To calculate the speed of a satellite in a circular orbit, you can use the formula:
v = sqrt((G * M) / r)
where:
v = speed of the satellite
G = gravitational constant = 6.67 x 10^-11 N(m/kg)^2
M = mass of the Earth
r = radius of the circular orbit (distance from the satellite to the center of the Earth)
First, let's convert the height of the satellite from meters to kilometers:
2700 x 10^3 m = 2700 km
Next, let's calculate the radius of the orbit by adding the height of the satellite to the radius of the Earth:
r = (radius of the Earth) + (height of the satellite)
r = 6371 km + 2700 km
r = 9071 km
Now, we can plug in the values into the formula:
v = sqrt((G * M) / r)
v = sqrt((6.67 x 10^-11 N(m/kg)^2 * 5.98 x 10^24 kg)/(9071 km * 10^3 m/km))
v = sqrt(4.02 x 10^14 N( km^2 )/(9071 x 10^3 m))
v = sqrt(4.02 x 10^14 N( km * m)/(9071 x 10^3))
v = sqrt(4.02 x 10^11 N(m))/(9071 x 10)
v = sqrt(4.02 x 10^11)/90710
v ≈ 7790 m/s
Therefore, the speed of the satellite moving in a circular orbit about the Earth at a height of 2700 x 10^3 m is approximately 7790 m/s.