Undergrad Orbital maneuver by applying a thrust in the radial direction

[hutchphd]

If I were less lazy,

You wouldn't know a short fellow called Tom Sawyer would you ?...
Anyhow I took what @DrStupid did and made a little graph which I find useful. First I will choose some natural units $r_0,g_0, m=1$ to write the effective potential$$V_{eff}(r)=\frac 1 {2r^2}-\frac 1 r -a(r-1)$$ where I have changed the zero for the "added" radial potential . The graph and a "blown up" version near the minimum show the potential for various values of a. I think it comports with all the analyses.
I need pictures.

 

[jbriggs444]

You wouldn't know a short fellow called Tom Sawyer would you ?...

ROFL. Only a really smart person is good enough to do those boards.

 

[A.T.]

Anyhow I took what @DrStupid did and made a little graph which I find useful. First I will choose some natural units $r_0,g_0, m=1$ to write the effective potential$$V_{eff}(r)=\frac 1 {2r^2}-\frac 1 r -a(r-1)$$ where I have changed the zero for the "added" radial potential . The graph and a "blown up" version near the minimum show the potential for various values of a. I think it comports with all the analyses.
I need pictures.

Yes, thank you! This is what I envisioned in post #56. I added some additional marks to your plot. For thrust higher than 0.125 the right maximum of the potential will drop below the value of the circular orbit (dotted red line) and can be overcome to escape.