Tangential velocity of external satellite

[jhonconnor]

Homework Statement

Two satellites move in circular orbits around the Earth. The radius of the orbit of the outer satellite is three times that of the inner satellite (measured from the center of the Earth). If the modulus of the inner tangential velocity is v then that of the outer satellite is:

So I guess a_1 = a_2 where
a = (v_t)^2/r
and I found that
v_2 = sqrt(3)v_1
but the correct answer is
v_2 = v_1/sqrt(3)

Could you explain me what I'm doing wrong?

Relevant Equations

a = (v_t)^2/r
v_t = w*r

 

[mjc123]

Why do you assume a1 = a2?

 

[kuruman]

Check this reference.

 

[jhonconnor]

Why do you assume a1 = a2?

Because I tried to get tangential velocity of external satellite with that condition

 

[jhonconnor]

Check this reference.

Ohhhhh, it means that is another kind of problem. I thought that the problem can be solved with circular motion, but I didn't consider the orbital motion and the influence of the gravitational force. Thanks a lot

 

[bdrobin519]

Would this not be the same?

 

[kuruman]

Would this not be the same?

The same as what?

 

[kuruman]

Ohhhhh, it means that is another kind of problem. I thought that the problem can be solved with circular motion, but I didn't consider the orbital motion and the influence of the gravitational force. Thanks a lot

But it is circular motion. The satellites go around the center of the Earth at constant speed just like a mass at the end of a string. The difference is in the nature of the force that provides the centripetal acceleration. The kinematics are the same.