Question

5. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each satellite is given below. Which satellite has the greatest speed?

Answer 1

The options of the question are missing. I have attached it.

Answer:

Satellite in option B will have the greatest speed.

Explanation:

From kepplers third law, we know that

V² = GM/R

Thus, v = √(GM/R)

Where;

v is velocity

G is gravitational constant

M is mass

R is radius

Looking at the options, let's start from the first one;

Option A

Here, mass = (1/2)m and radius = R

So, v = √(GM/R) thus v = √(G(m/2)/R) = √(Gm/2R)

Option B

Here, mass = m and radius = (1/2)R

Thus v = √(Gm/(R/2)) = √(2Gm/R)

Option C

Here, mass = m and radius = R

Thus v = √(Gm/R)

Option D

Here, mass = m and radius = 2R

Thus v = √(Gm/(2R))

Now, inspecting all the options, it's clear that option B will have the greatest velocity because it's numerator is the biggest and will in turn lead to higher velocity.