Determine the speed of an artificial earth satellite if it moves in a circular orbit at an altitude of 2600 km

Determine the speed of an artificial earth satellite if it moves in a circular orbit at an altitude of 2600 km above the Earth’s surface. (M3 = 6 * 10 ^ 24 kg; R3 = 6.4 * 10 ^ 6m.)

Given:
h = 2600 km;
M3 = 6.4 * 10 ^ 6 m;
G = 6.67 * 10 ^ -11 H * m ^ 2 / kg ^ 2.
Find: V.
Decision:
1) First, for convenience, we will translate the height into another system of calculation, namely kilometers to meters.
h = 2600 km = 2600000 m = 2.5 * 10 ^ 6 m.
2) To find the speed, we use this formula: V = root of (G * (M3 / R3 + h)).
3) Substitute the values we know and get the answer.
V = root of (6.67 * 10 ^ -11 * (6 * 10 ^ 24 / 6.4 * 10 ^ 6 + 2.5 * 10 ^ 6)) = root of (4.002 * 10 ^ 14/8, 9 * 10 ^ 6) = root of 4.49663 * 10 ^ 7 = 6705 m / s = 6.7 km / h.
Answer: 6.7 km / h