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My orbit is in the equatorial plane. When i apply thrust in the y or x axis, it rotates around the focus or planet - see red and blue orbit in the image below. I know the the semi-major-axis and eccentricity of the ellipse before and after the thrust.

see red and blue orbit

Please help me to find the angle around the focus.

Note :- Argument of periapsis and ascending node are undefined because the inclination is zero.

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The argument of periapsis is the in-plane angle between an orbit's periapsis and its ascending node.

It is correct that for an equatorial orbit with an inclination of exactly 0° (or 180°), the argument of periapsis is strictly undefined, as is the longitude of the ascending node. In these cases, however, it is convention to set the longitude of the ascending node to 0° from some reference direction (typically the vernal equinox for geocentric orbits), meaning we measure the argument of periapsis directly from the reference direction. This is called the longitude of periapsis and is used instead of the argument of periapsis.

Therefore in the given diagram, both orbits would conventionally have their respective longitude of periapsis measured from the same reference direction, allowing us to differentiate them.

This document has some great detail on understanding this, page 13 in particular.

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  • $\begingroup$ If i set ascending not zero and calculate the argument of apsois , it then just angle theata or angle between the satellite and foci . $\endgroup$ – Yan Godara Jun 10 '18 at 10:14
  • $\begingroup$ Can you give me an example of calculation.because right ascension also like theata as mentione in above comment. $\endgroup$ – Yan Godara Jun 10 '18 at 10:17
  • $\begingroup$ Also by Wikipedia , argument of periapsis is zero for such orbits. $\endgroup$ – Yan Godara Jun 10 '18 at 10:25
  • $\begingroup$ The document I've linked explains this really well. Essentially, because the longitude of ascending node is undefined, we can just pick an arbitrary one and use it, as long as we're consistent between orbits. By convention, we use the longitude which is measured from the vernal equinox. $\endgroup$ – Jack Jun 10 '18 at 10:26

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