digitCruncher

@DarkSlimus : You earn 1.7361e-5 SP for each BP . That is to say, you can earn less than one SP per ship.

@Parallax: ... That is so cool. I have been playing a Hard campaign with three mods: Kerbal Construction Time, Remote Tech, and TAC Life Support. As a result, my space program is 81 days old ... and I have made Kerbals go into orbit of Kerban once, and only launched one unmanned rocket. So after scrounging enough funds and science to unlock satellites, I built my first satellite in this campaign: the Sattle I-a. (I also built part of an identical second satellite: the imaginatively named Sattle I-. I had been hurting for funds, so I was totally stoked when I got two equatorial satellite missions at the same time, which have been historically super easy for me. And because they were so far out (both have periapsis above 10 Mm, beyond the Mün), they paid pretty well too. Unfortunately, my simulations didn't detect one problem: The Sattle I was equipped with the Communotron 16, which has a range of 2.5 Mm. Remote Tech meant I was unable to control the apoapsis burn, so I was unable to complete the mission. I didn't want to cancel those missions and go back to 'Explore Kerbin' missions (which I *hate*), so I thought long and hard on a better solution. After looking hard at the numbers, I decided to redesign the Sattle I to build a massive 'space ladder' of communotrons. 5 modified Sattle I's with two communotrons would orbit Kerbal at 2.5, 3.97, 6.30, 8.25, and 10 Mm circular orbits. This means that they would have 1:2:4:6:8 orbital period ratios, but all be within 2.5 Mm of each other at their closest approach. Unfortunately, they would only align once every 3 Kerbal months, and the space ladder would only work when it was aligned. Realizing this was a daunting task, I knuckled down on the redesign ... and discovered that I had recently unlocked the Comms DTS-M1: A directional antenna with a range of 50 Mm (just past Minmus). So now all the Sattle II-a needed was two of these (I put three on just to be sure), and then it could act as both a relay for Sattle I-a, and a valid satellite target for the second equatorial satellite mission! Now I just need to wait for it to be built. Which will take 7 more days >.> . The Sattle I will still be used for close range satellites under 2.5 Mm, as Sattle I has so few parts that the boosters can be recovered, making the Sattle I about 25% cheaper than the Sattle II, but I think the Sattle II will be the workhorse satellite for Kerbin-based unmanned missions.

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.