A space shuttle orbits at an altitude of approximately 200km above the surface of the Earth. If the radius of the Earth itself is 6380 km, what’s the acceleration due to gravity at the altitude of the space shuttle?

It is 9.81 m/s^2, multiplied by an inverse square law term,

(6380/6580)^2,
to accounnt for the reduction with increased distance from the center of the earth.

g' = 9.81*0.940 = 9.22 m/s^2

The acceleration due to gravity depends on the distance from the center of the Earth. To calculate the acceleration due to gravity at the altitude of the space shuttle, we need to first find the distance from the center of the Earth to the shuttle's altitude.

The total distance from the center of the Earth to the shuttle's altitude is the sum of the Earth's radius and the altitude of the shuttle. Given that the radius of the Earth is 6380 km and the altitude of the shuttle is 200 km, the total distance is:

Total distance = radius of Earth + altitude of shuttle
Total distance = 6380 km + 200 km
Total distance = 6580 km

Now that we have the total distance from the center of the Earth to the shuttle's altitude, we can use the formula for the acceleration due to gravity to calculate it. The formula for acceleration due to gravity is:

acceleration due to gravity = G * (mass of the Earth) / (distance from the center of the Earth)²

Where:
G = 6.67430 x 10^-11 m^3 kg^-1 s^-2 (gravitational constant)
mass of the Earth = 5.972 x 10^24 kg (mass of the Earth)

First, we need to convert the total distance to meters:

Total distance = 6580 km * 1000 m/km
Total distance = 6580000 m

Now, we can substitute the values into the formula:

acceleration due to gravity = (6.67430 x 10^-11 m^3 kg^-1 s^-2) * (5.972 x 10^24 kg) / (6580000 m)²

Calculating this expression will give us the acceleration due to gravity at the altitude of the space shuttle.