# Calculating Gravitational Attraction Involving Massless Objects

Using the formula $F=G\frac{m_1m_2}{d^2}$ where $m_1$and $m_2$ are the masses of two objects, $G$ is the gravitational constant, and $d$ is the distance between the objects, it is possible to calculate the force of the gravitational attraction between the objects in Newtons. However, since light is affected by black holes, the property required to interact gravitationally is energy, not mass.

How can I calculate the gravitational attraction between objects using their energies instead of their masses?

## 1 Answer

The harsh answer is, "by solving Einstein's field equations". That is an extremely more difficult problem than using Newton's law -- the equations take up at least a page when you write them out.

However for the case of light near a black hole, you can treat the black hole as unaffected by the light, and instead solve the null geodesic equation. This is still harder than Newton's law, but it's at least tractable, compared to Einstein's field equations. For Schwarschild black holes, the Wikipedia article has much information.