Final answer:
To find the distance from the center of the planet to the satellite, the gravitational force acting as the centripetal force is equated to mv^2/r, and after substituting the given values, the distance r can be calculated.
Step-by-step explanation:
To find the distance from the center of the planet to the satellite, we can use the formula for gravitational force as the centripetal force required for circular motion. The gravitational force is given by Newton's law of universal gravitation: F = Gm1m2/r2, where F is the force between the masses, G is the gravitational constant (6.674×10−12 Nm2/kg2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two masses. The centripetal force required to keep the satellite in orbit is F = mvv2/r, where mv is the mass of the satellite and v is its orbital speed.
Setting the gravitational force equal to the centripetal force and solving for r, we get r = Gm2/v2. Plugging in the given values (m2 = 4 x 1020 kg, v = 10000 m/s, and G = 6.674×10−12 Nm2/kg2), we calculate the distance r.
Therefore, the distance from the center of the planet to the satellite is r = (6.674×10−12 Nm2/kg2 × 4 x 1020 kg) / (10000 m/s)2. After calculating, we find the distance r which provides the answer to the student's question.