It shouldn't; orbits have many other factors that determine thier path. But, do you mean lower mass of the primary body or "orbiting" body? The mass can determine the orbit's decay, change, tidal locking, etc. but shouldn't have much to do with initial eccentricity.
i mean the orbiting body. Let's say there is a system that contains just two bodies orbiting a star, one with a higher mass than the other. which one would have a more elliptical orbit? Or does this depend on the mass of the star it's orbiting?
In a binary system with unequal masses each orbit, as seen from the Centre of Mass of the combined system, is the mirror image of the other with dimensions inversely proportional to the mass of each body.
The eccentricities are equal.
The ellipticity of an orbit is not determined uniquely by the values of the masses in the system -- it depends also on its history and initial conditions. In other words, I could take the three-body system you describe above and give a kick to either one of the planets, making its orbit more elliptical.
One reason you might find that lower mass objects tend to have more elliptical orbits is that it takes less energy to disturb them. For example, I can send a satellite into an elliptical orbit with a small amount of fuel, while doing the same with the earth would require an enormous quantity of energy.
Thank you, that helps alot!
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