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Let me discuss a simpler version of your rocket-question: one where there is no gravity, so that we don't have to worry about gravitational potential energy. Consider a rocket in free space (vacuum), and consider that the rocket is at rest. Now the rocket fires it's engine for a short time. The engine accelerates the rocket. The rocket now has kinetic ...

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Nuclear rocket motors work by heating a gas and allowing it to expand out of the exhaust. To get the most thrust from your gas you want the momentum of the gas molecules to be as high as possible, because the force is equal to the rate of change of momentum of the gas molecules. Suppose the nuclear reactor heats the gas to a temperature $T$, then the ...

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As rockets have finite fuel capacity and important parameter is how much rocket velocity can be achieved in a given situation per unit of fuel mass consumed. The higher the exhaust velocity the more effectively the fuel mass is utilised. Issues such as energy required are also important but generally exhaust velocity or "specific impulse" is amongst the most ...

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Actually you can go to the orbit of Jupiter with a $\approx 2500$ tonnes rocket and a $3$ tonnes payload. From there you can use an ionic engine. A rocket launched from the equator of Jupiter that turns at $12.6~\text{km}/\text{s}$ needs just an increase in speed $v = 29.5~\text{km}/{\text{s}}$. $$v_{rj}:= 12.6~{\text{km}}/{\text{s}} \;\;\; R_j := ... 16 Let's assume you mean that Earth now has the mass of Jupiter (as opposed to actually launching from the literal planet Jupiter - whole different question...). Then: radius of Earth = 6.4 \times 10^6~\text{m} mass of Jupiter = 1.9 \times 10^{27}~\text{kg} Escape velocity, v_\text{escape} = \sqrt{\frac{2GM}{r}} This gives a value for ... 10 Hey! The question keeps getting edited! Make up your mind! You asked about Mars originally, then edited the question. Actual, real Jupiter is flat out impossible. Does it have a surface to launch from? Who knows? What's the pressure at that depth? Can our probes even survive at that depth? Probably not? What if Earth had the mass of Jupiter? More ... -1 No, water moving out of a bottle rocket is not nearly fast enough to generate the energy sapping shock waves and mach which the converging-diverging nozzle seeks to eliminate. 2 Normally, the Lagrangian (in Cartesian coordinates) for an object of mass m in a potential V would be$$L=T-V\to\frac{1}{2}m(\dot{x}^2+\dot{y}^2+\dot{z}^2)-V(x,y,z)\tag{1}$$It then follows that for a coordinates q,$$\frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{\partial L}{\partial\dot{q}}\right)=\frac{\partial L}{\partial ...

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To get a spacecraft to the Moon we normally use a Hohmann transfer orbit. The fuel is used in two steps: increase the velocity of the scapecraft to put it into an elliptical orbit with its apogee at the Moon. when the spacecraft reaches the Moon increase its velocity again to match the velocity of the Moon. The amount of fuel required is described by the ...

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