# Gravitational red shift

## Homework Statement

After a star like the Sun has exhausted most of the hydrogen in its core it expands and cools to form a red giant. Eventually, when it has exhausted all its nuclear fuel, it sheds its outer layers and contracts and becomes a white dwarf of similar size to the Earth as shown below. Note that the mass of the sun is 2 × 1030 kg, the radius of the Earth is 6,380 km and Newton's gravitational constant G is 6.67 × 10–11 Nm2 kg–2.

Light leaving the surface of a star of mass M and radius R is stretched in wavelength (i.e. "gravitationally red-shifted") by an amount Δλ/λ = GM/(Rc2) where c is the speed of light.

Calculate the gravitational red shift for light leaving the surface of the white dwarf

## The Attempt at a Solution

I tried substituting the values into the formula Δλ/λ = GM/(Rc2) but that didn't produce the right answer...

Then I tried using the "scape speed" equation is given by

$$v_{esc}=\sqrt{\frac{2GM}{R}}$$

Where G is the gravitational constant. M is the mass of the white dwarf and R is its radius converted to meters.

But this didn't work either. The right answer has to be 0.000279. Can anyone explain to me how the got this answer? I have an exam tomorrow...