Answer to Question #266926 in Mechanics | Relativity for Jay ar

Question

The moon is 3.9 × 10⁵ km from Earth's center and 1.5 × 10⁸ km from the Sun's center. The masses of earth and the sun are 6.0 × 10²⁴ kg and 2.0 × 10³⁰ kg, respectively. Find the ratio of the gravitational fields due to Earth and the Sun at the center of the Moon.

Answer 1

Explanation & Calculations

• The field due to sun is

$\qquad\qquad \begin{aligned} \small E_s&=\small G\frac{m_s.m_m}{(1.5\times10^8\times10^3m)^2}\cdots (1) \end{aligned}$

• That due to earth is

$\qquad\qquad \begin{aligned} \small E_e&=\small G\frac{m_e.m_m}{(3.9\times10^5\times10^3m)^2}\cdots(2) \end{aligned}$

• By (2) $\small \div$ (1), (ratio should be carefully determined from the question)

$\qquad\qquad \begin{aligned} \small E_e:E_s&=\small \frac{E_e}{E_s}\\ &=\small \frac{m_e}{m_s}\times\frac{(1.5\times10^{11})^2}{(3.9\times10^8)^2}\\ &=\small \frac{(6\times10^{24}kg)}{(2\times10^{30}kg)}\times\frac{(1.5\times10^{11})^2} {(3.9\times10^8)^2}\\ &=\small 0.4 \end{aligned}$