To get an idea of how much we're losing to friction due to impacts (whether directly against the ship or against a field generated by the ship) we're going to consider the impact of the interstellar medium on ships as they move through hyperspace. To do this, we're going to take some information and use it to compute a rough average of how much acceleration is needed to propel a ship at certain speeds. To do this, we're going to need some key information:
The average density of interstellar medium: We will assume a Cold Neutral Medium (20 to 50 atoms/cm3) as an analog for a hyperlane.
The speed of light, which we will average out to be 300x106 m/s for convenience.
The front face area of the Millennium Falcon (compressed to a single, flat face for convenience): 25m x 7m (approx)
The relative atomic mass of hydrogen (H1) at 1.00794u, with an Atomic Mass Unit of 1.66x10-27kg. Hydrogen will be used as an analog due to making up 75% of the universe.
First, we will compute the mass of the hydrogen in a given centimeter of interstellar space, with an average of 35 atoms/cm
3. The approximate weight of a hydrogen atom is 1.00794 x 1.66x10
-27 = 1.6732x10
-27 kg. Given that there are approximately 35 atoms/cm
3, that gives an approximate mass of 58.5613x10
-27 kg/cm
3, or 58.5613x10
-21 kg/m
3Given how fast the ship is moving, the approximate number of atoms encountered per second will depend on the speed of the vessel, but with the approximate cross-sectional area of the
Millennium Falcon and a depth of 300x10
6 m/s, this gives a volume of 25m x 7m x 300x10
6 = 52.5x10
9 m
3.
So, if the
Millennium Falcon encountered every atom in its way traveling at the speed of light every second, it would be continuously slamming into the equivalent mass of 3.07447x10
-9 kg every second. Using the equation KE = 0.5(mass)(velocity)
2, this yields KE=0.5(3.07447x10
-9 kg)(300x10
6 m/s)
2 = 138.351x10
6 Joules. To convert this to Newtons, we will divide it by 300x10
6 meters due to the energy being expended over that distance to equal 0.4612 Newtons.
Using calculations for the mass of the Millennium Falcon, we can estimate the mass to be approximately 1.5x10
6 kg. Since F=ma, 0.4612N = 1.5x10
6a, meaning a = 307.447x10
-9 m/s
2. This means that very little energy is actually needed to maintain the speed of light once the ship reaches it, assuming the hyperdrive is operational of course.
To calculate this for, say, 1000c, we must consider the change in volume of atoms. The equivalent mass is now 3.07447x10
-6 kg, but the distance traveled is now 300x10
9 m. The kinetic energy becomes 138.351x10
15 J, which means the equivalent force being applied to the
Millennium Falcon is 461.1703x10
3 N. The new acceleration being applied to the
Falcon is now 0.3074 m/s
2. Again, this is for very thin interstellar medium.
To look at the same 1000c through much denser medium, such as nebulas and dense pockets of gas and dust, we will take the average for molecular clouds, with a density of 10
2 to 10
6 atoms/cm
3, averaging 10
4 atoms/cm
3. Running the numbers yields an equivalent mass/second of 878.42x10
-6 kg, which is much greater than it was in our analog hyperlane. The acceleration needed to keep the
Millennium Falcon moving is now 87.84 m/s
2, or 8.96g.
In essence, like we would expect, the more friction due to the interstellar medium we have, the greater the acceleration is, and the more power is needed. So, once a starship like the
Millennium Falcon encounters enough mass that the friction from individual atoms builds up to start opposing forward acceleration, what will eventually happen is that the ship is no longer accelerating and thus its forward velocity is maintained.