Measurement of the radial velocity of the Sun as a star by means of a reflecting solar system body. The effect of the body rotation

TL;DR

This paper investigates how the rotation of solar system bodies affects the measurement of the Sun's radial velocity via reflected sunlight, highlighting the importance of accounting for rotational Doppler shifts for precise observations.

Contribution

It introduces a geometric model to quantify the rotational effects on radial velocity measurements of the Sun reflected by minor bodies, considering spherical and ellipsoidal shapes.

Findings

Rotation can cause up to 2.4 m/s perturbation in radial velocity measurements.

The effect vanishes only when the body's rotation axis aligns with the Sun and Earth.

A general model is provided to estimate the rotational impact based on shape and orientation.

Abstract

Minor bodies of the solar system can be used to measure the spectrum of the Sun as a star by observing sunlight reflected by their surfaces. To perform an accurate measurement of the radial velocity of the Sun as a star by this method, it is necessary to take into account the Doppler shifts introduced by the motion of the reflecting body. Here we discuss the effect of its rotation. It gives a vanishing contribution only when the inclinations of the body rotation axis to the directions of the Sun and of the Earth observer are the same. When this is not the case, the perturbation of the radial velocity does not vanish and can reach up to about 2.4 m/s for an asteroid such as 2 Pallas that has an inclination of the spin axis to the plane of the ecliptic of about 30 degrees. We introduce a geometric model to compute the perturbation in the case of a uniformly reflecting body of spherical or triaxial ellipsoidal shape and provide general results to easily estimate the magnitude of the effect.