How to calculate ambient temperature in space or in orbit?

[SoRobby]

How would I go about calculating the ambient temperature in low Earth orbit (LEO) at approximately 400 km? What equations should I be referencing to determine the temperature of sun light side and/or eclipse side?

Thanks!

 

[russ_watters]

How would I go about calculating the ambient temperature in low Earth orbit (LEO) at approximately 400 km? What equations should I be referencing to determine the temperature of sun light side and/or eclipse side?

Thanks!

Welcome to PF!

"Ambient" means the temperature of the environment -- do you mean the temperature of an object?

 

[SoRobby]

"Ambient" means the temperature of the environment -- do you mean the temperature of an object?

It is correct how it's being asked. I am trying to calculate the heat flux loss due to radiation, to do that I need to determine the ambient temperature of the surrounding area, thus being space at 400 km.

 

[russ_watters]

It is correct how it's being asked. I am trying to calculate the heat flux loss due to radiation, to do that I need to determine the ambient temperature of the surrounding area, thus being space at 400 km.

Edit:
Space is transparent...

 

[SoRobby]

Edit:
Space is transparent...

I am attempting to calculate either the power or heat flux radiated in a space environment from an object with an emissivity value of 0.86. However, before I can calculate the heat flux or power radiated, the ambient temperature must be determined, and it is that I am having trouble quantifying.

Heat Flux for radiation.
Q = εσ(T⁴_surface - T⁴_ambient)

 

[russ_watters]

I am attempting to calculate either the power or heat flux radiated in a space environment from an object with an emissivity value of 0.86. However, before I can calculate the heat flux or power radiated, the ambient temperature must be determined, and it is that I am having trouble quantifying.

Heat Flux for radiation.
Q = εσ(T⁴_surface - T⁴_ambient)

Is this homework? Is there more to the problem or were you given any more guidance? T_ambient is the temperature of whatever is around your object that it is exchanging radiation with. So, what is it exchanging radiation with?

 

[SoRobby]

No this is not a homework problem. I am setting up a transient thermal simulation for a SmallSat and verifying the simulation results with collected data from previous CubeSat/SmallSat missions. Everything has been validated however I believe I am using the wrong ambient temperature for "worst hot case" scenario which assumes the spacecraft is in a sun-synchronous orbit. The object would be radiating heat outward into a vacuum (hence the importance to know the ambient temperature, which is what's making this difficult...)

The current model accounts direct solar radiation, planetary albedo and diffuse radiation and accounting for the different material properties/components that are influenced by the heat fluxes. While space isn't a true vacuum, especially in LEO the temperature is still reasonably high compared to other parts of our solar system, I just don't know how high.

The atmospheric pressure around 400 km is about 1*10^-8 Pa (from information I found online). Since space isn't a true vacuum I suppose to could determine the particle density per unit for the composition of the region and calculate the temperature from there? I am just not really sure how to go about this.

 

[russ_watters]

The object would be radiating heat outward into a vacuum (hence the importance to know the ambient temperature, which is what's making this difficult...)

The current model accounts direct solar radiation, planetary albedo and diffuse radiation and accounting for the different material properties/components that are influenced by the heat fluxes. While space isn't a true vacuum, especially in LEO the temperature is still reasonably high compared to other parts of our solar system, I just don't know how high.

The atmospheric pressure around 400 km is about 1*10^-8 Pa (from information I found online). Since space isn't a true vacuum I suppose to could determine the particle density per unit for the composition of the region and calculate the temperature from there? I am just not really sure how to go about this.

You're taking the wrong approach. I'm trying to make you think and lead you toward the answer. Please think about what I'm saying: space (the atmosphere at 400km) is transparent, so how can it radiate?

 

[Chestermiller]

See the section in this article on Ionospheric Model: https://en.wikipedia.org/wiki/Ionosphere. It may have references to appropriate literature.

 

[SoRobby]

You're taking the wrong approach. I'm trying to make you think and lead you toward the answer. Please think about what I'm saying: space (the atmosphere at 400km) is transparent, so how can it radiate?

Assuming I am understanding what you mean by transparent, no atmosphere (or it becomes negligible) then the only way heat or energy can be removed from an object in space is through radiation or emitting EM waves.

 

[russ_watters]

Assuming I am understanding what you mean by transparent, no atmosphere (or it becomes negligible) then the only way heat or energy can be removed from an object in space is through radiation or emitting EM waves.

You already know that; that's why you are using the radiation equation. That isn't what I asked.

Let's try this: you are standing in the middle of a room, radiating heat. What are you radiating heat to?

 

[SoRobby]

Let's try this: you are standing in the middle of a room, radiating heat. What are you radiating heat to?

If standing in a room with a medium, I would be radiating heat to that medium, heating up the surrounding volume ever so slightly.

 

[russ_watters]

If standing in a room with a medium, I would be radiating heat to that medium, heating up the surrounding volume ever so slightly.

No. The medium (air) is transparent. It is not absorbing your radiation or radiating toward you. So there must be something else exchanging radiation with you.

 

[SoRobby]

No. The medium (air) is transparent. It is not absorbing your radiation or radiating toward you. So there must be something else exchanging radiation with you.

Then you'd be radiating off to infinity or until it hits something? I think I'm more confused then ever now.

 

[russ_watters]

Then you'd be radiating off to infinity or until it hits something? I think I'm more confused then ever now.

Actually, you are finally moving closer to the answer! Though frankly, with the level of detail you gave about the problem, this is pretty surprising...

For the example I gave you (a room), there is no "infinity"; so what are you exchanging radiation with?

 

[SoRobby]

Actually, you are finally moving closer to the answer! Though frankly, with the level of detail you gave about the problem, this is pretty surprising...

For the example I gave you (a room), there is no "infinity"; so what are you exchanging radiation with?

In the room scenario I’d be the walls, within a space environment I’d be primarily Earth (excluding sun, moon, and other planets). So the ambient temperature should be the wall temperature, or in space I’d be Earth?

 

[russ_watters]

In the room scenario I’d be the walls, within a space environment I’d be primarily Earth (excluding sun, moon, and other planets). So the ambient temperature should be the wall temperature, or in space I’d be Earth?

Yes! But there is a problem still: the Earth isn't completely wrapped around you, so you have to use geometry to find the fraction of the "ambient" it represents. Same for the sun, if you are trying to use the same approach.

Now, what about the rest of space not facing the Earth? What are you exchanging radiation with? This was your main question...

 

[SoRobby]

Yes! But there is a problem still: the Earth isn't completely wrapped around you, so you have to use geometry to find the fraction of the "ambient" it represents. Same for the sun, if you are trying to use the same approach.

Now, what about the rest of space not facing the Earth?

The part of surface not facing Earth would be radiating to deep space which contains an ambient temperature of 3k. This doesn’t seem right though.

On the sides that are perpetually to the nadir vector would have its radiation value as a function of the view factor.

 

[russ_watters]

The part of surface not facing Earth would be radiating to deep space which contains an ambient temperature of 3k. This doesn’t seem right though.

That is indeed the correct answer. Satellites can get quite cold using radiation alone.

On the sides that are perpetually to the nadir vector would have its radiation value as a function of the view factor.

Yes.