Question How it is possible if the planet has more mass can revolve around sun in a elliptical orbit ?

[pruthvi]

consider a giant planet have a 3/4 mass of it sun and with the distance of 50AU from the sun.
does the planet revolve around in a elliptical orbit because the mass of the planet is high so there barycenter is half the distance between them so it look like binary star system but the question is as per Kepler rules the plant should revolve around the sun in a elliptical orbit. How it is possible in this case to say that the planet is in elliptical orbit ?

 

[Unclear Engineer]

Your hypothesized "planet" 3/4 the mass of our Sun would likely be a star, itself. Probably a red dwarf. So, you are actually talking about a binary star system. Astronomers have found many such systems.

As you said, both bodies orbit their common barycenter, and could be in elliptical orbits around that. Obviously, they are always on opposite sides of their barycenter as they orbit. But, their orbits can be elliptical rather than only circular. They have the same period, of course. They just don't need to have a constant separation distance.

Try to envision a couple of balls tied together with a spring, set spinning around each other. They an oscillate closer together and farther apart as they spin around their common center.
Now, think of the two balls having substantially different masses. The lighter one will spring in and outward more than the heavy one. because the the force between them is the same on both, but the lighter one reacts more to the force than the heavy one. But, both will move toward and away from each other. A physical spring would not make exactly elliptical orbits, but when the "spring" really is mutual gravitational attraction with an inverse dependence on the square of the separating distance, then their motions are going to be elliptical orbits.