I was pondering Mars missions and wondered about what kind of vehicle an astronaut on Mars would need in order to get home. My first thought was that mars gravity is .38 that of earth, so he would need a rocket about 38% as large to get off of mars as he needed to get off of earth, This of course neglects the fact that when he left earth he had to take his return vehicle with him, and also neglect the fact that the martian atmosphere is thinner, but at this point I'm not ready to think those factors yet. So, in order to understand the relationship between the gravity of the planet and what size rocket that planet would require in order to leave it, I decided to try understand 4 simpler scenarios... 1. Rocket leaves earth and enters earth orbit. 2. Rocket leaves mars and enters mars orbit 3. Rocket leaves earth, travels to mars on a 1 way trip. 4. Rocket leaves mars, travels to earth on a 1 way trip. If you neglect the atmosphere and only consider gravity, does #2 require a rocket 38% as large as #1, or are there compounding factors that make the relationship exponential or some other function of gravity? Is the difference between #3 and #4 basically just the difference between 1 and 2 plus the ability to change orbital energy with respect to the sun by the same amount? In other words, if identical craft were already in orbit around earth and mars, could each make the transfer into orbit around the other planet? Or are the requirements different one way vs. the other?