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I am currently trying to figure out how I can use Microsoft Excel to calculate the ballistic trajectory of a test particle released from the inner Lagrange point in a semidetached binary. To keep things simple, I am using a two-dimensional coordinate system, and I am assuming that the initial conditions of the test particle have very little impact on the trajectory.

So far, I have the conditions of the semidetached binary determined: in the xy plane I have the accreting star located at the origin, and I have the center of mass of the binary and Lagrange Point L1 correctly positioned on the x axis. I have also graphed the radius of the accreting star. All other parameters are also available.

I understand the forces at work, although I am not too familiar with how the directions should be specified for the Coriolis and centrifugal forces on the test particle. I am familiar with the Roche potential of the system, yet I do not know how to apply it to this particular case in determining trajectories. I have also read several publications, including one which has several graphs (the ones on the left side) of what I would like to achieve with this spreadsheet: http://www.astro.psu.edu/~mrichards/research/tomog.gif" The problem is that none of them have gone into detail on how such graphs were derived. So this is as far as I have gotten with my spreadsheet. I would be thankful of someone could lead me in the right direction in calculating these trajectories.

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# Trajectory of a Test Particle in a Semidetached Binary

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