Final answer:
The speed of a satellite in a stable circular orbit about the Earth can be calculated using the formula v = sqrt(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the center of the Earth and the satellite. By plugging in the given values for the radius of the Earth and the height of the satellite, we can find the speed in m/s.
Step-by-step explanation:
A satellite moving in a stable circular orbit about the Earth can be described by the formula:
v = sqrt(GM/r)
Where v is the speed of the satellite, G is the gravitational constant, M is the mass of the Earth, and r is the distance between the center of the Earth and the satellite. To calculate the speed, we need to know the radius of the orbit, which is the sum of the radius of the Earth and the height of the satellite above the Earth's surface.
Let's first calculate the radius of the orbit:
r = R + h
where R is the radius of the Earth (6370 km) and h is the height of the satellite (3600 km).
Plugging in the values, we get:
r = 6370 km + 3600 km = 9970 km
Now we can calculate the speed:
v = sqrt(GM/r)
Using the values G = 6.67 x 10^-11 m^3/kg/s^2 and M = 5.97 x 10^24 kg, and converting km to m:
v = sqrt((6.67 x 10^-11 m^3/kg/s^2)(5.97 x 10^24 kg)/(9970 km * 1000 m/km))
Calculating this expression gives us the speed of the satellite in m/s.