A photon rocket is a science fiction device, a spaceship operating via the rocke

Question

A photon rocket is a science fiction device, a spaceship operating via the rocket principle but whose exhaust is light. (Assuming there is a power source aboard adequate to its needs, a photon rocket does not consume fuel to provide thrust.) The momentum transfer for emission of light is the same as for complete absorption of the light (albeit in the opposite direction, obviously). The Space Shuttle had a loaded mass of just over 2000 metric tons, and its onboard main engine (this does not include the two solid rocket boosters which provided most of the thrust during launch) could provide this mass with an acceleration of1.1 m s^2 . Estimate the radiant power needed in a photon rocket that is to provide this thrust; compare it to world electrical power generation (roughly 2.5 TW at this time).

Explanation / Answer

Assume the radiant power in photon rocket= x Watt

As, Momentum of a photon = E/c

where 'E' is the energy of photon and 'c' is the velocity of light.

Momentum of light per sec = x/c (as 'x' Joule of energy is emitted per sec)

As Momentum transfer for emission of light is same as for complete absorption of light,

So Momentum transfer for light

emission per sec = x/c

According to newton's second law, F= dP/dt

So, Force exerted by emission of light = Momentum transfer by light per sec

So, Force exerted= x/c

This force exerted will be in upward direction as emission of light takes place in downward direction.

Let Force exerted by onboard main engine = F

So, F - weight of rocket= mass× acceleration

=> F - 2000×1000×9.8 = 2000×1000×1.1

=> F= 21800000 N

So, radiant power needed in photon rocket that can provide this thrust= x/c = F

=> x = F × c

=> x = 21800000x 300000000

=> x = 6540 TW

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