Parallax Distance Inverse Cross-Scan - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

A parallax-distance cross-scan varies parallax across rows and reads off the inverse distance d = 1 / p (in parsec when p is in arcsec), showing how the measured angular shift maps to distance. The arithmetic is exact only for the stated parallax values and rows in the ideal small-angle model. Real observations add noise, calibration, extinction, limb darkening, cadence, geometry assumptions, and measurement/source uncertainty.

Three exact rows show the inverse parallax-distance relation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Distance index is the inverse of parallax index

The checked source uses parallax index one fifth, so the distance index is five and the product stays one.

p=\tfrac{1}{5},\quad d=5,\quad p d=1

Smaller parallax means larger distance

Three finite rows make the inverse relation visible: when parallax shrinks from one fourth to one tenth, distance grows from four to ten.

\begin{array}{c|c|c}p&d&p d\\\frac{1}{4}&4&1\\\frac{1}{5}&5&1\\\frac{1}{10}&10&1\\\end{array}