ISR 2024-08: Some Details Related to Velocity Aberration
June 24, 2024P. R. McCullough
We describe some details related to changes in image scale induced by velocity aberration of starlight. We investigated whether an update was warranted to the HST keyword VAFACTOR, which quantifies the dimensionless factor by which the image scale is changed by velocity aberration at the mid-point in time of an exposure. Nominally, the factor differs from unity by ±1E-4 or less. We quantify each of the following effects on VAFACTOR: a) using the classical formula instead of the relativistic one, b) evaluating it at an inappropriate time, e.g. at the start of an exposure, and c) evaluating it at mid-exposure instead of averaging it over the entire exposure. Respectively, the three effects can produce errors in VAFACTOR as large as a) 1.0E-8, b) 0.8E-6 T, and c) 4.5E-9 T², with the exposure time T expressed in minutes. Whereas the first effect is negligible and the second effect is only hypothetical, the third effect has the potential to be marginally significant in rare circumstances, but we expect will never matter in practice. Based on this analysis, no updates are indicated to the formulas used for FITS keywords VAFACTOR (HST) or VA SCALE (JWST).