A satellite of mass m is in Keplerian orbit around a parent body of mass M m. The satellite has total energy E and angular momentum l, where angular momentum is measured about the parent body and the zero of potential energy is at infinity. Detnermine the semimajor axis a and the eccentricity e of the orbit, in therms of the above quantities and Newton'ss constant G (use the symbol, not the numerical value). HINT: Find the relation amonb the energy, angular momentum and orbit raduis at the apside of the orbit. Solve this relation for the apsidal radii r*, and use thed fact that the apsidal radii are r*= a(1+-e)

Question

A satellite of mass m is in Keplerian orbit around a parent body of mass M >>m. The satellite has total energy E and angular momentum l, where angular momentum is measured about the parent body and the zero of potential energy is at infinity. Detnermine the semimajor axis a and the eccentricity e of the orbit, in therms of the above quantities and Newton'ss constant G (use the symbol, not the numerical value). HINT: Find the relation amonb the energy, angular momentum and orbit raduis at the apside of the orbit. Solve this relation for the apsidal radii r*, and use thed fact that the apsidal radii are r*= a(1+-e)