Sirius B Gravitational Redshift Visualization

A demonstration of gravitational time dilation at the surface of a white dwarf

The big idea: Light escaping Sirius B loses energy and stretches (shifts red). We predict how much with Einstein's formula; telescopes measure it. They agree — so General Relativity works!

1. Sirius B Data

Property Value
Mass 1.017 M☉ (solar masses)
Radius 0.0084 R☉ (~5,850 km)
Surface velocity shift 80.65 km/s
Surface temperature 25,000 K
Distance from Earth 8.6 light-years

2. Gravitational Redshift Formula

z = GM / (R · c²)
z
Gravitational redshift — the fractional change in wavelength (Δλ/λ) or frequency of light escaping a gravitational well
G
Gravitational constant ≈ 6.67430 × 10⁻¹¹ m³/(kg·s²)
M
Mass of the compact object (in kg)
R
Radius at the emission surface (in m)
c
Speed of light ≈ 2.998 × 10⁸ m/s

3. Calculations

Mass in SI units
2.023e+30 kg
Radius in SI units
5.844e+6 m (5844 km)
Theoretical z (GM / Rc²)
z = 2.570507e-4
Observed z (v/c = 80.65 km/s ÷ c)
z = 2.690194e-4
Comparison: The observed redshift agrees with the theoretical prediction to within 4.66%. This close agreement provides observational support for General Relativity in the strong-field regime near a white dwarf.

4. What Does "Redshift" Actually Mean?

In plain English: Light leaving Sirius B has to "climb" out of its strong gravity. Like a ball rolling uphill, it loses energy. For light, that means each wave gets slightly longer — shifted toward the red end of the spectrum. We measure this as a "velocity" of about 80 km/s (equivalent to the star moving away at that speed).

At surface of Sirius B — tight, short waves (bluer)
↓ Light climbs out of gravity well — loses energy, waves stretch
As seen from Earth — longer waves (redshifted)

5. Theoretical vs Observed Redshift

Einstein's formula predicts a value. Telescopes measure what we actually see. They match closely — that confirms General Relativity!

(z ≈ 0.00027 means each light wave is stretched by about 0.027% — tiny, but measurable with precise spectrographs.)

Comparison of gravitational redshift values

Predicted by Einstein's formula z = 2.57 × 10⁻⁴
2.57 × 10⁻⁴
Measured by telescopes (80.65 km/s shift) z = 2.69 × 10⁻⁴
2.69 × 10⁻⁴

6. Explanatory Notes

Gravitational time dilation: This visualization demonstrates the gravitational redshift predicted by General Relativity. Light escaping from the intense gravitational field near the surface of Sirius B loses energy, causing its wavelength to stretch (redshift) and its frequency to decrease. Equivalently, time runs slower in stronger gravitational fields — a clock at the surface of Sirius B would tick more slowly than a clock far away.

Why Sirius B? Sirius B is a white dwarf, the dense remnant of a star. With roughly the mass of the Sun compressed into a sphere only slightly larger than Earth, its surface gravity is enormously stronger than the Sun's. This makes the gravitational redshift measurable, unlike the much smaller effect on the Sun.

Astronomical observation: This result comes from spectroscopic observations of light from Sirius B, not from a laboratory experiment. Astronomers measure the Doppler-like shift in spectral lines and interpret it as gravitational redshift. The close agreement between the observed value and the theoretical prediction from Einstein's General Relativity provides strong confirmation of the theory.

Part of Vector-Star Probability DynamicsTheory · Experiments · Better Terminology