One of the propulsors of spaceships may be

One possible way for spacecraft to move is to use a “light sail,” which is a mirror film that receives a pulse when light hits it. The initial speed of the ship is v1 = 7.9 km/s (first space velocity), and the final speed v2 = 11.2 km/s (second space velocity). If light falls on the “sail” normally and the mass of the ship with the “sail” is m = 500 tons, then how many photons (particles of light) should be reflected from the “light sail” if the mass of the photon mf = 0.5*10-35 kg ?

To calculate the number of reflected photons, you need to use the law of conservation of momentum. When falling on a “light sail”, the luminous flux will transmit to it an impulse equal to the impulse of the photons that will be reflected from it. Using the formula for the momentum of light: p = E/c, where E is the energy of the photon, and c is the speed of light, you can calculate the momentum of one photon:

pф = E/c = (h*ν)/c, where h is Planck’s constant, ν is the frequency of light.

To determine the number of reflected photons, you need to calculate the change in momentum that occurred when light was reflected from the “sail”. The change in momentum can be calculated using the formula:

Δp = 2pф(cosθ), where θ is the angle between the direction of light movement and the normal to the surface of the “sail”.

Thus, the number of reflected photons will be equal to:

N = Δp/ pф = 2mVsin(θ/2)/hν, where V = v2 - v1 is the change in the speed of the ship, and θ = 0 for light incident on the “sail” along the normal.

Substituting the known values, we get:

N = 2 * (500,000 kg) * (11.2 - 7.9 km/s) / (6.63 * 10^-34 J*s * 3 * 10^8 m/s) ≈ 2.5 * 10^24 photons.

Thus, in order for the “light sail” to bring the spacecraft to a given speed, about 2.5 * 10^24 photons need to be reflected.

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To solve this problem it is necessary to use the law of conservation of momentum. When light falls on a “light sail”, the light flux transfers to it an impulse equal to the impulse of the photons that will be reflected from it. Using the formula for the momentum of light: p = E/c, where E is the photon energy, and c is the speed of light, you can calculate the momentum of one photon: pf = E/c = (h*ν)/c, where h is Planck’s constant, ν is the frequency of light.

To determine the number of reflected photons, you need to calculate the change in momentum that occurred when light was reflected from the “sail”. The change in momentum can be calculated using the formula: Δp = 2pф(cosθ), where θ is the angle between the direction of light movement and the normal to the surface of the “sail”.

The number of reflected photons will be equal to: N = Δp/pф = 2mVsin(θ/2)/hν, where V = v2 - v1 is the change in the speed of the ship, and θ = 0 for light incident on the “sail” along the normal.

Substituting the known values, we get: N = 2 * (500,000 kg) * (11.2 - 7.9 km/s) / (6.63 * 10^-34 J*s * 3 * 10^8 m/s ) ≈ 2.5 * 10^24 photons.

Thus, in order for the “light sail” to bring the spacecraft to a given speed, about 2.5 * 10^24 photons need to be reflected.

So, one of the propulsors of spaceships could be a “light sail” - a mirror film that receives an impulse when light falls on it. For it to work, it is necessary that about 2.5 * 10^24 photons are reflected. You can purchase this product from our digital store and use it for your space adventures.

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Product description:

One of the engines of spaceships can be a “light sail”. This is a mirror film that receives a pulse when light shines on it. To use a "light sail" as a motor, it is necessary that the light falls on it normally.

To calculate the number of photons required to obtain an impulse, it is necessary to know the initial and final speed of the ship, as well as the mass of the ship with the “sail” and the mass of the photon.

In this case, the initial speed of the ship is v1 = 7.9 km/s, and the final speed is v2 = 11.2 km/s. The mass of the ship with the “sail” is m = 500 tons, and the mass of the photon is mf = 0.5*10-35 kg.

To solve the problem it is necessary to use the law of conservation of momentum. According to this law, the sum of the system impulses before and after interaction must remain unchanged.

The calculation formula for determining the number of photons required to produce a pulse is as follows:

N = Δp/Δpф

where N is the number of photons, Δp is the change in the momentum of the ship with a “light sail”, Δpф is the momentum of one photon.

The change in momentum of a ship with a “light sail” can be determined by the formula:

Δp = mΔv

where Δv = v2 - v1 is the change in speed of the ship.

The momentum of one photon is determined by the formula:

Δpф = hf/c

where h is Planck's constant, f is the frequency of light, c is the speed of light.

Substituting known values, we get:

Δv = 11.2 km/s - 7.9 km/s = 3.3 km/s

Δp = 500 t * 3.3 km/s = 1.65 * 10^13 kg * m/s

Δpф = 6.626 * 10^-34 J * s * 5.45 * 10^14 Hz / 3 * 10^8 m/s = 1.13 * 10^-22 kg * m/s

N = 1.65 * 10^13 kg * m/s / 1.13 * 10^-22 kg * m/s = 1.46 * 10^35 photons

Thus, to obtain the required momentum of a ship with a “light sail”, it is necessary to reflect about 1.46 * 10^35 photons.

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