priscillianaw1

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 ${F}_{2}/{F}_{1}$?

What is the ratio ${F}_{2}/{F}_{1}$?

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 =$4R\text{}{F}_{2}$?

we know by teh law of gravitation, the force is given by

$F=G\frac{Mm}{{R}^{2}}$

where

M=mass of star

m= mass of planet

R=orbit radius

G=gravitationla constant

Gravitational force on first planet

${F}_{1}=\frac{GMm}{{R}^{2}}$

similary

${F}_{2}=\frac{GM(4m)}{(4R{)}^{2}}\phantom{\rule{0ex}{0ex}}{F}_{2}=\frac{GM(4m)}{16{R}^{2}}\phantom{\rule{0ex}{0ex}}{F}_{2}=\frac{GMm}{4{R}^{2}}\phantom{\rule{0ex}{0ex}}{F}_{2}=\frac{{F}_{1}}{4}$

or

$\frac{{F}_{2}}{{F}_{1}}=\frac{1}{4}$

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 =$4R\text{}{F}_{2}$?

we know by teh law of gravitation, the force is given by

$F=G\frac{Mm}{{R}^{2}}$

where

M=mass of star

m= mass of planet

R=orbit radius

G=gravitationla constant

Gravitational force on first planet

${F}_{1}=\frac{GMm}{{R}^{2}}$

similary

${F}_{2}=\frac{GM(4m)}{(4R{)}^{2}}\phantom{\rule{0ex}{0ex}}{F}_{2}=\frac{GM(4m)}{16{R}^{2}}\phantom{\rule{0ex}{0ex}}{F}_{2}=\frac{GMm}{4{R}^{2}}\phantom{\rule{0ex}{0ex}}{F}_{2}=\frac{{F}_{1}}{4}$

or

$\frac{{F}_{2}}{{F}_{1}}=\frac{1}{4}$

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?

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?

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