Elliptical focal point

[AuddieD2015]

Maybe it has been asked and answered and I just don't know how to search for it. I know there is an answer but it's the question that I think is off. So...

I suck at math. I can do a little basic algebra. That is why I am playing a game that is all about engineering and math! I have been going through sites reading about orbits and have found this. e=c/a where e is the eccentricity, c is the focal distance, and a is the semi-major axis. I know e and I know a. So c=a*e? Can I determine a periapsis and apoapsis from this and establish an orbit with the desired eccentricity and axis?

[Streetwind]

34 minutes ago, AuddieD2015 said:

Can I determine a periapsis and apoapsis from this...

Yes. a - c is the periapsis altitude, and 2a - (a - c) is the apoapsis altitude.

34 minutes ago, AuddieD2015 said:

...and establish an orbit with the desired eccentricity and axis?

No, because an orbit needs additional parameters. For a given AP/PE pair, there is an infinite number of possible orbits. You need to narrow it down further by supplying an inclination, and a longitude of the ascending node. That still leaves you with a technically infinite number of solutions, albeit in a narrow band. Specifiying the argument of periapsis finally results in a single, precisely defined orbit.

https://en.wikipedia.org/wiki/Orbital_elements

 

Edited January 31, 2023 by Streetwind

[Kerbart]

10 minutes ago, Streetwind said:

...and establish an orbit with the desired eccentricity and axis?

No, because an orbit needs additional parameters. For a given AP/PE pair, there is an infinite number of possible orbits. You need to narrow it down further by supplying an inclination, and a longitude of the ascending node. That still leaves you with a technically infinite number of solutions, albeit in a narrow band. Specifiying the argument of periapsis finally results in a single, precisely defined orbit.

https://en.wikipedia.org/wiki/Orbital_elements

OP asked for an orbit, not "the" orbit. Given a semi major axis and eccentricity, it should be easy to determine  AP and PE, given that the orbital body is going to be in one of the focal points of the ellipsis. Yes, there's an infinite number of options there, but you will know what the apoapsis and periapsis of any of those orbits will be.

[AuddieD2015]

This gets me a whole lot closer to where I am trying to get. The inclination is 90 since I am after a polar orbit. There's no rendezvous so the AN might not be needed. Thanks for the answer and additional (easy) maths!

[Kerbart]

Sketching helps, "+" indicates the focal points:

<-- x -->+<----- C ---->+<-- y -->

the full axis is x + C +y, and that's 2× the SMA

your periapsis is x or y, being SMA - ½C (and then subtract the radius of the planet)

your apoapsis is the periapsis + C, or the SMA + ½C (and again subtract the radius)

 

Good luck!

[AuddieD2015]

6 hours ago, Kerbart said:

Sketching helps, "+" indicates the focal points:

<-- x -->+<----- C ---->+<-- y -->

the full axis is x + C +y, and that's 2× the SMA

your periapsis is x or y, being SMA - ½C (and then subtract the radius of the planet)

your apoapsis is the periapsis + C, or the SMA + ½C (and again subtract the radius)

 

Good luck!

I immediately scribbled down the equations people supplied here and made it into the orbit I wanted as closely as my burn reaction time permitted.  It's my take on LandSat scaled down to Kerbin.