What is the weight of an astronaut inside a satellite in circular orbit?

[NasuSama]

Homework Statement

A satellite of mass M = 683 kg is in circular orbit at height ho = 6.15x106 m above the surface of the Earth. Find:

w, the weight of an astronaut of mass m = 75.5 kg inside the satellite.

Homework Equations

I believe it's something like:

F = Gm_1*m_2/r²

The Attempt at a Solution

For the first part of the problem, I've found that the acceleration due to gravity is around 2.55 m/s².

I used the form, but it's not right.

F = 6.67 * 10^(-11) * 5.98 * 10^(24) * 75.5 / (6.15 * 10^(6) + 6.37 * 10^6)² ≈ 192 N

 

[Spinnor]

If the satellite is in free-fall won't the astronaut weigh nothing?

 

[SammyS]

Homework Statement

A satellite of mass M = 683 kg is in circular orbit at height ho = 6.15x10⁶ m above the surface of the Earth. Find:

w, the weight of an astronaut of mass m = 75.5 kg inside the satellite.

Homework Equations

I believe it's something like:

F = Gm_1*m_2/r²

The Attempt at a Solution

For the first part of the problem, I've found that the acceleration due to gravity is around 2.55 m/s².

I used the form, but it's not right.

F = 6.67 * 10^(-11) * 5.98 * 10^(24) * 75.5 / (6.15 * 10^(6) + 6.37 * 10^6)² ≈ 192 N

You found the acceleration due to gravity. What is mass × acceleration due to gravity ?

 

[NasuSama]

You found the acceleration due to gravity. What is mass × acceleration due to gravity ?

Then, it's just F = ma, and it becomes...

F = 75.5 kg * 2.55 m/s²
= 192.525

However, the answer does not seem to be right. I don't get why this happens.

 

[SammyS]

Then, it's just F = ma, and it becomes...

F = 75.5 kg * 2.55 m/s²
= 192.525

However, the answer is not right. I don't get why this happens.

Do they mean apparent weight?

 

[NasuSama]

Do they mean apparent weight?

Yes, I believe that is what the question is trying to ask! My instructor is not good in wording the question, so I got that part wrong.

 

[NasuSama]

Actually, I need to find the weight of the astronaut IN the orbitting satellite!

 

[NasuSama]

Wouldn't the astronaut weigh 0 N because it's in free fall as someone just said?

 

[haruspex]

Wouldn't the astronaut weigh 0 N because it's in free fall as someone just said?

It depends what you mean by "weigh". If you stood the astronaut on a set of scales then yes, it would be 0. But if you mean the force exerted by gravity then your original answer is correct. In my view, the 0 answer comes about by using a non-inertial reference frame, which makes it as misleading as discussing centrifugal force.

 

[NasuSama]

It depends what you mean by "weigh". If you stood the astronaut on a set of scales then yes, it would be 0. But if you mean the force exerted by gravity then your original answer is correct. In my view, the 0 answer comes about by using a non-inertial reference frame, which makes it as misleading as discussing centrifugal force.

My original answer is correct if the question doesn't ask for apparent weight.

BUT I am not sure if the answer is 0 or not. The astronaut is in the orbiting satellite.

 

[NasuSama]

Haha. Very funny. Then, the answer is 0.