# Travel to another moon/planet/gravitational body

1. Mar 1, 2013

### season89

After looking at where the isogravitational point between the earth and the moon was, I thought about practically what sort of speed you would want to cross it at.

Of course, if time is not a factor, I imagine you would ideally want to expend as little fuel possible in getting from planet to planet (or planet to moon etc. etc.). Therefore you would want to cross this point at which the gravitational pull from both bodies cancel each other out at the slowest possible rate. I guess this would theoretically mean that you would spend eternity at the point.

In a practical sense though time is a factor, and more importantly if you have manned mission then there would be a trade off between the amount of fuel spent on getting to (and past) this point and completing the journey in a timely manner so that your crew don't starve. This brings up the other problem of time spent in space proportional to the amount of food (payload) needed in the shuttle, thereby requiring more fuel achieve escape velocity from the Earth.

Question:
I was wondering if anyone knew (for example on journeys to the moon) what speed at which this iso-gravitational point would be passed so as to minimise both fuel use and time spent on the journey. And if so, would there be a formula based on the distance between, and sizes of, both bodies. Finally I would love to find out whether there is a proposed limit to how far manned journeys could be (and the crew still be alive at the end of the journey).

Thanks,
Warwick

2. Mar 2, 2013

### Simon Bridge

Seeing as how journeys to the Moon have been done - why not just look up the Apollo flight data?

You'll find that there are many more variables than you are considering.
Usually the problem is done in terms of Hohmann transfer orbits... which will be what you want to look up as your next step.

3. Mar 2, 2013

4. Mar 2, 2013

### Simon Bridge

ITN exploits Lagrange points rather than the isogravitational points to minimize the energy to change trajectories. It's a valid observation though. What you are actually doing is balancing the dynamic play of forces (as momenta and potentials). The restraining factor - as OP says - becomes time rather than energy.

5. Mar 3, 2013

### Filip Larsen

I used the term iso-potential to give the OP a familiar concept to recognize. A more accurate description could be "travelling along tubular shaped stable and unstable manifolds that are linking together different Lagrange points in a multi-body system".

Section 2.1 of [1] gives an explanation of how these surfaces come about, but it is probably difficult to understand the nature of this without knowledge of dynamic system analysis (e.g. the concept and theory of stable and unstable manifolds). If the OP where to think of this as similar to travelling along iso-potential surfaces, he would not be too far of the mark. If he were to include rotation in the potential he would be conceptually quite close (compare with the plot of "effective potential" on [2]).

[1] http://www.gg.caltech.edu/~mwl/publications/papers/lunarGateway.pdf
[2] http://en.wikipedia.org/wiki/Lagrangian_point