# Photons and mometum

thatguy101

## Homework Statement

In space near earth, about 3.84*10^21 photons are incident per square meter. On average, the momentum of a photon is 1.3*10^-27. Assume we have a 1205 kg spaceship, and a square sail that is 26.3m wide.
How fast could the ship be travelling after 21 days?

F*Δt=m*v

## The Attempt at a Solution

I started out by finding the force the photons would have on 1 m^2 and then multplied that by 26.3 to get the force on the sail
$(1.30*10^-27)(*3.84*10^+21)*(26.3^2)$
and got .00345 N
Since F=ma, I divided that by 1205 to get 2.865*10^-6
I then took 21 days and changed it to 1814400 s. So i multiplied 2.865*10^-6 by1814400 to get 5.19914 m/s. Did i go wrong somewhere cause the computer says im wrong.

Homework Helper
Gold Member
Hello.

Is any information given about whether or not the photons are reflected back by the sail?

Homework Helper

## Homework Statement

In space near earth, about 3.84*10^21 photons are incident per square meter. On average, the momentum of a photon is 1.3*10^-27. Assume we have a 1205 kg spaceship, and a square sail that is 26.3m wide.
How fast could the ship be travelling after 21 days?

F*Δt=m*v

## The Attempt at a Solution

I started out by finding the force the photons would have on 1 m^2 and then multplied that by 26.3 to get the force on the sail
$(1.30*10^-27)(*3.84*10^+21)*(26.3^2)$
Your method is right. It may be a matter of significant figures. Try to work out the solution using symbols and plug in numbers at the end. It makes it easier to follow:

Fsail = dpship/dt= ndpph/dt = σAdpph/dt where σ is the number of photons per unit area