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I work on small application to apply impulsive maneuver on an orbit. I want to align two orbits in the same plane.

After the execution of the function, original orbit has the same inclination and longitude of ascending node of the target orbit but eccentricity, argument of perigee and perigee altitude have changed and I can't explain it...

Maybe it's normal but I find it hard to explain it.

Maneuver is executed where original plane crosses target plane.

If the longitude of asending node of both orbits are the same, the result is perfect.

I tried vector and analytics approach but in both cases other orbital parameters change anyway.

This is my example :

original orbit :

  • Perigee radius = 6700 km
  • Eccentricity = 0.3
  • Inclination = 40°
  • Longitude of Ascending Node = 20°
  • Argument of perigee = 10°

target orbit :

  • Perigee radius = 6700 km
  • Eccentricity = 0.3
  • Inclination = 45°
  • Longitude of Ascending Node = 35°
  • Argument of perigee = 10°

After alignment maneuver original orbit becomes :

  • Perigee radius = 5027 km
  • Eccentricity = 0.47
  • Inclination = 45°
  • Longitude of Ascending Node = 35°
  • Argument of perigee = 4.27°
  • Delta V : 1585.35 m/s

Thank you for your help :)

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    $\begingroup$ Could you explain how you're designing this maneuver? Are you doing a Lambert transfer? The original orbit should not change, and the target orbit should be reached. Instead, it seems like you're in a totally different orbit. $\endgroup$
    – ChrisR
    Commented Nov 8, 2021 at 17:03
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    $\begingroup$ Hello @ChrisR Is not a Lambert transfert. This plane alignement is the first step to be in proximity of target spacecraft. Next steps will be apsidal alignment and phasing. The example i've given is only for unit tests in application. $\endgroup$
    – sl20
    Commented Nov 8, 2021 at 17:08
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    $\begingroup$ if your ascending node match up as in your case, you are doing the impulse at the correct time. That's a good start. Your impulse vector normal to the plane of the intended orbit is correct too, because the inclination matches after the maneuver. But your impulse in the plane of the intended orbit is whacked. look there for your error. Bear in mind that you can almost never match plane, and ascending node, and perigee in one maneuver, the orbits would only cross planes, not meet in the same 3-d location where you do your burn. need 2 burns, usually. $\endgroup$
    – CuteKItty_pleaseStopBArking
    Commented Nov 8, 2021 at 18:06
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    $\begingroup$ Thank you @CuteKItty_pleaseStopBArking yes I understand we can't change orbital plane and perigee at same time (except in combined maneuver). But I don't understand why other parameters change only when longitude of ascending node are different between my two orbits. I had hope that there is a rule that says "if a maneuver changes longitude of ascending node, it will change orbit shape" ^^ $\endgroup$
    – sl20
    Commented Nov 8, 2021 at 19:08

2 Answers 2

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As CuteKitty_pleaseStopBArking mentioned, in this situation your original orbit and your target orbit do not share any points in common.

GeoGebra Graph: Comparing the two orbits
Geogebra graph of the two orbits
Original orbit is in red, target orbit in green. Reference direction is the positive x-axis, in red.

This will generally be the case of any pair of orbits around the same body whose Keplerian parameters differ only by Longitude of the Ascending Node unless at least one of the following is true:

  • The orbits are circular.
  • The inclination of the orbits are 0° or 180° (By convention, though, equatorial orbits typically are given the same longitude of the ascending node)

Since none of the above are the case using the parameters you provided, in this situation any single burn possible on the original orbit that puts the spacecraft in the plane of your target orbit (defined by the orbital inclination and and the longitude of the ascending node) will result in an orbit that has different other orbital parameters than your target orbit.

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  • $\begingroup$ Thank you very much, your explanation is very clear. Your tool for 3D graph is really useful. $\endgroup$
    – sl20
    Commented Nov 9, 2021 at 15:16
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If the only thing you check for is that the Longitude of the Ascending Node is correct, then it guarantees only that your new orbit lies in the correct plane and passes through the point where you do the maneuver. But there are infinitely many orbits in that plane which pass through that point, and you can end up in any of them.

If you want the maneuver to preserve the shape of the orbit (i.e., perigee radius and eccentricity), then you need additional constraints: that both the radial component of the velocity and the magnitude of the transverse component do not change. Note that even then, the argument of the perigee will change, unless the point you do the maneuver lies in the equatorial plane: the angle between the maneuver point and the perigee will stay the same, but because of the change of inclination, the angle between the maneuver point and the ascending node will change.

If you do the cheapest (in terms of $\Delta v$) impulse maneuver which puts you in the right orbital plane, then, from geometrical considerations, it preserves the radial component of the velocity, but decreases the transverse component, so it changes the shape of the orbit.

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  • $\begingroup$ Thank you, your answer perfectly complements the previous answer! $\endgroup$
    – sl20
    Commented Nov 9, 2021 at 15:18

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