Satellite A orbits a planet with a speed of 10,000 m/s. Satellite B is twice as massive as satellite A and orbits at twice the distance from the center of the planet. What is Satellite B's speed?

10000m/s

To find Satellite B's speed, we can use the principle of conservation of angular momentum. Angular momentum is constant as long as there are no external torques acting on the system.

Angular momentum, L, is given by the product of mass (m), velocity (v), and the radius (r) of the object orbiting around a center:

L = mvr

Since Satellite B is twice as massive as Satellite A, we can denote its mass as 2m. It orbits at twice the distance from the center of the planet compared to Satellite A.

Let's denote the velocity of Satellite B as vB and its radius as 2r (twice the radius of Satellite A).

Now, using the principle of conservation of angular momentum, we can equate the angular momentum of Satellite A (LA) to the angular momentum of Satellite B (LB):

L_A = L_B
m_A * v_A * r_A = (2m_A) * v_B * (2r_A)

Since m_A is common to both sides, we can cancel it out:

v_A * r_A = 2v_B * 2r_A

Simplifying,

v_A * r_A = 4v_B * r_A

Dividing both sides by r_A,

v_A = 4v_B

Now we can substitute v_A = 10,000 m/s (given in the question) and solve for v_B:

10,000 m/s = 4v_B

Dividing both sides by 4,

v_B = 10,000 m/s / 4

v_B = 2500 m/s

Therefore, Satellite B's speed is 2500 m/s.

centripetal force = gravitational force

mass*v^2/r=mass*(GMe/r^2)

v^2=GMe/r

So the velocity is dependent on the distance from the center of the Earth only (GMe is a constant).

I will be happy to critique your thinking on the answer.

vbv