<p>The formula for determining the acceleration due to gravity as a function of altitude is:</p>
<p><span class="math-container">$$g_h = \frac {gR^2}{(R+h)^2}$$</span></p>
<p>Where R is the radius of earth, g is the gravity of earth at sea level, and h is the height above sea level.</p>
<p>The full derivation from Newton's Law of Gravitation can be found here:</p>
<p><a href="https://www.doubtnut.com/qna/464549126" rel="nofollow noreferrer">https://www.doubtnut.com/qna/464549126</a></p>
<p>At 500km, <span class="math-container">$$g_h = 8.4 \frac m {s^2}$$</span></p>
<p>This is 85% of gravity at sea level. So why do astronauts experience <a href="https://www.esa.int/Science_Exploration/Human_and_Robotic_Exploration/mISSion_possible/Lesson_2_What_is_weightlessness_What_does_it_feel_like#:%7E:text=55107%20views%2045%20likes,gravity%20and%20regain%20their%20balance." rel="nofollow noreferrer">weightlessness</a>?</p>
<p>The reason that astronauts in high earth orbit experience weightlessness is because an orbit is essentially a constant, stable free fall around the planet. That's why orbital speeds are so high. To achieve these speeds, there can't be any atmosphere or things get too hot and the friction causes the orbit to decay.</p>
<p>For a space station like the ISS, the fuel costs for travel to and from the station favor a low orbit but the friction in the atmosphere favors a higher orbit. The balance is ~ 420 km which is the current avg. orbit height of the ISS.</p>

CC BY-SA 4.0
2024-10-14T08:43:00.060Z
This answer would be improved by stating the source of the equation and what the variables signify.
Fred
CC BY-SA 4.0
2024-10-14T14:47:09.580Z
@Fred Thanks for improving my answer. I've added your requests.
Stevan V. Saban
CC BY-SA 4.0
2024-10-13T17:20:28.933Z
2024-10-14T15:52:10.580Z
2024-10-14T15:52:10.580Z
Stevan V. Saban
<p>I think the question is based on a misunderstanding.</p>
<p>Gravity extends to infinity. Wherever you go in the universe, you will always be attracted to Earth -- the attraction will just be very low if you're far away. Gravity is responsible for the fact that space stations and satellites would really like to just fly off along a straight line, but the gravitational force provides what is necessary to tug them back onto what ends up being a circular (or perhaps elliptic) orbit. These orbits can be high above earth (say, where the moon orbits) or low (say, where the space station is).</p>
<p>Atmosphere also extends to very large distances -- it's just that when you're far enough away, the density of the atmosphere becomes so low that for all practical cases you don't have to worry about it. At distances like the space station, however, the station is continuously slowed down by the atmosphere on its circular orbit and has to continuously be re-accelerated (which in practice is done by pushing it back out to a higher orbit).</p>

CC BY-SA 4.0
2024-10-19T22:22:21.847Z
2024-10-19T22:22:21.847Z
Wolfgang Bangerth
<p>Current technology passenger planes (around year 2025) fly not higher than about 20 km above sea level, but the international space station is about 400 km above sea level, so I might bet that the international space station cannot orbit earth in less than 400 km above sea level, but I might be wrong and hence the question:</p>
<p>How far from sea level does gravity practically ends within the 500 km atmosphere?</p>

CC BY-SA 4.0
2024-10-12T17:02:22.077Z
The Moon is about 385,000 km above sea level and is still bound to Earth by gravity.
Jean-Marie Prival
CC BY-SA 4.0
2024-10-12T17:27:23.137Z
Is the current phrasing better? Anyway what I am ought to learn here is if we want to build a "flying cities", much larger than the international space station, in which people can reside years continuously without going down to earth's surface, how far should that be from sea level? Would 400 km also be enough or because the weight will be much bigger, more distance is needed?
hi_there
CC BY-SA 4.0
2024-10-12T23:08:21.697Z
Given you are after the altitude at which it would be best to place orbiting cities, this question would be better suited to SE Space Exploration. FYI geostationary satellites orbit at altitudes around 40 000 km.
Fred
CC BY-SA 4.0
2024-10-12T23:59:00.370Z
Gravity has no end - or the end is there where the gravitational influence of other bodies becomes equally important. But that is far beyond the Moon, and thus way beyond where we can talk about atmosphere. Do I misunderstand your question?
planetmaker
CC BY-SA 4.0
2024-10-13T01:52:09.207Z
@planetmaker my question is in the scope of the 500 km of the atmosphere (the exosphere and space don't have anything to do with my question).
hi_there
CC BY-SA 4.0
2024-10-13T06:43:55.707Z
cross-posting: https://space.stackexchange.com/questions/67118/is-there-a-plan-to-build-an-atmosphere-colony-a-cloud-city-on-earth
And I still don't get the question. Atmosphere has no abrupt end, and the ISS needs constant lift or it would crash within months to years
planetmaker
CC BY-SA 4.0
2024-10-13T08:46:49.470Z
From the question that has been cross posted on SE Space Exploration, in which you make reference to Venus you appear to be making unwarranted assumptions between Earth & Venus, particularly concerning the atmospheres of both planets. Compared to Venus, Earth's atmosphere is very thin & has a much lower density than the atmosphere on Venus. Consequently, what might be considered practical for the upper reaches of Venus' atmosphere is not practical for Earth. At heights of 400 km, the air is so thin around Earth it's **almost** non existent & would not support a Venusian style flying city.
Fred
CC BY-SA 4.0
2024-10-13T20:44:24.300Z
I didn't cross-post anything, I was suggested by you @Fred to ask on the the other website and I did that. I just want to know where and how on Earth a sky city could be created (a closed system with oxygen production from plants etc.) just without gravity or with very low gravity.
hi_there
CC BY-SA 4.0
2024-10-13T22:32:10.897Z
Anything in an atmosphere will not orbit the planet, but will fall down. Anything outside the atmosphere could as well be in deep space... the planet doesn't provide anything in that case (maybe except the guarantee that you will continue to orbit it and along with it the host star)
planetmaker
CC BY-SA 4.0
2024-10-13T23:34:12.477Z
A key thing... the space station orbits BECAUSE of gravity, not in spite of it.  If there were no gravity it would go off into space.  What wound hinder the space station at lower altitudes is the increased friction from increased atmosphere slowing it down.  Once there is no friction from atmosphere, any weight will comfortably orbit if it is given the right initial speed.  Only the remaining small influence factors like the solar winds would need to be adjusted for, just as it is for the space station.
JeopardyTempest
<atmosphere><sea-level><gravity><orbit>
How far from sea level does gravity practically ends within the 500 km atmosphere?
hi_there
# How far from sea level does gravity practically ends within the 500 km atmosphere?

(Asked by: username_0 on 2024-10-12)

Current technology passenger planes (around year 2025) fly not higher than about 20 km above sea level, but the international space station is about 400 km above sea level, so I might bet that the international space station cannot orbit earth in less than 400 km above sea level, but I might be wrong and hence the question:

How far from sea level does gravity practically ends within the 500 km atmosphere?

**Tags:** atmosphere, sea-level, gravity, orbit

> **Comments:**
> **username_1**: The Moon is about 385,000 km above sea level and is still bound to Earth by gravity.  
> **username_0**: Is the current phrasing better? Anyway what I am ought to learn here is if we want to build a "flying cities", much larger than the international space station, in which people can reside years continuously without going down to earth's surface, how far should that be from sea level? Would 400 km also be enough or because the weight will be much bigger, more distance is needed?  
> **username_2**: Given you are after the altitude at which it would be best to place orbiting cities, this question would be better suited to SE Space Exploration. FYI geostationary satellites orbit at altitudes around 40 000 km.  
> **username_3**: Gravity has no end - or the end is there where the gravitational influence of other bodies becomes equally important. But that is far beyond the Moon, and thus way beyond where we can talk about atmosphere. Do I misunderstand your question?  
> **username_0**: @username_3 my question is in the scope of the 500 km of the atmosphere (the exosphere and space don't have anything to do with my question).  
> **username_3**: cross-posting: https://space.stackexchange.com/questions/67118/is-there-a-plan-to-build-an-atmosphere-colony-a-cloud-city-on-earth And I still don't get the question. Atmosphere has no abrupt end, and the ISS needs constant lift or it would crash within months to years  
> **username_2**: From the question that has been cross posted on SE Space Exploration, in which you make reference to Venus you appear to be making unwarranted assumptions between Earth & Venus, particularly concerning the atmospheres of both planets. Compared to Venus, Earth's atmosphere is very thin & has a much lower density than the atmosphere on Venus. Consequently, what might be considered practical for the upper reaches of Venus' atmosphere is not practical for Earth. At heights of 400 km, the air is so thin around Earth it's **almost** non existent & would not support a Venusian style flying city.  
> **username_0**: I didn't cross-post anything, I was suggested by you @username_2 to ask on the the other website and I did that. I just want to know where and how on Earth a sky city could be created (a closed system with oxygen production from plants etc.) just without gravity or with very low gravity.  
> **username_3**: Anything in an atmosphere will not orbit the planet, but will fall down. Anything outside the atmosphere could as well be in deep space... the planet doesn't provide anything in that case (maybe except the guarantee that you will continue to orbit it and along with it the host star)  
> **username_4**: A key thing... the space station orbits BECAUSE of gravity, not in spite of it.  If there were no gravity it would go off into space.  What wound hinder the space station at lower altitudes is the increased friction from increased atmosphere slowing it down.  Once there is no friction from atmosphere, any weight will comfortably orbit if it is given the right initial speed.  Only the remaining small influence factors like the solar winds would need to be adjusted for, just as it is for the space station.  

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## 2 answers

### Answer by username_5 on 2024-10-13. Score: 4

The formula for determining the acceleration due to gravity as a function of altitude is:

$$g\_h = \frac {gR^2}{(R+h)^2}$$

Where R is the radius of earth, g is the gravity of earth at sea level, and h is the height above sea level.

The full derivation from Newton's Law of Gravitation can be found here:

<https://www.doubtnut.com/qna/464549126>

At 500km, $$g\_h = 8.4 \frac m {s^2}$$

This is 85% of gravity at sea level. So why do astronauts experience [weightlessness](https://www.esa.int/Science_Exploration/Human_and_Robotic_Exploration/mISSion_possible/Lesson_2_What_is_weightlessness_What_does_it_feel_like#:%7E:text=55107%20views%2045%20likes,gravity%20and%20regain%20their%20balance.)?

The reason that astronauts in high earth orbit experience weightlessness is because an orbit is essentially a constant, stable free fall around the planet. That's why orbital speeds are so high. To achieve these speeds, there can't be any atmosphere or things get too hot and the friction causes the orbit to decay.

For a space station like the ISS, the fuel costs for travel to and from the station favor a low orbit but the friction in the atmosphere favors a higher orbit. The balance is ~ 420 km which is the current avg. orbit height of the ISS.

> **Comments:**
> **username_2**: This answer would be improved by stating the source of the equation and what the variables signify.  
> **username_5**: @username_2 Thanks for improving my answer. I've added your requests.  

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### Answer by username_6 on 2024-10-19. Score: 2

I think the question is based on a misunderstanding.

Gravity extends to infinity. Wherever you go in the universe, you will always be attracted to Earth -- the attraction will just be very low if you're far away. Gravity is responsible for the fact that space stations and satellites would really like to just fly off along a straight line, but the gravitational force provides what is necessary to tug them back onto what ends up being a circular (or perhaps elliptic) orbit. These orbits can be high above earth (say, where the moon orbits) or low (say, where the space station is).

Atmosphere also extends to very large distances -- it's just that when you're far enough away, the density of the atmosphere becomes so low that for all practical cases you don't have to worry about it. At distances like the space station, however, the station is continuously slowed down by the atmosphere on its circular orbit and has to continuously be re-accelerated (which in practice is done by pushing it back out to a higher orbit).


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