Satellite. calculate radius of orbit

[evan b]

Homework Statement

satellite is in a circular orbit around the earth. The period of the satellite is 25.4 hr. Calculate the radius of the orbit of the satellite. Data: Mass of the Earth = 5.98 x 1024 kg

 

[Rake-MC]

We have two equations we should use:

$$v = \frac{2\pi r}{T}$$

and

$$v = \sqrt{\frac{GM}{r}}$$

let them equal each other, then solve for r.

 

[baba89]

, Gravitational Constant = 6.67 x 10-11 N-m2/kg2

The radius of the orbit of the satellite can be calculated using the following formula:

r = ∛(GMT^2/4π^2)

Where r is the radius of the orbit, G is the gravitational constant, M is the mass of the Earth, and T is the period of the satellite in seconds.

Plugging in the given values, we get:

r = ∛((6.67 x 10^-11 N-m^2/kg^2)(5.98 x 10^24 kg)(25.4 hr x 3600 s/hr)^2/4π^2)

= ∛(1.08 x 10^14 m^3/s^2)

= 4.22 x 10^7 meters

Therefore, the radius of the orbit of the satellite is approximately 42,200 kilometers.