Planet heating with eccentricity

[Helio]

I stumbled across a statement that eccentric orbits will heat a planet more than circular orbits. This isn't all that intuitive, perhaps not even true. The most amount of time will be away from the host star, so this will make it colder than normal, but the brief time at periapsis will make much hotter than normal.

The inverse square law on the radiation is a big deal. The percent increase in radiation for a given time interval at approach will be great than the percent decrease near periapsis.

I'd like to attempt to calculate it myself but I'm having trouble finding the equation for solving the location of a planet along its elliptical orbit. Does anybody know where I can find the equation for time and location? I'd even be okay if I had a way to calculate the area for segments so I could just use Kepler's law.

 

[vincenzosassone]

I stumbled across a statement that eccentric orbits will heat a planet more than circular orbits. This isn't all that intuitive, perhaps not even true.

I don't know the equations to calculate this, but I know something that maybe can help you. You have said that the planets with the eccentric orbit would be colder than the planets with the circular orbit, and I agree. But you also heard the contrary... Maybe who says this take into account a planet with the atmosphere, who keeps the planet hot because of the greenhouse effect. Correct me if I wrong, but it is a possible solution seen that the atmosphere would care about the warm of the planet during the period in which it is far away from the star