Question

Compare the gravity between these pairs, each consisting of an Earth-like planet and its star. You are given the mass of the planet in Earth masses, the mass of the star in Sun masses, and the distance in AUs.

Answer 1

Ranking from lowest to highest gravity: Pair 2 < Pair 4 < Pair 1 < Pair 3

Explanation:

The question is incomplete: find the missing table in attachment.

The magnitude of the gravitational force between two objects is given by  the equation:

$F=G\frac{m_1 m_2}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

m1, m2 are the masses of the two objects

r is the separation between them

Let's now rewrite the gravitational force between each of the 4 pairs:

1)

$F=G\frac{(1M_E)(1M_S)}{(1AU)^2}=G\frac{M_EM_S}{AU^2}$

2)

$F=G\frac{(1M_E)(2M_S)}{(2AU)^2}=\frac{1}{2}G\frac{M_EM_S}{AU^2}$

3)

$F=G\frac{(2M_E)(1M_S)}{(1AU)^2}=2G\frac{M_EM_S}{AU^2}$

4)

$F=G\frac{(4M_E)(2M_S)}{(3AU)^2}=\frac{8}{9}G\frac{M_EM_S}{AU^2}$

Therefore, we can rank the pairs from the lowest force of gravity to the highest force of gravity as follows:

Pair 2 < Pair 4 < Pair 1 < Pair 3

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