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?
Plot for shooting at 45 deg (as the problem specifies) starting with v=0.8146 Vesc and hitting the N. Pole of planet #2 is
here.
Plot for (accidentally) shooting straight up, at v=0.98 Vesc and hitting is
here. Is the best 0.98 or 1.00? Perhaps I have an accuracy problem in my simulations? I was loose with the constants.... Programs and data tables are linked in previous posts.
If you worry that the planets don't touch in these figures, note
that the two axes are not scaled the same. The planets do indeed osculate!
Q2: I have been using Excel to plot, and it is miserable. Please - can someone suggest a plotting package that interfaces with coding well?
I imagine using Python is the solution. I am on an Apple WorkBook Pro using - aak - Fortran, but g77+excel is not a good environment. (IDL, my old go to, is too expensive.)
Many thanks!
Steve Lord
lord_91106@yahoo.com
Edited on August 3, 2020, 6:49 pm
two plots and two questions....
