Answer to Question #266922 in Mechanics | Relativity for Jay ar

Question

The planet Saturn has about 100 times the mass of the earth and is about 10 times farther from the sun than the earth is. Compared to acceleration of the earth caused by the sun's gravitational pull, how great is the acceleration of saturn due to the sun's gravitation?

Answer 1

$\text{for Earth:}$

$F_1 = G\frac{m_{e}M_{s}}{r_1^2}$

$\text{where: }$

$G - \text{universal gravity constant}$

$m_e - \text{mass of Earth}$

$M_s - \text{mass of Sun}$

$r_1 - \text{distance between Earth and Sun}$

$F_1 = m_ea_1$

$a_1 =\frac{F_1}{m_e}=G\frac{M_{s}}{r_1^2}$

$\text{for Saturn:}$

$F_2 = G\frac{m_{s}M_{s}}{r_2^2}$

$\text{where: }$

$m_s - \text{mass of Saturn}$

$r_2 - \text{distance between Saturn and Sun}$

$F_2 = m_sa_2$

$a_2 =\frac{F_2}{m_c}=G\frac{M_{s}}{r_2^2}$

$r_2 = 10*r_1$

$a_2 ==G\frac{M_{s}}{100*r_1^2}$

$a_2 = \frac{1}{100}a_1$

$\text{Answer:}$

$\text{The acceleration of Saturn due to the gravity of the Sun }\newline \text{is 100 times less than the acceleration of the Earth}\newline \text{due to the gravity of the Sun.}$