Final answer:
To determine the periods and forces on satellites S2 and S3 orbiting a planet, and the kinetic energy ratio between satellites S1 and S3, we use Kepler's Third Law and Newton's law of universal gravitation, considering orbital physics concepts like circular orbits, gravitational force, and kinetic energy.
Step-by-step explanation:
The student's question pertains to the concepts of celestial mechanics and satellite motion, specifically relating to the periods and forces of satellites orbiting a planet and the kinetic energy ratio between two satellites. The orbital period of a satellite, according to Kepler's Third Law, is determined by the radius of the orbit and is independent of the satellite's mass. To calculate the periods of satellites S2 and S3, we apply Kepler's Third Law, which tells us that the square of the period is proportional to the cube of the semi-major axis (radius, in the case of circular orbits) of the orbit. The forces on satellites S2 and S3 depend on the gravitational force exerted by the planet, which can be found using Newton's law of universal gravitation. Moreover, the kinetic energy ratio K1/K3 for satellites S1 and S3 can be determined using the definition of kinetic energy (K = 0.5 * m * v^2), and the velocity can be found from the orbital speed formula which is a function of the gravitational constant, the mass of the planet, and the radius of the orbit.