On the moon's surface, the force of gravity exerted by the moon on a camera is 2.4 N. What is the force of gravity exerted by the moon on the camera when it is in orbit with a radius = to twice the moon's radius?
1/4 as much as it is on the surface of the moon. It varies inversely with the square of the distance from the center of the moon
Thanks!
To determine the force of gravity exerted by the moon on the camera when it is in orbit with a radius equal to twice the moon's radius, we can use the formula for gravitational force:
F = (G * M1 * M2) / r^2
Where:
F is the force of gravity,
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2),
M1 and M2 are the masses of the two objects (in this case, the camera and the moon),
and r is the distance between the centers of the two objects.
Given that the force of gravity exerted by the moon on the camera on the moon's surface is 2.4 N, we can set up an equation to solve for M2, the mass of the moon:
2.4 = (G * M1 * M2) / r^2
In this case, M1 refers to the mass of the camera, but since we are not given this value, we don't need to know it to find the force of gravity when the camera is in orbit with a radius twice that of the moon.
Now, let's calculate the force of gravity when the camera is in orbit with a radius equal to twice the moon's radius.
If the radius of the moon is R, then the radius of the camera's orbit is 2R.
Using the given information, the force of gravity on the moon's surface (2.4 N), and rearranging the formula, we can solve for the mass of the moon (M2):
2.4 = (G * M_moon * M_camera) / R^2
Since we are interested in calculating the force of gravity when the camera is in orbit with radius 2R, we can rewrite the equation as follows:
F = (G * M_moon * M_camera) / (2R)^2
F = (G * M_moon * M_camera) / 4R^2
To find the force of gravity on the camera when it is in orbit with a radius twice that of the moon's radius, we need to determine the value of M_moon. Unfortunately, we do not have enough information to calculate it.