A simple formula for a planet's mean annual insolation by latitude

TL;DR

This paper introduces a sixth order Legendre series expansion method to efficiently approximate a planet's mean annual insolation by latitude, offering faster calculations with minimal accuracy loss.

Contribution

The paper presents a novel, simplified formula using Legendre series for calculating planetary insolation, improving computational speed over existing methods.

Findings

Faster computation of insolation with minimal accuracy loss

Comparison shows good agreement with existing literature

Method applicable to planets with varying obliquity angles

Abstract

In this paper, we use a sixth order Legendre series expansion to approximate the mean annual insolation by latitude of a planet with obliquity angle $\beta$, leading to faster computations with little loss in the accuracy of results. We discuss differences between our method and selected computational results for insolation found in the literature.