Calculate the force of Earth's gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth's surface if its mass is 1550 kg.

Newton has a neat law of gravity:

Fg= G Me Ms /distance^2

That leads to the inverse relation.
The weight at Earth's surface is mg, which is at one Earth radii.
So if you go one more Earth radii, the weight will be mg/2^2
and if you go one more, as you asked, the weight will be mg/3^2

To calculate the force of Earth's gravity on a spacecraft, you can use the equation for gravitational force:

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

Where F is the force of gravity, G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects (in this case, the mass of the spacecraft and the mass of the Earth), and r is the distance between the centers of the two objects.

In this case, the mass of the spacecraft is given as 1550 kg, and the distance from the surface of the Earth to the spacecraft is given as 12,800 km, which is equivalent to 2 Earth radii.

To calculate the force of gravity on the spacecraft, you need to convert the distance from kilometers to meters. There are 1000 meters in a kilometer, so the distance can be calculated as:

r = 12,800 km * 1000 m/km = 12,800,000 m

Now, we can enter the values into the equation:

F = (6.674 × 10^-11 N m^2/kg^2 * 1550 kg * 5.972 × 10^24 kg) / (12,800,000 m)^2

Simplifying the equation:

F = (6.674 × 10^-11 N m^2/kg^2 * 1550 kg * 5.972 × 10^24 kg) / 163,840,000,000 m^2

Now, we can calculate the force of gravity:

F = 1.944 × 10^7 N

Therefore, the force of Earth's gravity on the spacecraft 12,800 km above the Earth's surface is approximately 1.944 × 10^7 Newtons.