Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 3.004km.
force due to gravity=force due centepetal
G*Me*/(re+3e6m)^2=v^2/(re+3e6) where re is the radius of earth in meters.
solve for v.
To calculate the speed of a satellite in a stable circular orbit about the Earth, we need to use the formula for the orbital speed:
v = √(GM/r)
where:
- v is the orbital speed (in meters per second)
- 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)
- r is the distance between the center of the Earth and the satellite (in meters)
First, we need to convert the height of the satellite into meters. Since the height is given as 3.004 km, we multiply it by 1000 to convert it to meters:
height = 3.004 km * 1000 = 3004 meters
Next, we need to calculate the total distance from the center of the Earth to the satellite. This is done by adding the radius of the Earth to the height of the satellite. The radius of the Earth is approximately 6371 km, which we convert to meters by multiplying by 1000:
radius = 6371 km * 1000 = 6,371,000 meters
Now, we can calculate the distance between the center of the Earth and the satellite by adding the height and the radius:
r = 6,371,000 meters + 3004 meters = 6,374,004 meters
Finally, we can use the formula to calculate the orbital speed:
v = √(6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg / 6,374,004 meters)
Calculating this using a calculator or computer program, we find that the speed of the satellite is approximately 7741 meters per second (m/s).