position on the earth as a local latitude and longitude.

Use of time[edit]

Main article: Marine chronometer Today

The considerably more popular method was (and still is) to use an accurate timepiece to directly measure the time of a sextant sight. The need for accurate navigation led to the development of progressively more accurate chronometers in the 18th century (see John Harrison). Today, time is measured with a chronometer, a quartz watch, a shortwave radio time signal broadcast from an atomic clock, or the time displayed on a satellite time signal receiver.[1] A quartz wristwatch normally keeps time within a half-second per day. If it is worn constantly, keeping it near body heat, its rate of drift can be measured with the radio and, by compensating for this drift, a navigator can keep time to better than a second per month. When time at the prime meridian (or another starting point) is accurately enough known, celestial navigation can determine longitude, and the more accurately time is known the more accurate the latitude determination. At latitude 45° one second of time is equivalent in longitude to 1,077.8 ft (328.51 m), or one-tenth of a second means 107.8 ft (32.86 m).[2]

Traditionally, a navigator checked his chronometer(s) from his sextant, at a geographic marker surveyed by a professional astronomer. This is now a rare skill, and most harbormasters cannot locate their harbor's marker. Ships often carried more than one chronometer. Chronometers were kept in gimbals in a dry room near the center of the ship. They were used to set a hack watch for the actual sight, so that no chronometers were ever exposed to the wind and salt water on deck. Winding and comparing the chronometers was a crucial duty of the navigator. Even today, it is still logged daily in the ship's deck log and reported to the Captain before eight bells on the forenoon watch (shipboard noon). Navigators also set the ship's clocks and calendar. Two chronometers provided dual modular redundancy, allowing a backup if one should cease to work, but not allowing any error correction if the two displayed a different time, since in case of contradiction between the two chronometers, it would be impossible to know which one was wrong (the error detection obtained would be the same of having only one chronometer and checking it periodically: every day at noon against dead reckoning). Three chronometers provided triple modular redundancy, allowing error correction if one of the three was wrong, so the pilot would take the average of the two with closer readings (average precision vote). There is an old adage to this effect, stating: "Never go to sea with two chronometers; take one or three."[3] Vessels engaged in survey work generally carried many more than three chronometers – for example, HMS Beagle carried 22 chronometers.[4]

Modern celestial navigation[edit]

The celestial line of position concept was discovered in 1837 by Thomas Hubbard Sumner when, after one observation, he computed and plotted his longitude at more than one trial latitude in his vicinity – and noticed that the positions lay along a line. Using this method with two bodies, navigators were finally able to cross two position lines and obtain their position – in effect determining both latitude and longitude. Later in the 19th century came the development of the modern (Marcq St. Hilaire) intercept method; with this method the body height and azimuth are calculated for a convenient trial position, and compared with the observed height. The difference in arcminutes is the nautical mile "intercept" distance that the position line needs to be shifted toward or away from the direction of the body's subpoint. (The intercept method uses the concept illustrated in the example in the “How it works” section above.) Two other methods of reducing sights are the longitude by chronometer and the ex-meridian method.

While celestial navigation is becoming increasingly redundant with the advent of inexpensive and highly accurate satellite navigation receivers (GPS), it was used extensively in aviation until the 1960s, and marine navigation until quite recently. However; since a prudent mariner never relies on any sole means of fixing his position, many national maritime authorities still require deck officers to show knowledge of celestial navigation in examinations, primarily as a backup for electronic/satellite navigation. One of the most common current usages of celestial navigation aboard large merchant vessels is for compass calibration and error checking at sea when no terrestrial references are available.

The U.S. Air Force and U.S. Navy continued instructing military aviators on celestial navigation use until 1997, because:

  • celestial navigation can be used independently of ground aids.
  • celestial navigation has global coverage.
  • celestial navigation can not be jammed (although it can be obscured by clouds).
  • celestial navigation does not give off any signals that could be detected by an enemy.[5]

The United States Naval Academy (USNA) announced that it was discontinuing its course on celestial navigation (considered to be one of its most demanding non-engineering courses) from the formal curriculum in the spring of 1998.[6] In October 2015, citing concerns about the reliability of GPS systems in the face of potential hostile hacking, the USNA reinstated instruction in celestial navigation in the 2015 to 2016 academic year.[7][8]

At another federal service academy, the US Merchant Marine Academy, there was no break in instruction in celestial navigation as it is required to pass the US Coast Guard License Exam to enter the Merchant Marine. It is also taught at Harvard, most recently as Astronomy 2.[9]

Celestial navigation continues to be used by private yachtsmen, and particularly by long-distance cruising yachts around the world. For small cruising boat crews, celestial navigation is generally considered an essential skill when venturing beyond visual range of land. Although GPS (Global Positioning System) technology is reliable, offshore yachtsmen use celestial navigation as either a primary navigational tool or as a backup.

Celestial navigation was used in commercial aviation up until the early part of the jet age; early Boeing 747s had a "sextant port" in the roof of the cockpit.[10] It was only phased out in the 1960s with the advent of inertial navigation and Doppler navigation systems, and today's satellite-based systems which can locate the aircraft's position accurate to a 3-meter sphere with several updates per second.

A variation on terrestrial celestial navigation was used to help orient the Apollo spacecraft en route to and from the Moon. To this day, space missions such as the Mars Exploration Rover use star trackers to determine the attitude of the spacecraft.

As early as the mid-1960s, advanced electronic and computer systems had evolved enabling navigators to obtain automated celestial sight fixes. These systems were used aboard both ships and US Air Force aircraft, and were highly accurate, able to lock onto up to 11 stars (even in daytime) and resolve the craft's position to less than 300 feet (91 m). The SR-71 high-speed reconnaissance aircraft was one example of an aircraft that used a combination of automated celestial and inertial navigation. These rare systems were expensive, however, and the few that remain in use today are regarded as backups to more reliable satellite positioning systems.

Intercontinental ballistic missiles use celestial navigation to check and correct their course (initially set using internal gyroscopes) while flying outside the Earth's atmosphere. The immunity to jamming signals is the main driver behind this seemingly archaic technique.

X-ray pulsar-based navigation and timing (XNAV) is an experimental navigation technique whereby the periodic X-ray signals emitted from pulsars are used to determine the location of a vehicle, such as a spacecraft in deep space. A vehicle using XNAV would compare received X-ray signals with a database of known pulsar frequencies and locations. Similar to GPS, this comparison would allow the vehicle to triangulate its position accurately (±5 km). The advantage of using X-ray signals over radio waves is that X-ray telescopes can be made smaller and lighter.[11][12][13] On 9 November 2016 the Chinese Academy of Sciences launched an experimental pulsar navigation satellite called XPNAV 1.[14][15] SEXTANT (Station Explorer for X-ray Timing and Navigation Technology) is a NASA-funded project developed at the Goddard Space Flight Center that is testing XNAV on-orbit on board the International Space Station in connection with the NICER project, launched on 3 June 2017 on the SpaceX CRS-11 ISS resupply mission.[16]


Celestial navigation training equipment for aircraft crews combine a simple flight simulator with a planetarium.

An early example is the Link Celestial Navigation Trainer, used in the Second World War.[17][18] Housed in a 45 feet (14 m) high building, it featured a cockpit accommodating a whole bomber crew (pilot, navigator, and bombardier). The cockpit offered a full array of instruments which the pilot used to fly the simulated airplane. Fixed to a dome above the cockpit was an arrangement of lights, some collimated, simulating constellations from which the navigator determined the plane's position. The dome's movement simulated the changing positions of the stars with the passage of time and the movement of the plane around the earth. The navigator also received simulated radio signals from various positions on the ground. Below the cockpit moved "terrain plates" – large, movable aerial photographs of the land below – which gave the crew the impression of flight and enabled the bomber to practice lining up bombing targets. A team of operators sat at a control booth on the ground below the machine, from which they could simulate weather conditions such as wind or cloud. This team also tracked the airplane's position by moving a "crab" (a marker) on a paper map.

The Link Celestial Navigation Trainer was developed in response to a request made by the Royal Air Force (RAF) in 1939. The RAF ordered 60 of these machines, and the first one was built in 1941. The RAF used only a few of these, leasing the rest back to the US, where eventually hundreds were in use.

See also[edit]


  1. ^Mehaffey, Joe. "How accurate is the TIME DISPLAY on my GPS?". Archived from the original on 4 August 2017. Retrieved 9 May 2018.
  2. ^Errors in Longitude, Latitude and Azimuth Determinations-I by F.A. McDiarmid, The Royal Astronomical Society of Canada, 1914
  3. ^Brooks, Frederick J. (1995) [1975]. The Mythical Man-Month. Addison-Wesley. p. 64. ISBN .
  4. ^R. Fitzroy. "Volume II: Proceedings of the Second Expedition". p. 18.
  5. ^U.S. Air Force Pamphlet (AFPAM) 11-216, Chapters 8–13
  6. ^Navy Cadets Won't Discard Their SextantsArchived 2009-02-13 at the Wayback Machine, The New York Times By DAVID W. CHEN Published: May 29, 1998
  7. ^Seeing stars, again: Naval Academy reinstates celestial navigationArchived 2015-10-23 at the Wayback Machine, Capital Gazette by Tim Prudente Published: 12 October 2015
  8. ^Peterson, Andrea (17 February 2016). "Why Naval Academy students are learning to sail by the stars for the first time in a decade". The Washington Post. Archived from the original on 22 February 2016.
  9. ^Astronomy 2 Celestial Navigation by Philip SadlerArchived 2015-11-22 at the Wayback Machine
  10. ^Clark, Pilita (17 April 2015). "The future of flying". Financial Times. Archived from the original on 14 June 2015. Retrieved 19 April 2015.
  11. ^Commissariat, Tushna (4 June 2014). "Pulsars map the way for space missions". Physics World. Archived from the original on 18 October 2017.
  12. ^"An Interplanetary GPS Using Pulsar Signals". MIT Technology Review. 23 May 2013.
  13. ^Becker, Werner; Bernhardt, Mike G.; Jessner, Axel (2013-05-21). "Autonomous Spacecraft Navigation With Pulsars". arXiv:1305.4842. doi:10.2420/AF07.2013.11.
  14. ^Krebs, Gunter. "XPNAV 1". Gunter's Space Page. Archived from the original on 2016-11-01. Retrieved 2016-11-01.
  15. ^"Chinese Long March 11 launches first Pulsar Navigation Satellite into Orbit". 10 November 2016. Archived from the original on 24 August 2017.
  16. ^"NICER Manifested on SpaceX-11 ISS Resupply Flight". NICER News. NASA. December 1, 2015. Archived from the original on March 24, 2017. Retrieved June 14, 2017.
  17. ^"World War II". A Brief History of Aircraft Flight Simulation. Archived from the original on December 9, 2004. Retrieved January 27, 2005.
  18. ^"Corporal Tomisita "Tommye" Flemming-Kelly-U.S.M.C.-Celestial Navigation Trainer −1943/45". World War II Memories. Archived from the original on 2005-01-19. Retrieved January 27, 2005.

External links[edit]

Media related to Celestial navigation at Wikimedia Commons


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