There are two identical uniform spherical planets of radius R. The first has its center at the origin of the xyz coordinate system. The second has its center at (2R, 0, 0). The planets are touching.
A projectile is launched from the "North Pole" of the first planet at (0, 0, R) with its initial velocity pointed in the direction of the vector (1, 0, 1).
Let the escape speed relative to the planet's surface be ve. Note that here, the escape escape is for a single planet in isolation (following the typical convention).
With the given launch vector, let v0 be the minimum launch speed for the projectile to reach the "North Pole" of the second planet at (2R, 0, R).
How are the two speeds ve and v0 related?
(In reply to
Some thoughts and a maximum by broll)
I confess I do not follow the logic here - part of the problem is
my trying to visualize the larger sphere (made from two point masses, no?) And the projectile already in orbit in this system...
So I am unable to understand which V(e) your v(o) is in terms of.
But if there is a v(o) (written as a factor times the original v(e) of
one sphere which you might suggest, I will put it in the simulator and
see what happens....
re: Some thoughts and a maximum
