space ship

Can We reach the Stars?
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Challenges

Speed:

Getting there in a reasonable time - The most obvious challenge to practical interstellar travel is speed. Our nearest neighboring star is 4.2 Light Years away.

Mass:

Rockets use too much propellant - A less obvious challenge is overcoming the limitations of rockets. The problem is fuel, or more specifically, rocket propellant.

Energy:

Our third big challenge is energy - Even if we had a non rocket space drive that could convert energy directly into motion without propellant, it would still require a lot of energy. border

Physics

Classical Physics

Newton's laws of motion

  1. "An object at rest or in uniform motion in a straight line will remain at rest or in the same uniform motion unless acted upon by an unbalanced force."
  2. "The acceleration a of an object is directly proportional to the total unbalanced force F exerted on the object, and is inversely proportional to the mass m of the object (in other words, as mass increases, the acceleration has to decrease)." F=m*a
  3. "For every action there is an equal and opposite reaction."

Momentum conservation

In an isolated system, the total momentum is constant.

Energy conservation

In an isolated system, the total energy is constant.

Einstein's special theory of relativity

  1. There is no invariant "fabric of space" relative to which an absolute speed could be defined or measured. The terms "moving" or "resting" make only sense if they refer to a certain other frame of reference. The perception of movement is always mutual; the starship pilot who leaves Earth could claim that he is actually resting while the solar system is moving away.
  2. The speed of light, c=3*108m/s in the vacuum, is the same in all directions and in all frames of reference. This means that nothing is added or subtracted to this speed, as the light source apparently moves.
One of the most popular examples used to illustrate the effects of Special Relativity is the addition of velocities. It is obvious that in the realm of very slow speeds it's possible to simply add or subtract velocity vectors from each other. Lets assume a passenger on a train moving at the speed v walks with the speed w in the direction of the motion of the train, his speed to an observer would be v+w. Lets instead assume the train travels at the half speed of light (v=c/2), and the passenger instead turn on a flashlight. To the passenger, the speed of the light from the flashlight would be c. The speed of the light off the flashlight to an observer would also be c, so we can not simply add velocities!
formula
Eq. 1
To describe the acceleration phase as observed from Earth's frame of reference, the simple relation v=at for non-relativistic movements has to be modified as follows:
formula
Eq. 2
To obtain the covered distance x after a certain time t, the speed v as given in Eq. 2 has to be integrated over time:
formula
Eq. 3
Mass is not an invariant property. Consider two identical rockets that started together at t=0 and now move away from the launch platform in opposite directions, each with an absolute speed of w. Each pilot sees the launch platform move away at w, while Eq. 1 shows us that the two ships move away from each other at a speed u<2w. The "real" center of mass of the whole system of the two ships would be still at the launch platform, however, each pilot would see a center of mass closer to the other ship than to his own. This may be interpreted as a mass increase of the other ship to m compared to the rest mass m0 measured for both ships prior to the launch:
formula
Eq. 4

If a "starship" accelerates at a rate of 1 G , its speed is increasing by 10 m/sec each second. If we divide the speed of light, 300,000,000 m/sec, by 10 m/sec2, we find that the time to reach the speed of light is 347 days. However, Eq. 4 shows that the force necessary to maintain this rate of acceleration increases as velocity increases because the mass of the ship increases with velocity, so the calculated time for acceleration to light-speed assumes the force applied can be continuously increased at a rate which compensates for the continuous increase in mass.
graph
Fig. 1
So each object has a rest mass m0 and an additional mass m-m0 due to its speed as seen from another frame of reference. This is actually a convenient explanation for the fact that the speed of light cannot be reached. The mass increases more and more as the object approaches c, and so would the required momentum to propel the ship. Finally, at v=c, we would get an infinite mass, unless the rest mass m0 is zero. The latter must be the case for photons which actually move at the speed of light, which even define the speed of light.

Rocket Performance

Rocket propulsion (as a generic term for any drive using accelerated particles) can be described by momentum conservation, resulting in the following simple equation:
formula
Eq. 5
The left side represents the infinitesimal speed increase (acceleration) dv of the ship with a mass m, the right side is the mass decrease -dm of the ship if particles are thrusted out at a speed w. This would result in a constant thrust and therefore in a constant acceleration, at least in the range of ship speeds much smaller than c. Eq. 5 can be integrated to show the relation between an initial mass m0, a final mass m1 and a speed v1 to be achieved:
formula
Eq. 6
Let us assume a photon drive as the most advanced conventional propulsion technology, so that w would be equal to 90% of c, the speed of light. The fuel would be matter and antimatter in the ideal case, yielding an efficiency near 100%, meaning that according to Eq. 6 almost the complete mass of the fuel could contribute to propulsion. If relativistic effects are taken into account the formula has to be modified in the following way:
formula
Eq. 7
The structure and payload could still be as much as 50% of the total mass of the starship, if it's going to be accelerated to 0.6c. However, the mass increase at high sublight speeds as given in Eq. 4 spoils the efficiency of any available propulsion system as soon as the speed gets close to c, since the same thrust will effect a smaller acceleration. If we assume that the ship first accelerates to 0.6 and then decelerates to zero on the flight to Proxima Centauri, we will get a starship mass of 25% of the original starship mass.
For comparison some basic facts about the Saturn V:
Weight : 6,200,000 lb (with propellant), 430,000 lb (dry)
Payload : 270,000 lb in low earth orbit, 100,000 lb translunar
The payload and structure to low earth orbit of Saturn V was 11% of total liftoff mass!
Let us assume a starship with this very advanced photon drive, were to reach Proxima Centauri, about 4ly away from Earth.
Flight to Proxima Centauri Speed Distance Earth time
Acceleration 5 m/s2 0 to 0.6c 0.4ly 1.5 years
Constant speed 0.6c 3.4ly 5.7 years
Deceleration -5 m/s2 0.6c to 0 0.4ly 1.5 years
Total - 4.2ly 8.7 years

With todays physics it is possible to send a space probe to Proxima Centauri orbit with reasonable payload and recieve a radio signal back within 13 Years. But We don't have the technology Yet! border

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