Answer to Question #281027 in Astronomy | Astrophysics for Fazilah

Question

If the satellite S2 at a distance 6850000 m from the center of the earth, determined the orbital period of the satellite.

[Mass of earth, M = 5.97x 〖10〗^24kg, G=6.67x〖10〗^(-11) 〖Nm〗^2 〖kg〗^(-2)

Answer 1

Explanations & Calculations

• For this, you need to consider the equation used for the gravitation between two bodies.

$\qquad\qquad \begin{aligned} \small F&=\small ma\cdots[\text{to the satellite towards the center of its orbit}]\\ \small G\frac{M_em_s}{r^2}&=\small m_sr\omega^2\\ \small G\frac{M_e}{r^2}&=\small r\omega^2\\ \small G\frac{M_e}{r^2}&=\small r(\frac{2\pi}{T})^2\\ \small T^2&=\small4\pi^2.r.\frac{r^2}{GM_e}\\ \small T^2&=\small 4\pi^2.\frac{r^2}{GM_e} \\ \small T&=\small \sqrt{4\pi^2.\frac{r^3}{GM_e}}\\ &=\small\sqrt{4\pi^2.\frac{(6.85\times10^6\,m)^3}{(6.67\times10^{-11}Nm^2kg^{-2})(5.97\times10^{27}\,kg)}}\\ &=\small \sqrt{31866.27\times\frac{m^3}{kgms^{-2}.m^2.kg^{-2}.kg}}\\ &=\small \sqrt{31866.27\,s^2}\\ &=\small 178.51\,s \end{aligned}$

• You need to subject the quantity you need to get an answer for, once you know the equation and substitute the values and get the answer.
• I have provided a step by step guide to the final answer.
• Newtons need to be written in SI units to figure out the final unit.

• I believe you can substitute the given values into the equation and get the answer if that was the case no point in posting this question.
• Next time you post one, do mention where you really lag in getting the answer, is it the equation, any calculation or need to recheck the answer you already got.