A planet orbits around its sun on an elliptic orbit, and loses mass slowly due to evaporation. How will the parameters of the orbital ellipse change as a function of time? Could we do a generalisation and mathematically model it?
The mass of a planet does not affect its orbit significantly unless it is a very large planet. On the opposite end of the spectrum would be a very small mass planet that was evaporating, and that is essentially what a comet is. It's all Keplerian, though comets can have their orbits affected slightly by the tiny push they get from the evaporating gases. So it's not the change in mass, but how the evaporation actually happens, but this is a small effect. Even a large planet like Jupiter does not affect the Sun much (the Sun orbits around a point that is not even external to the Sun), so losing mass would not affect the orbit of Jupiter in any significant way either.