Question

3. A satellite is in orbit around some mystery planet. You observe that it takes 3 earth days, or (86,400*3) seconds for this satellite to orbit the mystery planet. a) If the object is located at 7 X 105 meters from this planet, determine the mass of the planet.

Answer 1

Answer:

3 x 10^18 kg

Explanation:

Time period, T = 3 days = 86400 x 3 = 259200 seconds

r = 7 x 10^5 m

Let M be the mass of planet

Use the formula of time period of satellite

$T = 2\pi \sqrt{\frac{r}{GM}}$

Where, G be the universal gravitational constant.

$M=\frac{4\pi ^{2}r^{3}}{GT^{2}}$

By substituting the values

$M=\frac{4\times 3.14 \times 3.14\times \left ( 7\times 10^{5} \right )^{3}}{6.67\times 10^{-11}\times 259200\times 259200}$

M = 3 x 10^18 kg

Thus , the mass of planet is 3 x 10^18 kg.