Describe the motions of a system consisting of two objects or systems interacting only via gravitational forces.

In a system consisting only of a massive central object and an orbiting satellite with mass that is negligible in comparison to the central object’s mass, the motion of the central object itself is negligible.

The motion of satellites in orbits is constrained by conservation laws.

In circular orbits, the system’s total mechanical energy, the system’s gravitational potential energy, and the satellite’s angular momentum and kinetic energy are constant.

In elliptical orbits, the system’s total mechanical energy and the satellite’s angular momentum are constant, but the system’s gravitational potential energy and the satellite’s kinetic energy can each change.

The gravitational potential energy of a system consisting of a satellite and a massive central object is defined to be zero when the satellite is an infinite distance from the central object \[U_g = -G \dfrac{m_1 m_2}{r}\]

The total energy of a system consisting of a satellite orbiting a central object in a circular path can be written in terms of the gravitational potential energy of that system or the kinetic energy of the satellite \[K = - \dfrac{1}{2} U\] \[E_{total} = \dfrac{1}{2} U = - \dfrac{GMm}{2r}\]

The escape velocity of a satellite is the satellite’s velocity such that the mechanical energy of the satellite-central-object system is equal to zero.

When the only force exerted on a satellite is gravity from a central object, a satellite that reaches escape velocity will move away from the central body until its speed reaches zero at an infinite distance from the central body

The escape velocity of a satellite from a central body of mass M can be derived using conservation of energy laws. \[v_{esc} = \sqrt{\dfrac{2GM}{r}}\]