Although they dont have mass, photons--traveling at the speed of light-- have mo

Question

Although they dont have mass, photons--traveling at the speed of light-- have momentum. space travel experts have thought of capitalizing on this fact by constructing solar sails-- large sheets of material that would work by reflecting photons. since the momentum of the photon would be reversed, an impulse would also be exerted on the sail, providing a force. in space near the earth, about 3.84 x10^21 photons are incident per square meter per second. on average, the momentum of each photon is 1.30 x10^-27 kg m/s. got a 1,460. kg spaceship starting from rest and attached to a squae sail 24.0 m wide, how fast could the ship be moving after 1 hour? one week? one month? how long would it take the ship to attain a speed of 8,050/m/s, roughly the speed of the space shuttle in orbit?

Explanation / Answer

Here ,

number of photons , N = 3.84 *10^21 Photons/(m^2 . s)

area of sail , A = 24^2 m^2

A = 576 m^2

mass , m = 1460 Kg

impulse per photon , I = 1.3 *10^-27 Kg.m/s

Using second law of motion

let the speed after 1 hour is v

1460 * v = 576 * 1.3 *10^-27 * 3.84 *10^21 * 3600

v = 7.09 *10^-3 m/s

the speed of the spaceship is 7.09 *10^-3 m/s

--------------------------------

after one week

1460 * v = 576 * 1.3 *10^-27 * 3.84 *10^21 * 3600 * 24 * 7

v = 1.191 m/s

the speed of the spaceship is 1.191 m/s

-----------------------------

after 1 month

1460 * v = 576 * 1.3 *10^-27 * 3.84 *10^21 * 3600 * 24 * 30

v = 5.104 m/s

the speed of the spaceship is 5.104 m/s
-----------------------------------------

let the time taken is t

1460 * 8050 = 576 * 1.3 *10^-27 * 3.84 *10^21 * t

t = 4.087 *10^9 s

t = 47308 days

t = 129 years

the time taken will be 129 years

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