1. How much stronger is the gravitational force of the Sun on Earth, compared to the gravitational force of the Sun on Pluto?

Question

Full question: How much stronger is the gravitational force of the Sun on Earth, compared to the gravitational force of the Sun on Pluto? Pluto’s semimajor axis is 40 AU, and its mass is 0.002 times the mass of the Earth. (HINT: This problem can be solved using a ratio, without plugging in values for the masses or gravitational constant.)

Answer 1

Gravitational force increases linearly with mass and decreases quadratically with distance.

Mass of Pluto is smaller than mass of Earth by a factor of 0.002,

which reduces the gravitational force by the same factor.

The distance between the Sun and Pluto is 40 times greater, which reduces the

force by a factor of 40².

Therefore in total the ratio between the two forces is

40²/0.002 = 800,000