I just did some quick maths (and assuming my formulas are correct), beaming at it with a 10 MW laser would cause it to speed up by 0.001 m/s² assuming the sail has 20 kg mass. So not very much, but also not nothing.
I guess the formula to calculate the momentum p of light is p = E/c where c is the speed of light and E is the energy.
So, if the Energy is 10 MW, or alternatively, 10 MJ/sec, then E = 1e7 J. c = 3e8 m/s.
p = E/c = 1e7/3e8 J/(m/s) = 1e7•1e-17/3e8 kg•(m/s)²/(m/s) = 3e-2 kg•(m/s).
(Since E = m•c², 1 kg • c² = 1 kg • (3e8 m/s)² = 1e17 kg•(m/s)².)
Now, if we assume that that momentum gets transferred to the sail, which weighs approximately 20 kg, then we get the velocity of the sail: v = p/20 kg = 3e-2 kg•(m/s)/20 kg ≈ 1e-4 m/s. And this transfer of momentum happens every second, so the acceleration is roughly 1e-4 m/s², or 0.001 m/s².
5 Comments
threelonmusketeers@sh.itjust.works · 5 pts · 2y
@Rangelus@lemmy.nz You were curious about this.
Rangelus@lemmy.nz · 2 pts · 2y
Cheers mate. Neat stuff!
I wonder how much force a sail of that size is expected to produce?
nikaaa@lemmy.world · 2 pts · 2y
I just did some quick maths (and assuming my formulas are correct), beaming at it with a 10 MW laser would cause it to speed up by 0.001 m/s² assuming the sail has 20 kg mass. So not very much, but also not nothing.
intensely_human@lemm.ee · 1 pts · 2y
Can that calculation be done assuming conservation of momentum and the laser’s power?
How’d you calculate it? Does the area of the sail figure into your calculations?
nikaaa@lemmy.world · 3 pts · 2y
Oh yes, of course:
I guess the formula to calculate the momentum p of light is p = E/c where c is the speed of light and E is the energy.
So, if the Energy is 10 MW, or alternatively, 10 MJ/sec, then E = 1e7 J. c = 3e8 m/s. p = E/c = 1e7/3e8 J/(m/s) = 1e7•1e-17/3e8 kg•(m/s)²/(m/s) = 3e-2 kg•(m/s).
(Since E = m•c², 1 kg • c² = 1 kg • (3e8 m/s)² = 1e17 kg•(m/s)².)
Now, if we assume that that momentum gets transferred to the sail, which weighs approximately 20 kg, then we get the velocity of the sail: v = p/20 kg = 3e-2 kg•(m/s)/20 kg ≈ 1e-4 m/s. And this transfer of momentum happens every second, so the acceleration is roughly 1e-4 m/s², or 0.001 m/s².