Question

A 150 kg satellite is in circular orbit with radius 7.1x10⁶ m around another planet. If its orbital period is 14 hours, what is the planets mass?

Answer 1

The mass of the planet is approximately 1.41×10²⁴ kg.

Step-by-step explanation:

To find the planet's mass, you can use Kepler's third law of planetary motion, which relates the orbital period T, the semi-major axis a (which is the radius in a circular orbit), and the mass of the central body

M (the planet in this case).

The formula is given by:

T2 = 4π2/GM . a3

where:

T is the orbital period,

G is the gravitational constant (

G≈6.674×10−11m3kg−1s−2),

M is the mass of the central body (the planet),

a is the semi-major axis (radius in a circular orbit).

First, convert the orbital period from hours to seconds:

T=14hours×3600s/hour

Now, plug in the known values and solve for M:

(14×3600)2 = 4π2/6.674×10−11 ×(7.1×106)3×M

After calculating, you should be able to find the mass M of the planet.