- #1
Trollfaz
- 144
- 14
Avatar 3 Fire and Ash is out but I promise I won't post any spoilers for this movie. But after watching the 3.5 h long Sci Fi movies I studied the physics of it's ISV here
The events took place on Pandora a habitable exo moon orbiting a gas giant that itself orbits the Alpha Centauri system 4.34 ly away from Earth. It is nearly impossible for conventional space shuttle to reach there due to immense distances. For a space shuttle traveling at 100,000km/h, it takes 46900 years to reach.
The ISV in Avatar franchise travels at 0.7c and hence should not be powered by conventional chemical propellants as they are too weak to reach such speeds. The initial acceleration from Earth takes roughly 6 months to reach 0.7c by using matter-anti matter reactors and a solar sail being continuously struck by a high power laser from Earth to push the ship forward as photons carries momentum ##\lambda=\frac{h}{p}##. The empty ISV has a mass m. The total KE it has at cruising speed is
$$KE=(\gamma-1)mc^2$$
With
$$\gamma=\frac{1}{\sqrt{1-0.7^2}}=1.40$$
And hence the KE is ##0.4mc^2##. Assuming the solar sail contributes to half the energy and the matter antimatter reactor contributed to the other half, hence the total mass of matter anti matter needed is 0.2m. The anti matter is stored in a vacuum chamber trapped by strong magnet fields and cooled to near absolute 0 to prevent premature annihilation from accidental contact with the matter.
It travels at constant speed of 0.7c during majority of it's journey without any additional assistance from the engines since there is nothing to resist it's motion in a vacuum.
In the final 6 months of it's journey, the matter anti matter reactors rapidly decelerates the ship as it reaches the Alpha Centauri system. But by relying entirely on the matter anti matter reactors, it will take too much additional mass on the ship to store the fuel so I believe that it can exploit the radiation from the Alpha Centauri stars to assist in slowing it down.
From a static observer it takes 6.2 years to reach but relativistic time dilation is in effect for passengers on the ship and we established that the Lorentz constant is roughly 1.40 so time is experienced by the passengers on the ship 1.40 times slower and they have to wait 4.43 years which is a little bit longer the same time it takes for light from Earth to reach there from a static observer's POV. Assuming constant velocity entirely throughout the journey but it should take longer than that due to initial acceleration to 0.7 c and deceleration.
If light takes n years to travel to a distant location from a stationary POV, a spaceship moving at x times the speed of light takes ##\frac{n}{x}## years to reach the destination from a stationary POV while passengers on the spaceship wait ##n\frac{x}{\sqrt{1-x^2}}## years to reach for a positive value of x smaller than 1. By solving the equation
$$\frac{x}{\sqrt{1-x^2}}=1$$
The spaceship takes, from it's POV less than, 4.34 years to reach Alpha Centauri if it were to travel faster than ##\sqrt{0.5}## c
The events took place on Pandora a habitable exo moon orbiting a gas giant that itself orbits the Alpha Centauri system 4.34 ly away from Earth. It is nearly impossible for conventional space shuttle to reach there due to immense distances. For a space shuttle traveling at 100,000km/h, it takes 46900 years to reach.
The ISV in Avatar franchise travels at 0.7c and hence should not be powered by conventional chemical propellants as they are too weak to reach such speeds. The initial acceleration from Earth takes roughly 6 months to reach 0.7c by using matter-anti matter reactors and a solar sail being continuously struck by a high power laser from Earth to push the ship forward as photons carries momentum ##\lambda=\frac{h}{p}##. The empty ISV has a mass m. The total KE it has at cruising speed is
$$KE=(\gamma-1)mc^2$$
With
$$\gamma=\frac{1}{\sqrt{1-0.7^2}}=1.40$$
And hence the KE is ##0.4mc^2##. Assuming the solar sail contributes to half the energy and the matter antimatter reactor contributed to the other half, hence the total mass of matter anti matter needed is 0.2m. The anti matter is stored in a vacuum chamber trapped by strong magnet fields and cooled to near absolute 0 to prevent premature annihilation from accidental contact with the matter.
It travels at constant speed of 0.7c during majority of it's journey without any additional assistance from the engines since there is nothing to resist it's motion in a vacuum.
In the final 6 months of it's journey, the matter anti matter reactors rapidly decelerates the ship as it reaches the Alpha Centauri system. But by relying entirely on the matter anti matter reactors, it will take too much additional mass on the ship to store the fuel so I believe that it can exploit the radiation from the Alpha Centauri stars to assist in slowing it down.
From a static observer it takes 6.2 years to reach but relativistic time dilation is in effect for passengers on the ship and we established that the Lorentz constant is roughly 1.40 so time is experienced by the passengers on the ship 1.40 times slower and they have to wait 4.43 years which is a little bit longer the same time it takes for light from Earth to reach there from a static observer's POV. Assuming constant velocity entirely throughout the journey but it should take longer than that due to initial acceleration to 0.7 c and deceleration.
If light takes n years to travel to a distant location from a stationary POV, a spaceship moving at x times the speed of light takes ##\frac{n}{x}## years to reach the destination from a stationary POV while passengers on the spaceship wait ##n\frac{x}{\sqrt{1-x^2}}## years to reach for a positive value of x smaller than 1. By solving the equation
$$\frac{x}{\sqrt{1-x^2}}=1$$
The spaceship takes, from it's POV less than, 4.34 years to reach Alpha Centauri if it were to travel faster than ##\sqrt{0.5}## c