Build your own analemma

TL;DR

This paper provides a step-by-step tutorial for constructing Earth's analemma using vector analysis and numerical methods, making it accessible for undergraduate physics students to visualize Earth's orbital geometry.

Contribution

It introduces a practical, educational approach to constructing the analemma through vector analysis and numerical computation, enhancing understanding of Earth's orbital mechanics.

Findings

Analemma shape results from Earth's axial tilt and orbital ellipticity.

Vector analysis effectively models Earth's solar position over a year.

Numerical methods enable visualization of Earth's orbital geometry.

Abstract

Earth's analemma is the lopsided figure eight marked out over a year by the position of the Sun in the sky observed at the same clock time each day. It shows how solar time deviates from clock time. The analemma's shape results from the tilt of Earth's axis of rotation relative to the plane of its orbit around the Sun and from the elliptical shape of that orbit. This tutorial paper uses vector analysis of the Earth-Sun geometry and a numerically generated quantitative description of Earth's motion around the Sun to construct Earth's analemma. To visualize the geometry and the motion that give rise to the analemma is challenging, but this construction is a project within the capability of physics students who have had basic undergraduate mechanics.