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

In summary, the problem asks to find the weight of an astronaut of mass 75.5 kg inside a satellite of mass 683 kg in circular orbit at a height of 6.15x10^6 m above the surface of the Earth. The formula used is F = Gm_1*m_2/r², and the acceleration due to gravity is found to be approximately 2.55 m/s². Using F = ma, the weight of the astronaut is calculated to be 192.525 N. However, it is also mentioned that in a free-fall state, the astronaut would weigh 0 N. It is unclear if the question is asking for apparent weight or actual weight.
  • #1
NasuSama
326
3

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
 
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  • #2
If the satellite is in free-fall won't the astronaut weigh nothing?
 
  • #3
NasuSama said:

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 ?
 
  • #4
SammyS said:
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.
 
Last edited:
  • #5
NasuSama said:
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?
 
  • #6
SammyS said:
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.
 
  • #7
Actually, I need to find the weight of the astronaut IN the orbitting satellite!
 
  • #8
Wouldn't the astronaut weigh 0 N because it's in free fall as someone just said?
 
  • #9
NasuSama said:
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.
 
  • #10
haruspex 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.

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.
 
  • #11
Haha. Very funny. Then, the answer is 0.
 

What is the "Weight planet problem"?

The "Weight planet problem" is a hypothetical scenario in which a person's weight is affected by the gravitational pull of different planets in our solar system. It is often used as a thought experiment to understand the concept of weight and gravity.

How does the weight of a person on Earth compare to their weight on other planets?

The weight of a person on other planets will vary depending on the planet's size and mass. For example, on Mercury, a person would weigh approximately 38% of their weight on Earth, while on Jupiter, they would weigh approximately 254% of their weight on Earth.

What factors affect a person's weight on different planets?

The main factor that affects a person's weight on different planets is the planet's gravity. The stronger the gravitational pull, the more the person will weigh. The size and mass of the planet also play a role, as well as the person's own weight and mass.

Is there a planet where a person would weigh nothing?

Technically, no. Every planet has some gravitational pull, no matter how small. However, if we were to hypothetically consider a planet with extremely low gravity, like a small asteroid, a person's weight would be significantly reduced, but not completely zero.

Why do astronauts appear weightless in space?

Astronauts appear weightless in space because they are in a state of free-fall around the Earth. This creates the illusion of weightlessness because there is no support force acting on their bodies, similar to being in an elevator that is falling freely. However, they still have weight and mass, and their weight would change if they were to land on a different planet with a different gravitational pull.

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