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

It is defined to be precisely 9.80665 m/s2 or 35.30394 (km/h)/s (32.174 ft/s2 or 21.937 mph/s)

To find the acceleration due to gravity at the altitude of the space shuttle, we can use the formula for the gravitational force:

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

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

First, we need to calculate the distance between the center of the Earth and the space shuttle. It is given that the altitude of the space shuttle is 200 km, so we add this to the radius of the Earth:

r = 6380 km + 200 km
r = 6580 km

Next, we can plug the values into the formula:

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

Now, since we want to find the acceleration due to gravity at the altitude of the space shuttle, we need to rearrange the formula. We know that the force of gravity is equal to the mass of the shuttle multiplied by the acceleration due to gravity (F = m * a). Therefore, we can rewrite the formula as:

a = G * (m2 / r^2)

Now, we can use the given values:

G = 6.67430 x 10^-11 N(m/kg)^2
m2 = mass of the Earth (approximately 5.972 x 10^24 kg)
r = 6580 km (which needs to be converted to meters)

Converting km to meters:
1 km = 1000 meters
6580 km = 6580 * 1000 meters
r = 6,580,000 meters

Finally, we can calculate the acceleration due to gravity at the altitude of the space shuttle:

a = G * (m2 / r^2)

Now, let's plug in the values:

a ≈ (6.67430 x 10^-11 N(m/kg)^2) * (5.972 x 10^24 kg) / (6,580,000 meters)^2

Solving this equation should give us the value of the acceleration due to gravity at the given altitude of the space shuttle.

Since the earth is not a perfect sphere, there is no actual radius for the Earth. If there was one, the distance would be way outside the earth's atmosphere, meaning it would be in space. Space has 0 gravity, which means everything is weightless. That means the satellite would be 0 pounds at that distance.