Calculating strange orbital periods

[James.Denholm]

Hey all,
I was just wondering, is there an equation out there that will (painlessly) give the orbital period of an orbit where the perihelion and aphelion are very, very different.

I ask only because I realise from working out the total orbital period, I can work out the time it takes to travel between the perihelion and the aphelion, hence work out how long an optimum hohman[sic?] transfer should be, hence work out what the relative positions of the two planets (ie, Jupiter should be x degrees "in fount" of Earth in it's orbit), hence be able to eye-ball possible launch dates in Celestia. I'd prefer to do it this way, rather than press buttons in TransX or IMFD because it keeps my brain more active, and makes me feel like I've accomplished something before I've taken off. :lol:

 

[agentgonzo]

http://en.wikipedia.org/wiki/Orbital_period#Two_bodies_orbiting_each_other

The semi-major axis can be calculated by the average of PeA and ApA.

 

[James.Denholm]

Heh, thanks agentgonzo. I probably should have thought of that first. :lol:

Although, surely "Small body orbiting a central body" would be more relevant than "Two bodies orbiting each other", eh?

 

[agentgonzo]

The equations work for any two body system, not just where one body is of negligible mass (note that it says that a is the sum of the simi-major axes). It will work fine for a small body orbiting a central body too though!

 

[James.Denholm]

Oh, right. Thanks again, agentgonzo!

 

[tblaxland]

If you scroll up that wikipedia page, you will find this which you should find a more accurate (at least for vessel masses up to about 4e21 kg in heliocentric orbits):

The reason is that u (mu) is known with better accuracy than G or M. See here for more info:
http://en.wikipedia.org/wiki/Standard_gravitational_parameter#Terminology_and_accuracy

EDIT: You may also be interested in this:
Ballistic Trajectory Planner: http://astrojava.com/btp/

About porkchop plots:
http://en.wikipedia.org/wiki/Porkchop_plot