An iterative method for obtaining a nonlinear solution for the temperature distribution of a rotating spherical body revolving in an eccentric orbit

An iterative method for determining the temperature distribution in a rotating spherical body with an eccentric orbit around a star is developed. The heating term is expanded into the Fourier series with respect to the mean anomaly and the spherical harmonics with respect to the longitude and colatitude of a spherical body. The obtained formula is suitable for the eccentricity less than about 0.7. The remaining procedure to determine the temperature using an iterative method is the same as that described in Sekiya and Shimoda (2013). The method for determining the change rates of orbital elements due to the Yarkovsky effect is also developed. Our method is applicable to any value of the rotation period of a body. The errors of our results are less than 1%. Our results can be used to test a grid-based numerical code.