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I am trying to calculate momentum transferred by a Photon for Solar Sails speed (not exactly a photon because of wave-particle duality but i will consider it a Photon for this Question), So I had the following results: 2.998×10^-47 kilogram meters per second (with Rest Mass only)

I used Wolfram Alpha with Sir Newtons Second Law (p = mv) to Calculate it

Since light has no acceleration but velocity, I have calculated it's momentum so p=mv

I read on this ScienceDirect Article that Photons have are rest mass of 10 -54 kg

I did'nt find Relativistic Mass of A Photon with 780 Nanometer Wavelength Light

I want to find out if my value is correct, how much would it differ with Relativistic Mass (Since i calculated it with rest mass)?

Can you please help me? I am new to equations

2 Answers2

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When dealing with photons it is better to think in terms of momentum rather than mass. A photon with frequency $\nu$ has momentum with magnitude $\frac {h \nu} c$. If the photon hits the light sail at an incident angle of $90$ degrees and if the light sail is perfectly reflective then the momentum of the photon is reversed, so the change in momentum of the photon is $2\frac {h \nu} c$. By conservation of momentum, the change in momentum of the light sail must also be $2\frac {h \nu} c$. If $N$ photons hit the light sail every second then the force exerted by the photons on the light sail is $2N\frac {h \nu} c$.

gandalf61
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Answer by gandalf61 is correct. Another notable fact is that for light in general (and therefore for photons in particular) the relationship between energy $E$ and momentum $p$ is $$ E = p c $$ when the light is all propagating in the same direction (e.g. plane waves). Therefore if you first calculate the energy in some light then you can get the momentum by dividing by $c$ (if the light is all going in the same direction).

Relating this to photons, we have for each photon $E = h f$ where $f$ is the frequency, and therefore $p = h f/c$ per photon. But you don't need to introduce photons. Just calculate the total energy arriving at the sail in some given time, and then use $p = E/c$. That's the momentum given to the sail if the energy is absorbed. If it is reflected then the total momentum change is $2E/c$.

Andrew Steane
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