Distance Calculation

📐 Using Parallax to Determine Distance¶

The principle is identical to how your two eyes perceive depth (stereoscopic vision).2 The distance between your two telescopes acts as the baseline (3$B$).4 The apparent shift in the object's position against a distant background is the parallax angle (5$p$).6

1. The Geometry and Formula¶

The setup forms a very long, skinny, right-angle triangle with the target object at the apex and your baseline on Earth as the short side.

For a sufficiently distant object where the parallax angle ($p$) is very small (in radians), the distance ($d$) is calculated using the following simplified trigonometric relationship:

$$d = \frac{B}{p}$$

$d$ = The distance to the target object.7
$B$ = The distance between your two telescope locations (the baseline).8 This must be accurately known using GPS.
$p$ = The measured parallax angle (the difference in the object's apparent angular position between the two sites, converted to radians).

⚠️ Important Distinction: Diurnal vs. Annual Parallax¶

The parallax you are generating is Diurnal Parallax (caused by your observing positions on Earth).

Diurnal Parallax (Your Method): Baseline is the distance between your telescopes (up to $\approx 12,742$ km, Earth's diameter). Used for measuring distances to objects within the Solar System and low-Earth orbit.
Annual Parallax (Traditional Stellar Method): Baseline is the diameter of Earth's orbit around the Sun (9$\approx 300$ million km).10 Used for measuring distances to nearby stars (like what the Gaia satellite does).11

Your distributed network is extremely well-suited for the short baseline, high-precision measurements of objects relatively close to Earth.