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.

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[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:

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