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NASA's solar sail successfully spreads its wings in space (www.space.com)

submitted 2 months ago by [email protected] to c/[email protected]

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[–] [email protected] 2 points 2 months ago* (last edited 2 months ago) (1 children)

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.

[–] [email protected] 1 points 2 months ago (1 children)

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?

[–] [email protected] 3 points 2 months ago

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.