I know the formulas for perihelion and aphelion distances in an orbit with SMA a and eccentricity e are a(1-e) and a(1+e), respectively. However, why is this? I can't seem to find any derivations for this anywhere and also cannot figure this out myself.
There's a classic physics problem that is:
If Earth is orbiting the Sun at 1 au from and is suddenly stopped. How long does it take to fall into the Sun (neglecting the size of the Sun/Earth)?
I know that a clever way to solve this problem is by using degenerate ellipses and an object...