The gravitational force between two asteroids 1200 km apart is 8400 N. Find the following changes in gravity (do not write units)
a) What is the force between them if the distance is 600 km?
F = k/d^2
so
k = F d^2
8400 (1200)^2 = F ( 600)^2
F = 8400 (2)^2 = 8400 * 4
Thanks SOOO much
To find the force between the asteroids if the distance is 600 km, we can use the inverse square law of gravity. The formula for gravitational force is:
F = G * (m1 * m2) / r^2
Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
We already have the force of gravity when the distance is 1200 km, which is 8400 N. Let's call this force F1 and the distance r1. So, we have:
F1 = G * (m1 * m2) / r1^2
Now, we want to find the force when the distance is 600 km. Let's call this force F2 and the distance r2. We have:
F2 = G * (m1 * m2) / r2^2
To find the ratio of F2 to F1, we can divide the second equation by the first equation:
F2/F1 = (G * (m1 * m2) / r2^2) / (G * (m1 * m2) / r1^2)
G, m1, and m2 are constants, so they cancel out:
F2/F1 = (r1^2 / r2^2)
Now, we substitute in the values we know:
F2/8400 = (1200^2 / 600^2)
To find F2, we multiply both sides by 8400:
F2 = 8400 * (1200^2 / 600^2)
Calculating this expression gives us the force between the asteroids when the distance is 600 km. Note that we kept the units out of the calculation as requested.