Gravitational Redshift Calculator

Redshift Parameter:

\\[ z = \frac{\Delta \lambda}{\lambda_0} = \frac{G M}{c^2 r} \\]

Redshifted Wavelength:

\\[ \lambda = \lambda_0 (1 + z) \\]

Where:

• \\(z\\): Redshift parameter (dimensionless)
• \\(\lambda_0\\): Emitted wavelength (nm)
• \\(\lambda\\): Redshifted wavelength (nm)
• \\(G\\): Gravitational constant (\\(6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\\))
• \\(M\\): Mass of gravitating body (kg)
• \\(c\\): Speed of light (\\(2.99792458 \times 10^8 \, \text{m/s}\\))
• \\(r\\): Radial distance from center of mass (m)

\\[ z = \frac{6.67430 \times 10^{-11} \times 5.972 \times 10^{24}}{(2.99792458 \times 10^8)^2 \times 6.371 \times 10^6} \approx 6.966 \times 10^{-10} \\] \\[ \lambda = 500 \times (1 + 6.966 \times 10^{-10}) \approx 500.00000035 \, \text{nm} \\]