Choosing Between Options: Reasons & Analysis

[Andrei0408]

Homework Statement

Which of the following is an action-reaction pair for a space station containing astronauts in orbit about
the earth?
A. the weight of the space station and the centripetal force on the space station
B. the weight of the astronauts and the centripetal force on the space station
C. the weight of the space station and the gravitational force of the space station on the earth
D. the weight of the astronauts and the gravitational force of the space station on the astronauts

Relevant Equations

F12 = -F21

Could you tell me which one of these, but also why because I want to understand. Thank you!

 

[PeroK]

Homework Statement:: Which of the following is an action-reaction pair for a space station containing astronauts in orbit about
the earth?
A. the weight of the space station and the centripetal force on the space station
B. the weight of the astronauts and the centripetal force on the space station
C. the weight of the space station and the gravitational force of the space station on the earth
D. the weight of the astronauts and the gravitational force of the space station on the astronauts
Relevant Equations:: F12 = -F21

Could you tell me which one of these, but also why because I want to understand. Thank you!

You must at least analyse the possible answers and give your ideas.

 

[etotheipi]

The two forces in a $\text{N}\text{III}$ force pair i) act on two different bodies, ii) are of the 'same type' iii) satisfy $\vec{F}_{21} = - \vec{F}_{12}$.

 

[Andrei0408]

You must at least analyse the possible answers and give your ideas.

I don't think it's either A or B since the centripetal force should act towards the centre of the orbit, and not on the space station. My guess would be C) but still I'm not fully convinced and I need some explanations

 

[PeroK]

I don't think it's either A or B since the centripetal force should act towards the centre of the orbit, and not on the space station. My guess would be C) but still I'm not fully convinced and I need some explanations

What doubts do you have about c)?

 

[Andrei0408]

What doubts do you have about c)?

Well, shouldn't the answer be stated as the gravitational force of the Earth, not the gravitational force of the space station on the Earth?

 

[etotheipi]

Well, shouldn't the answer be stated as the gravitational force of the Earth, not the gravitational force of the space station on the Earth?

The gravitational force of the Earth, on what?

 

[Andrei0408]

The gravitational force of the Earth, on what?

On the space station

 

[etotheipi]

On the space station

And if the Earth exerts a gravitational force on the station, the space station exerts...

 

[PeroK]

Well, shouldn't the answer be stated as the gravitational force of the Earth, not the gravitational force of the space station on the Earth?

The space station exerts a gravitational force on the Earth, does it not? And that must be one of a third-law pair. The other force being ...?

 

[Andrei0408]

The space station exerts a gravitational force on the Earth, does it not? And that must be one of a third-law pair. The other force in the being ...?

Nevermind, yes I was thinking about gravitational acceleration, that's why it wouldn't make sense

 

[etotheipi]

Nevermind, yes I was thinking about gravitational acceleration, that's why it wouldn't make sense

Well, if you ignore the two astronauts, then you arrive at the two body problem. This is a little more complicated than the common assumption that the Earth constitutes an inertial frame. In particular, you need to be careful about how you define your coordinates (origin at the centre of mass, perhaps?).

But, Newton $\text{III}$ always holds, all the time, in classical mechanics!

 

[Andrei0408]

Well, if you ignore the two astronauts, then you arrive at the two body problem. This is a little more complicated than the common assumption that the Earth constitutes an inertial frame. In particular, you need to be careful about how you define your coordinates (origin at the centre of mass, perhaps?).

But, Newton $\text{III}$ always holds, all the time, in classical mechanics!

Yes, thank you for taking the time to help me