Gravity and Orbital Velocity: Understanding a Common Misconception

[momoneedsphysicshelp]

Homework Statement

Two satellites are in the same circular orbit around the Earth. Satellite A has mass of m and satellite B mass of 2m. Which one of the following statements is true about the speeds of these satellites?

Relevant Equations

A: satellite A's velocity will be two times faster than satellite B

B: The two satellites have the same speed

C: Satellite B's velocity will be two times larger than Satellite A

D: We need to know the orbital radius in order to compare the speeds of the satellites

I need help with understanding this problem. I had initially chosen B, that the two satellites had the same speed because the mass does not effect the velocities of each of the satellites considering they are in orbit. But that answer was marked incorrect by my instructor. What other answer could it be and why was I wrong?

 

[phinds]

What will be the orbits of the two masses relative to each other?

 

[momoneedsphysicshelp]

What will be the orbits of the two masses relative to each other?

As per the information given in the problem the orbits will be of the same speed in the same circular orbital path?

 

[haruspex]

Homework Statement:: Two satellites are in the same circular orbit around the Earth. Satellite A has mass of m and satellite B mass of 2m. Which one of the following statements is true about the speeds of these satellites?
Relevant Equations:: A: satellite A's velocity will be two times faster than satellite B

B: The two satellites have the same speed

C: Satellite B's velocity will be two times larger than Satellite A

D: We need to know the orbital radius in order to compare the speeds of the satellites

I need help with understanding this problem. I had initially chosen B, that the two satellites had the same speed because the mass does not effect the velocities of each of the satellites considering they are in orbit. But that answer was marked incorrect by my instructor. What other answer could it be and why was I wrong?

I agree with your answer.

 

[Delta2]

I also agree with your answer.

If $g$ is the gravitational acceleration at the altitude of the common orbit, then $$g=\frac{V_A^2}{R_A}=\frac{V_B^2}{R_B}$$ and since $R_A=R_B$ (same orbit) it follows that $$V_A=V_B$$.

 

[momoneedsphysicshelp]

Thank you all, I will converse with my instructor regarding my reasoning.

 

[PeroK]

Answer D is a true statement. But, the question specifies that the orbital radii are the same.

 

[Orodruin]

Answer D is a true statement. But, the question specifies that the orbital radii are the same.

I do not read D that way. Since it is specified in the problem that the radii are the same, I read it as claiming that you need to know what the common radius is, which is wrong.

B is definitely correct and an instructor that marks it wrong even after this is pointed out should not be a physics instructor. The argument is very simple and already given in #5.