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I was working on desmos drawing transfer trajectories between the earth and moon. I managed to draw both the trajectories but i noticed something rather odd. The transfer orbits were different ellipses with the same apogee and perigee.enter image description here

My question is why and how are the orbits different even though the final destinations are same. My guess is that it might be due to the dependance of the orbit's equation on physical factors like mass of the planet,height,radius,etc{Note that these orbits aren't arbitrary ellipses but are the actual ellipses at height 0 derived using orbital mechanics}.

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  • $\begingroup$ How do numerical parameters differ in the two calculations? And what reference frame has been used? $\endgroup$
    – GiorgioP-DoomsdayClockIsAt-90
    Commented Feb 14 at 7:11
  • $\begingroup$ The numerical parameters differ in mass and radius, thats all. The reference frame is simply an outside observer in space $\endgroup$
    – Star Gazer
    Commented Feb 14 at 7:33
  • $\begingroup$ Then, the starting point, and consequently the trajectory changes as the radius changes. The outside observer in the space is not enough to clarify the reference frame. If you mean that it is an inertial frame, the picture is not clear. Even if the planet where the trajectory starts has a huge mass, the other planet should move. I have a hard time to understand why you get apparently perfect ellipses. $\endgroup$
    – GiorgioP-DoomsdayClockIsAt-90
    Commented Feb 14 at 10:39
  • $\begingroup$ Well this is an assumption where the planets stay stationary and all that happens is the creation of a transfer trajectory between the earth and the moon(both stationary). Now the problem arises when, first case, the satellite is at earth making a transfer trajectory to moon and the second case being, the satellite is at the moon making a trajectory to the earth. The ellipses formed are different. So to answer your question i havent taken the rotational factor here $\endgroup$
    – Star Gazer
    Commented Feb 14 at 12:36
  • $\begingroup$ If the spacecraft moves in the field of two planets, there is no reason the orbits should be elliptic. Even after reading the information in these comments, I still do not understand what you did in your simulation. I think some more detailed descriptions of the assumptions underlying your code are crucial to providing a useful answer. $\endgroup$
    – GiorgioP-DoomsdayClockIsAt-90
    Commented Feb 14 at 17:34

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