Calculating Photon Momentum and Speed for a 1205 kg Spaceship with a Square Sail

[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 traveling after 21 days?

Homework Equations

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 I am wrong.

 

[TSny]

Hello.

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

 

[Andrew Mason]

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 traveling after 21 days?

Homework Equations

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:

F_sail = dp_ship/dt= ndp_ph/dt = σAdp_ph/dt where σ is the number of photons per unit area

mΔv = FΔt = ΔtσAdp_ph/dt

AM