The orbital period of the satellite is 90 minutes, the satellite’s height above the earth is 320 km

The orbital period of the satellite is 90 minutes, the satellite’s height above the earth is 320 km, the radius of the earth is 6.400 km. Find the satellite speed?

To find the orbital speed of the satellite, we write the formula for the speed of a body’s revolution around a circle:

u = 2πr / T,

where r is the distance from a point on the circle to its center (radius);

T is the period of revolution of the body along the circumference.

We see that in this problem the radius will be the sum of the earth’s radius and the satellite’s height:

r = R + h.

We substitute it in the formula for the speed of rotation of the body:

u = 2π (R + h) / T = (2 * 3.14 * (6400 km + 320 km)) / 1.5 h = 6.28 * 6 720 km / 1.5 h = 42201.6 / 1 .5 = 28 134.4 km / h.

Answer: 28,134.4 km / h.