Orbital Eccentricity

[Vorg]

Have a mission to have a craft in orbit with certain science parts with an orbital inclination of 16 and a orbital eccentricity of .22. When I first got it up, it was at around 75k/84k and the box for eccentricity was checked, but the mission also required science at both low and high orbits. But now that it's at 350k/399k, I can't find an orbit that meets the .22. I dropped the pe to around 75k and it was still only .05. What ap/pe do I need to get it out to .22?

[Weywot8]

Easy in game method of finding out - just boost your Ap while at Pe until you fulfill the eccentricity requirements 

TL;DR answer: ~460km

Educational calculation: 

Semi-Major Axis, SMA = (Pe + Ap)/2, Pe, Ap measured from center of Kerbin instead of surface

Pe = SMA*(1-eccentricity), therefore, SMA = Pe/(1-eccentricity) = (75km +600km)/(1-0.22) = 675/0.78 = 865.4km

Ap  = 2SMA - Pe = 2(865.4)-675 = 1055.8km

Adjust for  Kerbin radius = 455.8km

 

[Snark]

17 hours ago, Vorg said:

Have a mission to have a craft in orbit with certain science parts with an orbital inclination of 16 and a orbital eccentricity of .22. When I first got it up, it was at around 75k/84k and the box for eccentricity was checked, but the mission also required science at both low and high orbits. But now that it's at 350k/399k, I can't find an orbit that meets the .22. I dropped the pe to around 75k and it was still only .05. What ap/pe do I need to get it out to .22?

Pe / Ap = (1 - e) / (1 + e).  So if your eccentricity e = 0.22, that means your ratio of Pe to Ap needs to be (1 - 0.22) / (1 + 0.22), or 0.6393.

So, you need to pick a value such that your Pe is 63.93% of your Ap.  Or, put another way, your Ap needs to equal your Pe times 1.5641.

[EDIT:  Note that the above advice refers to Pe and Ap in terms of radius, not altitude above planetary surface, as OhioBob points out below.  The "Pe" and "Ap" that the game reports are in altitude above surface.  Sorry, I should have been more clear.]

[Vorg]

Something isn't right. KER said eccentricity was at .027 (oh, and I was off by 100k, AP/PE was 250k/299k.) I dropped the PE to 190k and e only went up to .06495 according to KER. No were close to the .22 needed.

Just noticed that Precise Maneuver shows the ending e value. ended up with 75k/460k

Edited July 20, 2017 by Vorg

[Weywot8]

43 minutes ago, Vorg said:

I dropped the PE to 190k and e only went up to .06495 according to KER

KER is correct: your SMA is 600 + (190+299)/2 = 844.5, therefore eccentricity = 1 - [(600+300)/844.5]= 0.0645, close enough given rounding errors in input

Snark is also correct: Pe = 675, AP = 675*1.5641= 1055.76, adjusted to account for Kerbin radius, AP = 455.6 =~460km

Try again - you'll have to adjust both Pe and Ap of your current orbit to the TLDR answer: Pe/AP 75km x 460km

Edited July 20, 2017 by Weywot8

[OhioBob]

13 hours ago, Vorg said:

Something isn't right. KER said eccentricity was at .027 (oh, and I was off by 100k, AP/PE was 250k/299k.) I dropped the PE to 190k and e only went up to .06495 according to KER. No were close to the .22 needed.

Just noticed that Precise Maneuver shows the ending e value. ended up with 75k/460k

The problem is that you are using altitudes, not radii.  The Pe and Ap that you read in the game are altitudes, measured from the surface of the planet (sea level, or datum, to be exact).  The formula that @Snark gave you requires that you use radii, measured from the center of the planet.  You therefore must add the radius of the planet (600 km for Kerbin) to the altitudes that you read in the game.  So if you're reading Pe/Ap of 75/460 km in game, that's means your radii are 675/1060 km.  So you have 675/1060 = 0.637, which matches Snark's number (with some rounding error).
 

Edited July 20, 2017 by OhioBob
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