Final answer:
Kepler's third law states that the square of the period of a satellite in a circular orbit is directly proportional to the cube of the radius of the orbit. We can use this law to calculate the height of a satellite in a stationary orbit with a period of 24 hours.
Step-by-step explanation:
Kepler's third law states that the square of the period of a satellite in a circular orbit is directly proportional to the cube of the radius of the orbit. We can use this law to calculate the height of a satellite in a stationary orbit with a period of 24 hours.
First, we need to find the radius of the orbit. Since the period is 24 hours, we can use the known period and radius values from the given example to find a proportionality constant. Then, we can use this constant to find the height of the satellite in the stationary orbit.
By rearranging the equation, we can solve for the radius:
T² = k * r³
r = (T² / k)^(1/3)
Substituting the given period and radius values into the equation and solving, we find that the radius of the stationary orbit is approximately 42465 km. To find the height of the satellite in the stationary orbit, we subtract the radius of the Earth from the radius of the orbit:
height = radius - radius of Earth
height = 42465 km - 6380 km = 36085 km