For a satellite to be in a circular orbit 830 km above the surface of the earth, what orbital speed must it be given?

The gravitational attraction of the Earth provides the centripetal force that keeps the satellite in circular motion around it:

where the term on the left is the centripetal force, while the term on the right is the gravitational force, and
m is the mass of the satellite
v is its orbital speed
r is the distance of the satellite from the center of Earth
G is the gravitational constant
M is the Earth's mass

Simplifying, we get:

However, we must be careful: r is the distance of the satellite from the Earth's center, so we must add the Earth's radius (6370 km) to the distance of the satellite from the surface (830 km):

The Earth's mass is , so the orbital speed of the satellite is

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