Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 5400km.
To calculate the speed of a satellite in a stable circular orbit around the Earth at a given height, we can use the formula:
v = √(GM/r)
Where:
- v is the speed of the satellite
- G is the gravitational constant (approximately 6.674 × 10^-11 Nm^2/kg^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, let's convert the height of the satellite from kilometers to meters:
height = 5400 km = 5400000 m
Now, we need to determine the distance between the center of the Earth and the satellite. This can be calculated by adding the radius of the Earth to the satellite's height:
r = radius of the Earth + height
The average radius of the Earth is approximately 6,371 km. Converting this to meters:
radius of the Earth = 6,371 km = 6,371,000 m
Now we can calculate the distance:
r = 6,371,000 m + 5,400,000 m = 11,771,000 m
Plug the values into the formula to calculate the speed:
v = √((6.674 × 10^-11 Nm^2/kg^2) * (5.972 × 10^24 kg) / 11,771,000 m)
Solving this equation will give us the speed of the satellite in meters per second.