Rank the following objects, in order of their circular velocities, from smallest to largest

a. a 5-kg object orbiting earth halfway to the moon

b. a 10-kg object orbiting earth just above earth's surface

c. a 15-kg object orbiting earth at the same distance as the moon

show detail on calculations

a)

b)

c)

Explanation:

Assuming these objects are moving with uniform circular motion (and the orbit is perfectly circular), the velocity will be given by the following equation:

Where:  

is the velocity of the object, which is assumed as constant.  

is the Gravitational Constant  

is the mass of the object

is the radius of the orbit

Knowing this, let's begin with the answers:

In this case the radius of the orbit is the half of the distance between the Earth and the moon:

And the mass will be . So, the equation of the velocity is:

This is the velocity of the first object

Now the radius of the orbit is approximately the radius of the Earth:

And the mass is . So, the equation of the velocity is:

This is the velocity of the second object

With this last case, the radius of the orbit is equal to the distance between the Earth and the Moon:

And the mass is . So, the equation of the velocity is:

This is the velocity of the third object

Finally, comparing the velocity of the three objects we have: