Find the change in the gravitational force between two planets if the masses of both planets are doubled but the distance between them stays the same.
Express your answer as an integer.
force directly proportional to product ofmasses, inversely prop to square of distance.
changefactor= 2*2/1^2=4
5+4/8=19
frb
To find the change in gravitational force between two planets when their masses are doubled but the distance remains the same, we can use Newton's law of universal gravitation.
The formula for gravitational force between two objects is:
F = G * (m1 * m2) / r^2
Where:
- F is the gravitational force between the two objects,
- G is the gravitational constant (approximately 6.67430 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.
In this case, we will assume the initial masses of both planets are m1 and m2, and the distance between them is r. When the masses are doubled, the new masses become 2m1 and 2m2, while the distance remains unchanged (r).
To find the change in gravitational force, we need to compare the initial force (F_initial) with the final force (F_final) after doubling the masses:
F_initial = G * (m1 * m2) / r^2
F_final = G * ((2m1) * (2m2)) / r^2
Dividing the final force by the initial force will give us the change in gravitational force:
Change in force = F_final / F_initial
Let's plug in the values and calculate the change in gravitational force.
Change in force = (G * ((2m1) * (2m2)) / r^2) / (G * (m1 * m2) / r^2)
= (2m1 * 2m2) / (m1 * m2)
= 4
Therefore, the change in gravitational force between the two planets when both masses are doubled but the distance remains the same is 4.