A 360-kg satellite is in orbit around the Earth 10000 km above the Earth's surface.

(a) What is the weight of the satellite when in orbit? [Answer is in N]

(b) What was its weight when it was on the Earth's surface, before being launched? [Answer is in N]

(c) While it orbits the Earth, what force does the satellite exert on the Earth?
magnitude [Answer is in N]

When in orbit, an object is weightless.

weight on Earth: 360*9.8

Force: G Me*360/(re+1E7m)^2

To answer these questions, we need to understand the concept of weight and gravitational force.

(a) To find the weight of the satellite when in orbit, we can use the formula:

Weight = mass * gravity

where mass is the mass of the satellite and gravity is the acceleration due to gravity. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.

Given that the mass of the satellite is 360 kg, we can calculate the weight in newtons (N) as follows:

Weight = 360 kg * 9.8 m/s^2 = 3528 N

So, the weight of the satellite when in orbit is 3528 N.

(b) When the satellite was on the Earth's surface, its weight can be calculated in the same way but using the acceleration due to gravity on the surface, which is also approximately 9.8 m/s^2.

Using the same mass of 360 kg, we can calculate the weight in newtons (N) as follows:

Weight = 360 kg * 9.8 m/s^2 = 3528 N

So, the weight of the satellite when it was on the Earth's surface, before being launched, is also 3528 N.

(c) While the satellite orbits the Earth, it exerts a force on the Earth known as the gravitational force. According to Newton's third law of motion, the Earth exerts an equal and opposite force on the satellite.

The magnitude of the force that the satellite exerts on the Earth can be calculated using Newton's law of universal gravitation:

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

where G is the gravitational constant, m1 and m2 are the masses of the two objects (in this case, the satellite and the Earth), and r is the distance between their centers of mass.

Given that the mass of the Earth is much greater than the mass of the satellite, we can consider the mass of the satellite to be negligible compared to the mass of the Earth. Therefore, we can approximate the force exerted by the satellite on the Earth as:

Force = G * m1 / r^2

where m1 is the mass of the satellite and r is the distance between the satellite and the center of the Earth.

Using the given mass of the satellite as 360 kg and the distance of 10,000 km above the Earth's surface, we need to convert the distance to meters:

Distance = 10,000 km * 1,000 m/km = 10,000,000 m

Now, we can calculate the force using the formula:

Force = (6.673 * 10^-11 N(m^2/kg^2)) * 360 kg / (10,000,000 m)^2

Calculating this, we find:

Force ≈ 2.16 * 10^(-5) N

So, the magnitude of the force that the satellite exerts on the Earth while it orbits is approximately 2.16 * 10^(-5) N.