Question

The mass of Saturn is approximately 100 times that of the Earth, and the semimajor axis of Saturn’s orbit is approximately 10 AU.

(a) To this approximation, how does the gravitational force that the Sun exerts on Saturn compare to the gravitational force that the Sun exerts on the Earth?

(b) Which planet will experience greater acceleration? By what factor?

Answer 1

data which we should consider is that :

M_saturn = mass of the Saturn

= 5.683 *10²⁶ kg

M_Earth = 5.97*10²⁴ kg

M_sun= 2*10³⁰ kg

G= gravitational constant = 6.67 *10^-11 m³ Kg^-1 s^-2

so,

Gravitational Force exerted by the sun on Saturn = GM_S*M_sun /R²

= (6.67 *10^-11 * 5.683*10²⁶ *2*10³⁰) /( 1.5 *10 *10¹¹)²

= 3.37 *10²² N

but Gravitational Force exerted by the sun on Earth = GM_E*M_sun /R²

  = (6.67*10^-11 *5.97*10²⁴ *2*10³⁰) /(1.5 *10¹¹)²

= 3.54 *10²² N

A) so approximately the Forces exerted by the Sun on these planets  are the same.

B) talking about acceleration which can be found out by Newton's second law

F =m*a

so acceleration experienced by planet Saturn = F /m

=  3.37 *10²² / 5.683*10²⁶

  = 5.93 *10^-5 m/s²

and so therefore,

so acceleration experienced by planet earth = F /m

= 3.54 *10²²/ (5.97*10²⁴)

= 5.93*10^-3 m/s²

so,  planet Earth will experience greater acceleration than Saturn and 100 times more

or Saturn will experience one one-hundredth of Earth's acceleration.