Question

analyzing the relationship between mass and gravity
suppose for an unexplained reason a star near earth started shrinking. at what stage is the gravitational force between earth and the star the greatest?
stage 1
stage 2
stage 3
stage 4

stage	mass of earth (kg)	mass of star (kg)
2	$5.97 \times 10^{24}$	$2.7 \times 10^{27}$
3	$5.97 \times 10^{24}$	$5.0 \times 10^{26}$
4	$5.97 \times 10^{24}$	$4.5 \times 10^{23}$

Explanation:

Step1: Recall gravity force formula

The gravitational force between two objects is given by $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.

Step2: Identify constant variables

Here, $G$, $m_1$ (mass of Earth), and $r$ (distance between Earth and star, since the star only shrinks, distance stays the same) are constant. So $F$ is directly proportional to $m_2$ (mass of the star).

Step3: Compare star masses

Compare the star masses:
$1.8 \times 10^{30} > 2.7 \times 10^{27} > 5.0 \times 10^{26} > 4.5 \times 10^{23}$
The largest star mass is in Stage 1.

Answer:

Stage 1