Answer to Question #144595 in Mechanics | Relativity for Blu Seok

Question

As the Earth travels around the Sun the Moon is traveling around the Earth. Find the MAXIMUM speed of the Moon (relative to the Sun) as it travels around the Sun. The Earth’s orbital radius around the Sun is 1.5 X 1011 m and the Moon’s orbit has a radius of 3.85 X 108. The time for the Earth’s journey around the Sun is 3.156 X 107 s and the Moon takes 2.36 X 106 s to travel around the Earth.

Answer 1

Find the maximum speed when moving around the Earth: $v_1=\frac{2\times\pi\times R_E}{t_1}$ ,

And the earth around the sun for the moon $v_2=\frac{2\times\pi\times (R_E+R_S)} {t_2}$ ,

The total speed is $v=v_1+v_2=\frac{2\times\pi\times 3.85\times10^8}{2.36\times10^6}+$$\frac{2\times\pi\times (3.85\times10^8+1.5\times10^{11})}{3.156\times10^7}\approx30964.71$ m / s.