Parallax Calculator
Calculate stellar distances using the parallax method - the foundation of cosmic distance measurement
Parallax Distance Calculator
The apparent shift in star position due to Earth's orbital motion
Parallax Formula
D: Distance (parsecs)
P: Parallax angle (arcseconds)
Distance Results
Measurement Analysis
Example: Sirius Distance Calculation
Given Data
Star: Sirius (brightest star in night sky)
Parallax angle (Hipparcos data): 379.2 milliarcseconds (mas)
Convert to arcseconds: 379.2 × 10⁻³ = 0.3792 arcsec
Calculation
Using D = 1/P formula:
D = 1 / 0.3792 arcsec
D = 2.64 parsecs
Convert to light-years: 2.64 × 3.26 = 8.60 light-years
How Stellar Parallax Works
Baseline Measurement
Earth's orbit provides a 2 AU baseline
6-month observation period
Angle Measurement
Star appears to shift against distant background
Measured in tiny angles (arcseconds)
Distance Calculation
Apply simple trigonometry: D = 1/P
Distance in parsecs from angle in arcseconds
Angular Measurement Units
Reference: 1 arcsecond is like viewing a dime from 2.4 miles away!
Astronomical Distance Units
Parsec definition: Distance at which 1 AU subtends 1 arcsecond
Understanding Stellar Parallax
What is Parallax?
Parallax is the apparent shift in position of a nearby object against a distant background when viewed from two different positions. Hold a pencil at arm's length and close each eye alternately - the pencil appears to move relative to the background. This is parallax!
Stellar Parallax Method
- •Uses Earth's orbital motion as a 2 AU baseline
- •Measures tiny angular shifts in star positions
- •Foundation of the cosmic distance ladder
- •Most direct method for measuring stellar distances
Parallax Formula Derivation
From basic trigonometry:
tan(p) = (1 AU) / D
For small angles: tan(p) ≈ p (in radians)
D = (1 AU) / p = 1/P parsecs
Measurement Limitations
- Ground-based: Limited by atmospheric turbulence (~0.01" accuracy)
- Hipparcos: Space mission reaching 0.001" precision
- Gaia: Current mission with microarcsecond accuracy
- Range: Effective up to ~1000 parsecs with Gaia
Historical Significance
The first successful stellar parallax measurement was achieved in 1838 by Friedrich Bessel for the star 61 Cygni (0.314 arcseconds). This breakthrough proved that stars are at vast distances and that the Earth indeed orbits the Sun.
The term "parsec" comes from "parallax arcsecond" - the distance at which one astronomical unit subtends an angle of one arcsecond. This natural unit makes the parallax formula beautifully simple: D = 1/P.