Orbital Mechanics

[Spyritdragon]

Sorry, im a little big confused with Orbital Mechanics.

Im in an orbit, my ship is the little blue dot at the bottom, orbiting counterclockwise.

Why, if i burn prograde, does the other side of my orbit, the green arrow get larger, i.e. further away? I'd think that by adding extra speed facing to the right of my screen at the moment, it'd take longer for the planetary body to reverse that velocity, hence the part of my orbit to the right, by the red arrow, would grow. Why does the green arrow part grow instead?

[tntristan12]

The answer is probably more mathematical than necessary so I'll try to provide a qualitative explanation.

The planet's gravity is pulling you forever toward it, but when you increase your speed you do indeed travel farther. However, since the planet is pulling you around it it just so happens that you go farther around the other side of the planet.

If, however, you are not at periaps, and your orbit is not circular, burning prograde raised both ends of the orbit.

I've written a mathematical derivation of the equation that tells you what shape an orbit will take when given an initial set of parameters. PM me if you're interested!

[Kialar]

I'll try it in other words.

If your vessel is in an orbit around a planetary body, it it accelerated towards the gravity center.

If your kinetic energy (means your velocity) and the acceleration towards the gravity center are in balance, the orbit doesn't change.

When applying acceleration prograde (means doing a burn) the directions of burn (vessel acceleration), direction of gravity and actual energy of your vessel (velocity) add up to a new equilibrium of velocity and gravitational acceleration.

In your picture this new vector results in a change of the axis (the eccentricity) on the other side of the orbit.

Maybe this makes it more plausibel:

[Syhrus]

I like to think of orbiting as similar to throwing a ball up into the air. It will go up for a while, until its speed is overcome by gravity's acceleration and it falls back to earth. In orbit, you are doing the same thing, except that you are moving so quickly over the surface of the earth, that the ground is falling away from you faster than you can reach it ("aiming for the ground and missing") Michael from Vsauce does a better explanation here of what orbiting actually is.

The reason you speeding up one side of your orbit raises the other is also due to the fact that you are constantly falling. If you speed at the lowest point of your orbit, you essentially add more speed to your 'fall' around the planetary body. Halfway between the lowest point (where you sped up) and the highest point (180° out of phase from the lowest point), your 'fall' becomes more like a 'throw' out to the other side of your orbit. At this point, your ship flies higher until gravity stops its vertical speed and begins bringing it back down to earth (incidentally speeding it up again too, so your speed is the same when you reach your lowest point again).

Hope that helped!