The orbital velocity of an earth satellite in an orbit 400 mi above the earth?
To calculate the orbital velocity of a satellite, we need to use the equation for the orbital velocity:
v = √(G * M / r)
Where:
- v is the orbital velocity,
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
- M is the mass of the Earth (approximately 5.972 × 10^24 kg), and
- r is the distance between the center of the Earth and the satellite.
First, we need to convert the altitude of the satellite from miles to meters:
Altitude = 400 miles = 643,737.6 meters.
Next, we calculate the total distance between the center of the Earth and the satellite:
r = radius of the Earth + altitude
The radius of the Earth is approximately 6,371 kilometers, which is 6,371,000 meters.
r = 6,371,000 + 643,737.6 = 7,014,737.6 meters.
Now we can calculate the orbital velocity:
v = √(G * M / r)
v = √((6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.972 × 10^24 kg) / (7,014,737.6 m))
v ≈ 7,660.6 m/s (rounded to four significant figures).
Therefore, the orbital velocity of an Earth satellite in an orbit 400 mi above the Earth is approximately 7,660.6 m/s.