An object's orbit results from a balance of its forward motion with the downwards force of gravity (there is no sideways 'flinging out' force involved).

So, we'll get the most fuel-efficient control just by changing our mote's forward speed along an orbit (rather than simply firing towards or away from the attractior).

'Pro-burn' means to add forward thrust along an orbital path
'Retro-burn' means add reverse thrust along an orbital path

This novice pilot tries to reach a higher orbit just by blasting directly away from the planet.

Undesirable Results:

• Most of the thrust energy gets used up just shifting the centre of orbit
  
• Altitude gain is small, and at right-angles to intended travel
  
• Risk of crashing at the perigee (lowest point of orbit)

(Note: While it is possible to get about this way, it's very expensive in fuel).

It's better to do forward pro-burn burn at the 'perigee' (orbital low point)

Key Results:

• A larger elliptical obit extends out from the burn point
  
• The craft will always return exactly to the burn point - so no loss of altitude.
  
• The craft slows down the further it is from the attractor (an important point later)

-------------------------------------------------------------------------------------------------------


A longer 'pro-burn' is made at an elliptical orbit's 'apogee' (highest point)

Key Results:

• Rounds out the ellipse into a large circular obit
  
• Again the craft returns to the exact point of the burn
  
• Craft's speed becomes constant again

'Hohmann Transfers' link together the two manoeuvres just covered

• Two pro-burns are used to lift a craft into a high circular orbit.
  
• Note these burns are made on opposite sides of the attractor.
  
• Cheapest in fuel to achieve high orbit

The same processes with reversed burn direction to descend

• Two retro-burns are used to drop a craft down into a low circular orbit.
  
• Again, these burns are made on opposite sides of the attractor.
  
• Most economical and safest way to achieve low orbit.

Orbital rendezvous is always tricky and counter-intuitive.

If you're in orbit behind a blob, it seems sensible to power forward to catch it up. But this will actually send you away from it, As seen earlier, a simple pro-burn sends you immediately higher and slower - only distancing your from your target. Gravity is ironic.

One solution is to start with a short retro-burn to reduce your obit - moving you below but closer to your target and moving faster. Then, with good timing, do a longer pro-burn to round out your orbit again to your previous altitude - but now with some increased speed needed to chase down your prey.

Sorry no gif for this.

(work in progress - I'll add some screenshots if there's any real interest)

'Orbital insertion' means leaving orbit around one attractor, to take up orbit around another. Just like the Apollo Program used to do during their moon shots.


During the challenging "Epicycles" levels you have several 'moons' to visit. So you'll want to master Orbital Insertion.


General principles:

• Move indirectly between the smaller orbiting attractors, by way of making elliptical transfer orbits around the huge central attractor.
  
• Make these transfer orbits in reversed direction to the outer orbits
  
• Consequently the linked orbits form figure-of-eight patterns. These are cheap on fuel, while avoiding certain insertion approaches that can produce unwanted 'gravitational slingshots'

Walk-through:

1. Starting out in an anti=clockwise orbit around one of the moon attractors, be sure to gobble up everything circling its gravity well.
   
2. Then make a pro-burn when you're at the point in your orbit closest to the central attractor
   
3. With luck that will put you in an clockwise elliptical transfer orbit around the huge central attractor.
   
4. Relax and complete the low perigee turn through the middle of the map
   
5. Then, when you're back out this obit's apogee, there may or may not be another 'moon' to insert yourself in orbit around.
   
6. If there is one, make a retro-burn to slow yourself down enough to be captured by that moon's gravity. Your new orbit should be back in the original direction, going with the flow of the moon's cirling motes.
   
7. Rinse and repeat

University of Sydney
http://www.physics.usyd.edu.au/~helenj/Planets/orbits.html

NASA
https://science.nasa.gov/learn/basics-of-space-flight/chapter3-4/

Wikipedia
https://en.wikipedia.org/wiki/Orbital_mechanics#Practical_techniques
https://en.wikipedia.org/wiki/Space_rendezvous

https://youtu.be/T0qagA4_eVQ