A satellite orbits at an average altitude of h = 441 km. What is its orbital speed? Use REarth = 6370 km and mEarth = 5.98 x 1024 kg.

To find the orbital speed of a satellite, we can use the following formula:

v = sqrt(G * mEarth / r),

where v is the orbital speed, G is the gravitational constant (approximately 6.67 x 10^-11 N m^2 / kg^2), mEarth is the mass of the Earth, and r is the distance from the center of the Earth to the satellite.

In this case, we are given the average altitude of the satellite, h, which is the distance from the surface of the Earth to the satellite. To find r, we need to add the radius of the Earth to the altitude:

r = REarth + h.

Given that REarth = 6370 km and h = 441 km, we can substitute these values to find r:

r = 6370 km + 441 km.

Now, we need to convert the values to meters, as the gravitational constant has units in m^3 / kg / s^2:

r = (6370 km + 441 km) * 1000 m/km.

Next, we substitute the value of r into the formula to find the orbital speed:

v = sqrt(G * mEarth / r).

Given that mEarth = 5.98 x 10^24 kg and G = 6.67 x 10^-11 N m^2 / kg^2, we can substitute these values:

v = sqrt((6.67 x 10^-11 N m^2 / kg^2) * (5.98 x 10^24 kg) / r).

Finally, we evaluate this expression to find the orbital speed.