As a prelude to our more general study of orbital motion, lets have a look at the lagrangian for an object in a gravitational field. a satellite of mass m is in the vicinity of a planet of mass m. well study the motion in the plane containing the planet and the path of the satellite, so we can treat the problem as two-dimensional. part a using polar coordinates (r, ), write the lagrangian for the motion of the satellite under the in fluence of the planet's gravity. make sure you use the more general 1/r form of the gravitational potential, don't assume it's constant! ) part b write the euler-lagrange equations for fan your lagrangian from part . a should satisfy ol/= 0; identify the corresponding conserved quantity, and use the fact that this quantity is a constant of the motion to eliminate b and obtain a single equation of motion for h. show that there is one equilibrium value of r corresponding to a circular orbit.