Kepler

[logistic_guy]

Use $\displaystyle \text{Kepler}$'s laws and the period of the Moon $\displaystyle (27.4 \ \text{d})$ to determine the period of an artificial satellite orbiting very near the Earth's surface.

 

[khansaheb]

Use $\displaystyle \text{Kepler}$'s laws and the period of the Moon $\displaystyle (27.4 \ \text{d})$ to determine the period of an artificial satellite orbiting very near the Earth's surface.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[logistic_guy]

Kepler's third law is suffice to solve this problem.

$\displaystyle T^2 = \frac{4\pi^2 r^3}{Gm_E}$

This gives:

$\displaystyle \left(\frac{T_S}{T_{\text{Moon}}}\right)^2 = \left(\frac{r_S}{r_{\text{Moon}}}\right)^3$

where $\displaystyle r_{\text{Moon}}$ is the average distance from the Earth to the Moon.

Plug in numbers.

$\displaystyle \left(\frac{T_S}{27.4}\right)^2 = \left(\frac{6.38 \times 10^{6}}{3.84 \times 10^8}\right)^3$

This gives:

$\displaystyle T_S = 0.0586793 \ \text{d} = \textcolor{blue}{1.41 \ \text{h}}$