Relation between Semi-major Axis and Orbital Period

[Sarxis]

Kind of a general orbital mechanics/math/geometry question, but I'm wondering how the Semi-major axis relates to orbit time and if changing the apoapsis/periapsis while keeping the SMA the same changes the orbit. 

 

Just curious.

[Reusables]

Simple: https://en.m.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Third_law

Rather tham fiddling with the constants, comparing with the planets/moons works better.

(E.g. for Kerbin orbiter, compare with Mun)

Edited March 23, 2017 by Reusables

[Sarxis]

13 minutes ago, Abastro said:

Simple: https://en.m.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Third_law

Rather tham fiddling with the constants, comparing with the planets/moons works better.

(E.g. for Kerbin orbiter, compare with Mun)

" The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."  ~from the link.  

 

Ok!  So the SMA can be used to set up, say, a comms network by making sure that all satellites in their respective orbits keep overall equidistance from one another throughout their orbits (well, as long as the respective orbits aren't too eccentric that is).  Got it!

Edited March 23, 2017 by Sarxis

[Aegolius13]

If you're a KER user,  you can also add Orbital Period to the list of shown data.  I find that's the easiest way to synchronize my commsats.

[Sarxis]

1 hour ago, Aegolius13 said:

If you're a KER user,  you can also add Orbital Period to the list of shown data.  I find that's the easiest way to synchronize my commsats.

MechJeb myself.  Yeah, I could do that.  I guess having both the SMA and Orbital Period is probably moot.

[FancyMouse]

9 hours ago, Sarxis said:

MechJeb myself.  Yeah, I could do that.  I guess having both the SMA and Orbital Period is probably moot.

Not necessarily. I have both on my KER, and I do use both. SMA is for matching comm satellites (it's more precise there - for example my Mun network is at SMA 999999.999+-0.0005m). Orbital period for comparing with a target ship - a ratio of two periods can give me an idea of where the target ship is when the current ship orbits for 1 period. They just serve different purposes.

[Nicias]

I don't know if KER has it, but MechJeb has synodic period with target. That will tell you how long until the active object and the target are in the same relative positions in their orbits again. So if it is 10000 years, then one object will lap the other every 10000 years. I use that to sync up my relays. For solar relays using a thrust limited ion drive, I can get that number up in the trillions of years. That means that they will be off by less than a degree ever billion years, which seems sufficient.

[Spricigo]

4 hours ago, Nicias said:

I don't know if KER has it, but MechJeb has synodic period with target. That will tell you how long until the active object and the target are in the same relative positions in their orbits again. So if it is 10000 years, then one object will lap the other every 10000 years. I use that to sync up my relays. For solar relays using a thrust limited ion drive, I can get that number up in the trillions of years. That means that they will be off by less than a degree ever billion years, which seems sufficient.

More than sufficient. Actually some problems with rounding numbers may produce a noticeable disturbance on the orbit much sooner.