- #1
Flisp
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I try to calculate the speed curve of a relativistic rocket driven by a 100% efficient engine with constant thrust, when traveling to a distant star. All equations I can find consider constant acceleration, which of course is not working, since the ships mass decreases when the fuel is used, resulting in a low acceleration at the beginning and high acceleration/deceleration towards the end.
I tried using the relativistic momentum equation E² = p² + m² (using c = 1), and p = w * m,
(where E is energy, p momentum, m mass, and w proper speed) and assuming that the entire mass of the used fuel is transferred into momentum so that the energy of the rocket is constant. However, the momentum curve I get is steep at start and flat at the end (without deceleration). The resulting speed curve is steep at start, flattens and gets steeper again. I don't understand why. Burning constant amounts of fuel, I would expect a linear increase of momentum and an exponential increase of speed since less and less mass is accelerated by the constant force from the engine.
Where am I thinking wrong, here?
I tried using the relativistic momentum equation E² = p² + m² (using c = 1), and p = w * m,
(where E is energy, p momentum, m mass, and w proper speed) and assuming that the entire mass of the used fuel is transferred into momentum so that the energy of the rocket is constant. However, the momentum curve I get is steep at start and flat at the end (without deceleration). The resulting speed curve is steep at start, flattens and gets steeper again. I don't understand why. Burning constant amounts of fuel, I would expect a linear increase of momentum and an exponential increase of speed since less and less mass is accelerated by the constant force from the engine.
Where am I thinking wrong, here?