Find the change in the force of gravity between two planets when the masses of both planets are doubled, but the distance between them remains the same. Please include your work!

To find the change in the force of gravity between two planets when their masses are doubled, but the distance remains the same, we can use Newton's law of universal gravitation. The equation is given as:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximately 6.674 x 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.

Let's assume the initial masses of the two planets are m1 and m2, and the initial force of gravity between them is F1. We want to find the change in force when both masses are doubled, but the distance remains the same. So, the new masses will be 2m1 and 2m2.

The initial force of gravity can be calculated as:
F1 = G * (m1 * m2) / r^2

The new force of gravity can be calculated as:
F2 = G * (2m1 * 2m2) / r^2

Now, let's calculate the change in force:

Change in force = F2 - F1
= G * (2m1 * 2m2) / r^2 - G * (m1 * m2) / r^2
= G * (4m1 * m2) / r^2 - G * (m1 * m2) / r^2
= G * (4m1 * m2 - m1 * m2) / r^2
= G * (3m1 * m2) / r^2

Therefore, the change in force of gravity between the two planets when their masses are doubled, but the distance remains the same is given by G * (3m1 * m2) / r^2.

To find the change in the force of gravity between two planets when their masses are doubled but the distance remains the same, we can use Newton's law of universal gravitation:

F = G * ((m1 * m2) / r^2)

Where F is the force of gravity between two objects, G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.

Let's denote the initial masses of the two planets as m1 and m2.

If the masses of both planets are doubled (2 * m1) and (2 * m2), the new force of gravity can be calculated as:

F' = G * (((2 * m1) * (2 * m2)) / r^2)

Simplifying this expression, we get:

F' = 4 * G * ((m1 * m2) / r^2)

The change in the force of gravity is then given by:

ΔF = F' - F
= 4 * G * ((m1 * m2) / r^2) - G * ((m1 * m2) / r^2)
= 3 * G * ((m1 * m2) / r^2)

Therefore, the change in the force of gravity between the two planets when their masses are doubled but the distance remains the same is 3 times the original force of gravity.

Note: In this explanation, m1 and m2 are used to denote the masses of the two planets. However, if you have specific values for the masses and the distance, you can substitute them into the equation to calculate the change in the force of gravity.

Force = G times (m1 x m2)/r^2

If you double the masses your have 4 times the force. since the distance is the same and the "G" is a constant.