A satellite having orbital speed V orbits a planet of mass M.If the planet had half as much mass,the orbital speed of the satellite at the same distance from the center would be
A)V $$\sqrt { 2 }$$
B)2V.
C)V.
D)V/ $\sqrt { 2 }$
E)V/2.

Question

Quizplus · Accepted Answer

From the conservation of momentum, we have:

mv = m'v', where m is the mass of the planet, m' is the new mass of the planet (in this case, M/2), v is the initial orbital speed, and v' is the new orbital speed.

We can simplify this equation to:

v' = v(m/m')^(1/2)

Plugging in the values, we get:

v' = V($M/(M/2)$)^(1/2) = V/$\sqrt{2}$

Therefore, the new orbital speed is V/$\sqrt{2}$ when the mass of the planet is halved.

A Satellite Having Orbital Speed V Orbits a Planet of Mass