Al the astronaut has a weight of 1600 N when he is standing on the surface of earth. What is the force of gravity action on him when he is in space station orbiting earth at a distance of four earth radii from the center of the earth?

force of gravity?

F=1600/4^2
net force is zero, of course, as he is in orbit.

Your answer is correct, but the net force of an orbiting object is not zero. Objects in circular motion have a net force that points to the center of the circle that generates the centripetal force

To calculate the force of gravity on Al when he is in space orbiting the Earth, we can use the formula for gravitational force:

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

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2)
m1 and m2 are the masses of the two objects (in this case, Al and the Earth)
r is the distance between the centers of the two objects

In this case, Al's weight on Earth is given as 1600 N. Weight is a measure of the force of gravity acting on an object, so we can use this value as the force of gravity between Al and the Earth when he is on the surface.

Let's assume Al's mass is m and the mass of the Earth is M.

Given:
Force on the surface of the Earth, F' = 1600 N
Distance from the center of the Earth, r = 4 * Earth's radius

Step 1: Calculate the mass of Al in kilograms
We can use the formula for weight:
Weight = mass * gravity

1600 N = m * 9.8 m/s^2

Solving for m:
m = 1600 N / 9.8 m/s^2
m ≈ 163.265 kg

Step 2: Calculate the force of gravity in space station orbit
Substituting the values into the formula:

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

F = (6.67430 × 10^-11 N(m/kg)^2 * 163.265 kg * M) / (4 * Earth's radius)^2

Now, we need to determine the mass of the Earth, M.

The force of gravity on Earth's surface is: F' = G * m * M / (Earth's radius)^2

Solving for M:
M = (F' * (Earth's radius)^2) / (G * m)
M = (1600 N * (Earth's radius)^2) / (6.67430 × 10^-11 N(m/kg)^2 * 163.265 kg)

Earth's radius is approximately 6,371,000 meters. Plugging in the values, we can calculate M.

Finally, substitute M and other values back into the formula of F to determine the force of gravity in the space station orbit.