Orbital Mechanic Formulae (Difficult)

[digitCruncher]

So I am planning on making an Elite-ish type game as I am too cheap to fork over 40 pounds for Elite:Dangerous, and I need to brush up on my C# skills, and I have a lot of spare time over the summer holidays.

Here is the problem: I am hoping that I can make a space game without any FTL travel, but to do that, I need formulae for simple orbital conics. I play lots of KSP, but don't actually know how the formulae work, and just fly by tweaking the directions of the burns.

In all of these problems, assume only the Sun has mass, and assume only 2 dimensions. You don't need to solve them, but pointing me in the direction of references and formulae that might help would be greatly appreciated. My maths and physics skills are really good, if a little rusty, but all I see are differential equations everywhere on Wikipedia, and integration tends not to give very nice answers...

Question 1: A spaceship is traveling on a velocity vector 'v', at a position 's' from the Sun. Define the conic that that spaceship uses.

Question 2: A spaceship is traveling from a massless planet in a circular orbit 'r1' meters from the sun, to another massless planet in a circular orbit 'r2' meters from the sun. The second planet is 'O' radians anticlockwise from the first planet. The spaceship wishes to travel at a speed of 'v'. If it is possible, what direction should the spaceship travel to travel to the second planet?

Question 3: A spaceship is travelling from a massless station in an elliptic orbit, to another massless station in an elliptic orbit. Define the stations positions with regards to time however is most appropriate for your answer. The spaceship wishes to travel at a speed of 'v'. If it is possible, what direction should the spaceship travel to travel to the second station?

I would really like to avoid trying to solve it without using iterative solutions, as I feel that that probably would be very inefficient. But if I have the answer to the first question, I could use the answer to the first question + iterative solutions, and see how long it takes for a computer to solve it.

[Bill Phil]

I think your problem is assuming constant velocities...

[UmbralRaptor]

The easiest way with question 1 would probably be to look for the craft's specific orbital energy (or perhaps more generally find its orbital elements).

Questions 2 and 3 are more vector than scalar, but look related to interplanetary intercepts. Also, what Bill Phil said.

[lincourtl]

Here is the problem: I am hoping that I can make a space game without any FTL travel, but to do that, I need formulae for simple orbital conics. I play lots of KSP, but don't actually know how the formulae work, and just fly by tweaking the directions of the burns. ... My maths and physics skills are really good, if a little rusty, but all I see are differential equations everywhere on Wikipedia, and integration tends not to give very nice answers...

You may find this approach useful.

http://www.braeunig.us/space/interpl.htm

[kujuman]

For 1, the term you want to search is orbital state vector. There may be more now, but as of about 2 years ago, the best post I found was in the orbiter forum, a response to a question posed by one HarvesteR...