# Lowest possible altitude for a Satellite

• B
• jms4
In summary, the lowest altitude for a satellite to orbit the Earth is just above sea level, with the satellite achieving escape velocity and having enough thrust to overcome drag while navigating around landmasses. The exact altitude may vary depending on the orientation and drag-to-mass ratio of the satellite. Boosting may be required occasionally to maintain stability, with the frequency depending on the altitude and other factors.

#### jms4

What is the lowest altitude for a satellite to orbit?

russ_watters
Virtually any satellite in LEO is slowed by friction with rarefied atmosphere, causing it to lose altitude. They need the ability to boost themselves back up occasionally.
How low an orbit can be depends on how broadly you apply the term 'occasionally'.

At some altitude, its speed will be slowed so much that it needs to boost continually, just to stay at altitude.
In practical terms this too has a limit, due to a limited supply fuel as well as friction/shock heating destroying the craft.

Presumably, if boosting continually, it should no longer be considered 'orbiting'.

Demystifier and russ_watters
DaveC426913 said:
boosting continually
Single, un-boosted, complete (though decayed) revolution?

Bystander said:
Single, un-boosted, complete (though decayed) revolution?
Based on the data for Tiangong-1, the orbital decay gets that severe right about 140 km. The graph of altitude versus time gets steep there at the end.

http://www.satflare.com/track.asp?q=37820#TOP

Bystander
jbriggs444 said:
Based on the data for Tiangong-1, the orbital decay gets that severe right about 140 km. The graph of altitude versus time gets steep there at the end.

http://www.satflare.com/track.asp?q=37820#TOP
It looks steep based on the scale, but it is only losing about 1-2 km per orbit at that point, which is slower than walking speed (it's about 0.4 m/s). Google tells me an ISS orbit maintenance burn might be 1.3 m/s delta-V over 12 minutes (not sure how typical that is). Yes, if you burned continuously you'd run out of fuel fast, but in terms of the decay rate, at that point it was only about 5% of what a continuous burn could reverse in one orbit.

This is common fodder for sci-fi movies and I'd be curious to know if more can be said. Let's say we have enough fuel for a 1 hour burn, at the above acceleration rate. What is the minimum altitude you could recover from without being back in the same predicament in, say, a week?

russ_watters said:
This is common fodder for sci-fi movies
You're being generous.

Common fodder for sci-fi movies is that,the moment your engines stop, your orbit immediately starts decaying rapidly, even if you're as far out as the Moon.

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jim mcnamara said:
Can you clarify a bit?
Does the orbit have to be stable?
Did you try google first? I did:
https://en.wikipedia.org/wiki/Low_Earth_orbit
I did check that page, and It doesn't say anything about it, only examples of low Earth orbiting satellites like ISS

DaveC426913 said:
Virtually any satellite in LEO is slowed by friction with rarefied atmosphere, causing it to lose altitude. They need the ability to boost themselves back up occasionally.
How low an orbit can be depends on how broadly you apply the term 'occasionally'.

At some altitude, its speed will be slowed so much that it needs to boost continually, just to stay at altitude.
In practical terms this too has a limit, due to a limited supply fuel as well as friction/shock heating destroying the craft.

Presumably, if boosting continually, it should no longer be considered 'orbiting'.
Thank you, but at what altitude will it be stable, like it requires extremely low amount of boosting

Bystander said:
Single, un-boosted, complete (though decayed) revolution?
altitude where boosting is required very little far lower than the ISS for example

I don't think you're being fair to us. You seem to want an exact answer from us, but are only willing to vaguely specify the problem. "altitude where boosting is required very little" and "extremely low amount of boosting". How long is a piece of string?

The Wikipedia article has examples. You're not going to do any better than that.

russ_watters
jms4 said:
Thank you, but at what altitude will it be stable, like it requires extremely low amount of boosting

jms4 said:
altitude where boosting is required very little far lower than the ISS for example
The ISS requires monthly boosting. Does that satisfy "extremely low" or "very little"? Feels like a fair amount to me...

I don't think you're being fair to us. You seem to want an exact answer from us, but are only willing to vaguely specify the problem. "altitude where boosting is required very little" and "extremely low amount of boosting". How long is a piece of string?

The Wikipedia article has examples. You're not going to do any better than that.
I'm sorry if I'm being unfair, i just need an approximate value of range like periodic monthly boosting or something, so I could put in a minor part of project, not serious, so don't spend too much time thinking about it, but thank you anyway for helping out.

O
russ_watters said:
The ISS requires monthly boosting. Does that satisfy "extremely low" or "very little"? Feels like a fair amount to me...
Ok, fine that is fair enough for me, thank you.

jms4 said:
I'm sorry if I'm being unfair, i just need an approximate value of range like periodic monthly boosting or something, so I could put in a minor part of project, not serious, so don't spend too much time thinking about it, but thank you anyway for helping out.

russ_watters
jbriggs444 said:
That seems like a great application for in engines; I hadn't heard that had been done.

With a mass of about 1000 kg, that works out to an acceleration of about 0.1 m/s/orbit.

[edit: unit typo fixed]

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jbriggs444
And even if you can find a number for one satellite, the answer for other satellites depends on the orientation of that satellite and drag vs mass in that orientation.

Is this a trick question? I think the lowest possible altitude of a satellite orbiting the Earth would be just above sea level. The satellite would have to achieve escape velocity, have thrust available to overcome drag, and have to be able to navigate around landmasses, but technically that should qualify as a satellite in orbit.

Kyle Gonterwitz said:
Is this a trick question? I think the lowest possible altitude of a satellite orbiting the Earth would be just above sea level. The satellite would have to achieve escape velocity, have thrust available to overcome drag, and have to be able to navigate around landmasses, but technically that should qualify as a satellite in orbit.
For a smooth planet with no atmosphere, yes.

Kyle Gonterwitz said:
Is this a trick question?
Post #13 clarifies the purpose of the question. It is a practical matter -- roughly how high does one need to go so that the station keeping requirements are manageable.

russ_watters
Flight level 600 is at 60,000 ft which is the upper boundary of controlled airspace, that would be the practical, lowest possible altitude. Search for the relationship between altitude and atmospheric pressure to find that relationship, then go as high as needed to optimize a design based on propulsion energy needed to achieve the desired altitude at orbital/escape velocity with minimum thrust to overcome atmospheric density/drag for the duration of the mission.

glappkaeft said:
And even if you can find a number for one satellite, the answer for other satellites depends on the orientation of that satellite and drag vs mass in that orientation.
Yes. The ISS for example is particularly draggy and a google/eye all tells me it is much worse, losing about 7m/orbit or accelerating at 14m/s/orbit.

glappkaeft said:
And even if you can find a number for one satellite, the answer for other satellites depends on the orientation of that satellite and drag vs mass in that orientation.
And even for the same satellite, varying solar activity can have an effect on the Earth's atmosphere, which will cause the drag to change.

Kyle Gonterwitz said:
Flight level 600 is at 60,000 ft which is the upper boundary of controlled airspace, that would be the practical, lowest possible altitude. Search for the relationship between altitude and atmospheric pressure to find that relationship, then go as high as needed to optimize a design based on propulsion energy needed to achieve the desired altitude at orbital/escape velocity with minimum thrust to overcome atmospheric density/drag for the duration of the mission.
I don't understand where you are going with this. What is practical? We have craft operating at 60,000 or even 160,000 feet, but they don't use orbital mechanics to stay aloft, they use normal aerodynamic lift or buoyancy. Craft that rely primarily on orbital mechanics to stay aloft are not possible in that altitude range for a couple of reasons: they'd quickly burn up or run out of fuel.

DaveC426913 said:
Virtually any satellite in LEO is slowed by friction with rarefied atmosphere, causing it to lose altitude. They need the ability to boost themselves back up occasionally.
How low an orbit can be depends on how broadly you apply the term 'occasionally'.

At some altitude, its speed will be slowed so much that it needs to boost continually, just to stay at altitude.
In practical terms this too has a limit, due to a limited supply fuel as well as friction/shock heating destroying the craft.

Presumably, if boosting continually, it should no longer be considered 'orbiting'.
I am in complete agreement but we can say that the stratopause is about the lowest we can have a LEO satellite.

Kyle Gonterwitz said:
Is this a trick question? I think the lowest possible altitude of a satellite orbiting the Earth would be just above sea level. The satellite would have to achieve escape velocity, have thrust available to overcome drag, and have to be able to navigate around landmasses, but technically that should qualify as a satellite in orbit.
As previously pointed out, if it is continually thrusting - whether to maintain altitude or overcome drag - then it can't be considered 'orbiting'.

Well it depends on its purpose. If I remember correctly they intend to launch very low Earth orbit weather satellites that require continuous replacement as their orbits rapidly decay and they fall out of the sky. This will give them the ability to ID where hot spots are. But recent studies seem to indicate that most of the heat presently being generated are in dense jungle and not as presupposed by man's energy requirements. (This is also where the largest percentage of CO2 is being generated by rotting vegetation if I understand them correctly.)

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Tom Kunich said:
Well it depends on its purpose. If I remember correctly they intend to launch very low Earth orbit weather satellites that require continuous replacement as their orbits rapidly decay and they fall out of the sky.
The stratopause (circa 60 km) is a more appropriate altitude for sounding rockets than for satellites.

russ_watters
Kyle Gonterwitz said:
Is this a trick question? I think the lowest possible altitude of a satellite orbiting the Earth would be just above sea level. The satellite would have to achieve escape velocity, have thrust available to overcome drag, and have to be able to navigate around landmasses, but technically that should qualify as a satellite in orbit.
If you could really do that that on earth, like you said, just above sea level and make the satellite orbit just 1 circular orbit around earth, I will give you 100 trillion dollars of Zimbabwe. It is not practical but theoretical, and it's not possible on Earth but on a theoretical planet without any elevation and no atmosphere.

Kyle Gonterwitz said:
Flight level 600 is at 60,000 ft which is the upper boundary of controlled airspace, that would be the practical, lowest possible altitude. Search for the relationship between altitude and atmospheric pressure to find that relationship, then go as high as needed to optimize a design based on propulsion energy needed to achieve the desired altitude at orbital/escape velocity with minimum thrust to overcome atmospheric density/drag for the duration of the mission.
Thank you very much, but I'm not an aviation engineer, so if you could help or just show a few simple formulas that would be more than helpful

The top of the stratopause (60 km below the 50th parallel or so) has an atmospheric pressure of 7 x 10E-11. This is most assuredly enough drag to decay an orbit rapidly. But the major problem doesn't come from the density of the atmosphere but because an orbit this low requires a rather large velocity forcing the satellite to generate a great deal of drag from hitting a lot of molecules at this speed. What is it? - v = sqrt /Gravity x mass of satellite / actual radius of orbit.

So in truth we do have satellites as low as 100 miles but with the capacity to boost you CAN retain a LEO as low as the stratopause. The latest NASA weather satellite GOES has the capacity to boost its orbit but it has an elliptical orbit with a low of about 8,000 km putting it into the area of medium Earth orbit.

The normal definition of a low Earth orbit is anything below 3,000 km.

Presently SpaceX is planning on planting thousands of satellites into LEO around 1,200 km for more rapid world wide Internet access.

I have been unable to find the latest suggestions for very low Earth orbit weather satellites that would require constant renewal since they would be falling out of the sky almost like rain.

Tom Kunich said:
v = sqrt /Gravity x mass of satellite / actual radius of orbit
The mass of the satellite does not enter in (*). One can obtain the orbital velocity by equating the centripetal acceleration for a circular orbit ##a=\frac{v^2}{r}## with the centripetal acceleration provided by gravity ##a=\frac{GM}{r^2}##.
$$\frac{v^2}{r} = \frac{GM}{r^2}$$
$$v^2 = \frac{GM}{r}$$
$$v = \sqrt{\frac{GM}{r}}$$
The M in the numerator is the mass of the primary (e.g. the mass of the Earth), not the mass of the satellite.

For an orbit at an altitude of less than a few hundred km, the orbital radius will be approximately equal to the radius of the Earth and the orbital velocity will be approximately independent of altitude. About 8 kilometers per second. [Rule of thumb: orbital velocity = escape velocity divided by the square root of two]

(*) The mass of the satellite is irrelevant unless the satellite has significant mass compared to the primary. Then one has to consider that both primary and satellite are orbiting their combined center of mass.

russ_watters
Thanks, that was from memory and I probably was think it had to do with the moon's mass. A little difficult to concentrate when you're about to go to the dentist. And since my waiting 9 months for an implant to heal which just extremely painfully pulled out, at the moment it's even more difficult to concentrate.