# A satellite was placed in an orbit above the earth's atmosphere, at a distance of 15,000 km from the center of the earth. What is the orbital period (in hours) of the satellite?

##### 2 Answers

The orbital period of this satellite is 5.08 hours (5 hours, 5 minutes, 3 seconds to be precise!) .

#### Explanation:

We need Kepler's third law for this problem, but in the form that is often referred to as "Newton's derivation"

where G is the gravitational constant

Also, care must be taken to use base units for

Here is the solution:

Divide by 3600 (seconds in each hour) and you get

The orbital period is

#### Explanation:

Let the mass of the earth

Let the mass of the satellite be

Let the radius of the earth be

Let the radius of the satellite's orbit be

Let the gravitational constant be

There are

The velocity of the satellite is

The orbital period is

The distance is

Therefore,

So,