Hohmann Elliptic Transfer Orbit with Animation

Abstract

The main purpose of this article is to show how to use Hohmann elliptic transfer in two situations:
a- When one manned spaceship is trying to catch up with an other one
on the same circular orbit around Earth.
b- When delivering a payload from Earth to a space station on a circular
orbit  around Earth using 2-stage rocket .

The way we set up the problem is as follows:
Consider two manned spaceships with astronauts Sally & Igor , the latter
lagging behind Sally by a given angle = 4.5 degrees while both are on the same
circular orbit C2 about Earth. A  2d lower circular orbit  C1 is given.
Find the Hohmann elliptic orbit that is tangent to both orbits which allows
Sally to maneuver on C1 then to get back to the circular orbit C2 alongside Igor.

Though the math was correct , however the final result we found was not !!
It was somehow tricky to find the culprit!
We have to restate the problem to get the correct answer.
The animation was then set up using the correct data.
The animation is a good teaching help for two reasons:
1- it gives a 'hand on' experience for anyone who wants to fully understand it,
2- it is a good lesson in Maple programming with many loops of the type 'if..then'.

Warning

This particular animation is a hog for the CPU memory since data accumulated
for plotting reached 20 MB! This is the size of this article when animation is  
executed. For this reason and to be able to upload it I left the animation  
procedure non executed which drops the size of the article to 300KB.

Conclusion

If  I can get someone interested in the subject of this article in such away that he or
she  would seek further information for learning from other sources,  my efforts
would be well rewarded.