Whyx

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1. Elliptical Orbital Mechanics

Okay, I wanted to try and find a way to apply circular motion and gravitational field calculations to elliptical orbits to prove why all orbits must have opposite periapsis and aopsis and only one of each (as oppose to for example two opposite aopsis and two opposite periapsis) but I couldn't do it. Anyone with more experience give me a hand, it would be handy if the derivation tried to use relatively simple mechanics because I'm second year A level in the UK. Cheers
2. Large MkII SSTO Flight Path

Okay folks, ive built a ship based off of Matt Lowne’s Duna SSTO design and all I’ve done is replace the extra passenger space with science equipment in a cargo bay and a MKII docking port, which in total weighs less than the MkII passenger pay used by Matt. i can’t get the blasted thing into orbit. My current flight path is: fly 10 degrees on takeoff till I get to 300 ms^1. pitch up gradually to about 35 degrees (I start to lose speed very quickly if I pitch up any more as my thrust isn’t very large) once I get above 10000m I flatten out my trajectory. this is where my problems start, even in a power dive I cannot accelerate beyond 350ms^-1 with 4 RAPIERS I have to activate my 2 NERV engines to get myself past 400. once past 400 I have no problem getting up to 1200ms^-1 but my engines soon overheat so I have to switch to closed cycle. My closed cycle uses all my oxidiser so fast I can’t get my aopsis past 35000m and then I’m left with just NERV which can’t accelerate fast enough to get my aopsis high enough. i really don’t know what I’m doing wrong
3. Optimal Refuelling Tactic

Thanks for all the fantastic replies guys, I’ve built my surface station as an exercise in surface building because it’s something I’ve not done before. I’ve found it challenging to say the least. Based on the advice given I’m going to try and set up a network of refuelling around eve and Duna and eventually make a base on one - probably duna because that seems like a lot of fun
4. Optimal Refuelling Tactic

Okie dokie, I have a main equatorial Space Station at 100km above Kerbin and a refuelling station 50km above Minmus. I have a number of large orange fuel containers on my Kerbin SS that I wish to fill up. Is it more viable to place a mining vessel on Minmus and travel from Minmus to Kerbin orbit to refuel the Kerbin SS or do lots of little SSTO trips, the problem with SSTO is that I can't figure out how to get enough lifting power to bring a decent amount of fuel to orbit from Kerbin's surface. Any extra tips on refuelling would be greatly appreciated.