The gravitational force of a star on an orbiting planet 1 is F_1. Planet 2, which is four times as massive as planet 1 and orbits at four times larger distance from the star, experiences gravitational force F_2. What is the ratio F_2/F_1?

priscillianaw1

priscillianaw1

Answered question

2022-09-07

The gravitational force of a star on an orbiting planet 1 is F 1 . Planet 2, which is four times as massive as planet 1 and orbits at four times larger distance from the star, experiences gravitational force F 2 .
What is the ratio F 2 / F 1 ?

Answer & Explanation

Jane Reese

Jane Reese

Beginner2022-09-08Added 8 answers

Given that
The gravitational force of a star on an orbiting planet 1 is F 1
mass m, orbit R, force F 1
Planet 2, which is four times as massive as planet 1 and orbits at four times larger distance from the star, experiences gravitational force F 2
mass = 4m, orbit = 4 R   F 2 ?
we know by teh law of gravitation, the force is given by
F = G M m R 2
where
M=mass of star
m= mass of planet
R=orbit radius
G=gravitationla constant
Gravitational force on first planet
F 1 = G M m R 2
similary
F 2 = G M ( 4 m ) ( 4 R ) 2 F 2 = G M ( 4 m ) 16 R 2 F 2 = G M m 4 R 2 F 2 = F 1 4
or
F 2 F 1 = 1 4

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