Final answer:
To find the time interval during which the satellite remains above 300 km altitude, we can use Kepler's Third Law to calculate the periods of the satellite at the perigee and apogee altitudes.
The time interval is twice the difference between these periods.
Step-by-step explanation:
To find the time interval during which the satellite remains above an altitude of 300 km, we need to determine the time it takes for the satellite to travel from the perigee altitude of 200 km to the apogee altitude of 400 km and vice versa.
We can use Kepler's Third Law, which states that the period of an orbit is related to the radius of the orbit. The period of the satellite can be calculated using the formula: T = 2π √(r³/GM), where T is the period, r is the average radius, G is the universal gravitational constant, and M is the mass of the Earth.
By plugging in the average radius for the perigee and apogee altitudes, we can calculate the periods for both altitudes. The time interval during which the satellite remains above 300 km altitude is equal to twice the difference between the periods at the perigee and apogee altitudes.
Therefore, the correct answer is 20 minutes (C).