The distance of the planet Pluto from the Sun | vedclass

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(B) According to Newton's law of universal gravitation,the force exerted by the Sun on a planet is given by $F = \frac{G M m}{r^2}$,where $M$ is the m

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$1600: 1$

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(B) According to Newton's law of universal gravitation,the force exerted by the Sun on a planet is given by $F = \frac{G M m}{r^2}$,where $M$ is the mass of the Sun,$m$ is the mass of the planet,and $r$ is the distance between them.Let $m_e$ and $m_p$ be the masses of Earth and Pluto,and $r_e$ and $r_p$ be their respective distances from the Sun.Given $m_e = m_p$ and $r_p = 40 r_e$.The gravitational force on Earth is $F_e = \frac{G M m_e}{r_e^2}$.The gravitational force on Pluto is $F_p = \frac{G M m_p}{r_p^2}$.The ratio of the forces is $\frac{F_e}{F_p} = \frac{G M m_e / r_e^2}{G M m_p / r_p^2} = \frac{r_p^2}{r_e^2}$.Substituting $r_p = 40 r_e$,we get $\frac{F_e}{F_p} = \frac{(40 r_e)^2}{r_e^2} = 40^2 = 1600$.Thus,the ratio is $1600: 1$.

The distance of the planet Pluto from the Sun is $40$ times the distance of the Earth from the Sun. Assuming the masses of the Earth and Pluto are equal,find the ratio of the gravitational force exerted by the Sun on the Earth to that on Pluto.

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