# Calculate the total momentum of the photons

• Air

## Homework Statement

The solar sail uses “radiation pressure” caused by the momentum of photons of sunlight as they strike the sail. A sail with an area of $1.5 \times 10^6 m^2$ could be used to propel a spacecraft of mass $1.2 \times 10^3 kg$.
The energy $E$ and momentum $p$ of a photon are related by the expression $E = pc$, where $c$ is the speed of light.
Calculate the total momentum of the photons striking $1 m^2$ of sail in one second. Assume the solar radiation flux (intensity) is $1400 W m^{-2}$.

## Homework Equations

$p=mv$?

## The Attempt at a Solution

Can I have hint's on how to approach this.

The momentum eqaution that I know is $p=mv$ but I don't think I can use this.

If you multiply intensity by the area of the sail the units cancel to leave watts which is Joules per a second. Then if you multiply the intensity by the area you will get 1400W considering it is 1m(squared). Since the aircraft is in space any force is going to propel it so all you have do from here is find how Watts relates to momentum and you're set. Hope this helps.