How to show that the gravitational potential energy of a two particle system is -2 times the total kinetic energy, without using the virial theorem?
Consider a two-particle system with identical masses, orbiting in circles about their center of mass. I'm supposed to prove that: $$U_p = -2U_k$$ With $U_p$ potential energy of the system, and $U_k$ ...
tl;dr: Hohmann Transfer appears to be the optimal way to achieve a circular-to-circular orbit, but is it possible to lower the periapsis in order to achieve a more elliptical orbit with apoapsis at ...
The diagram in Why are L4 and L5 lagrangian points stable? shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly: If I ...