According to Newton’s second law:

$$
begin{align*}
F &= W \
&= m_{1} ~ a \
end{align*}
$$

As Newton’s law of universal gravitation, The force of gravity between two objects is given by

$$
begin{align*}
F_{m} &= G ~ dfrac{ m_{1} ~ M_{S} }{ r_{m}^{2} } \
end{align*}
$$

So, the spherical mass like the Sun exerts the same gravitational force on masses outside it as it would if all the mass of the sphere were concentrated at the Center of the sphere. So, to calculate the mass of the Sun you should Know the gravitational force between the Sun and a Planet, the separation between them, and the mass of the Planet.

As Newton’s law of universal gravitation, The force of gravity between two objects is given by

$$
begin{align*}
F_{m} &= G ~ dfrac{ m_{1} ~ M_{S} }{ r_{m}^{2} } \
end{align*}
$$

For simplicity we use Newton’s law of universal gravitation but actually, we should use Einstein’s theory of general relativity. We know that a black hole is an object with a gravitational field so strong that even light can’t escape from its field. We called it black because a black hole absorbs everything that comes nearby its gravitational field. As we know the light spectrum of the natural light is red, orange, yellow, green, blue, indigo, and violet. So, we call the black hole black because the black color isn’t apart of the light spectrum.

Solve for the first Case:

According to Newton’s second law, the force due to the gravity (Weight) is given by

$$
begin{align*}
F &= W \
&= m_{1} ~ a \
end{align*}
$$

As Newton’s law of universal gravitation, The force of gravity between two objects is given by

$$
begin{align*}
F &= G ~ dfrac{ m_{1} ~ m_{2} }{ r^{2} } \
&= m_{1} ~ a \
end{align*}
$$

Rearrange and solve for the acceleration due to the gravitational force:

$$
begin{align*}
a &= G ~ dfrac{ m_{2} }{r^{2} } \
end{align*}
$$

Solve for the second Case:

According to Newton’s second law, the force due to the gravity (Weight) is given by

$$
begin{align*}
F &= W \
&= m_{1} ~ a \
end{align*}
$$

As Newton’s law of universal gravitation, The force of gravity between two objects is given by

$$
begin{align*}
F &= G ~ dfrac{ m_{1} ~ m_{2}’ }{ r’^{2} } \
&= m_{1} ~ a \
end{align*}
$$

Rearrange and solve for the acceleration due to the gravitational force:

$$
begin{align*}
a’ &= G ~ dfrac{ m_{2}’ }{r’^{2} } \
&= G ~ dfrac{ 2m_{2} }{ left( 2 r right)^{2} } \
&= dfrac{1}{2} ~ G ~ dfrac{ m_{2} }{ r^{2} } \
&= dfrac{1}{2} ~ a
end{align*}
$$

So, if both the mass and the radius of the planet were doubled, then the acceleration due to gravity at its surface decreases to its half value (halved).

In order to evaluate the density of the star, we use the following relation:

$$
begin{align*}
rho &= dfrac{ m}{V}
end{align*}
$$

So, if the volume halved and the mass remained the same, then the density of the star is doubled. According to Newton’s second law, the force due to the gravity (Weight) is given by

$$
begin{align*}
F &= W \
&= m_{1} ~ a \
end{align*}
$$

As Newton’s law of universal gravitation, The force of gravity between two objects is given by

$$
begin{align*}
F &= G ~ dfrac{ m_{1} ~ m_{2} }{ r^{2} } \
&= m_{1} ~ a \
end{align*}
$$

Rearrange and solve for the acceleration due to the gravitational force:

$$
begin{align*}
a &= G ~ dfrac{ m_{2} }{r^{2} } \
end{align*}
$$

As we see if the mass of the star remains constant and the separation between the star and the spaceship, then both gravitational force between them and the acceleration due to gravity is remaining the same, too.