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Answer :
Final answer:
To calculate the total Δv of a two-stage rocket, we use the Tsiolkovsky rocket equation, separately for each stage and payload scenario, and sum the Δv values for both stages.
Explanation:
To determine the total Δv of a two-stage rocket, we can apply the Tsiolkovsky rocket equation, which is Δv = Isp * g0 * ln(m0/mf), where Isp is the specific impulse of the rocket stage, g0 is the standard acceleration due to gravity (9.81 m/s²), m0 is the initial total mass (propellant mass + dry mass + payload mass), and mf is the final mass (dry mass + payload mass).
For the first stage, the calculations would be as follows:
- For a 8 kg payload: Δv1 = 255 s * 9.81 m/s² * ln((115,000 kg + 9,500 kg + 8 kg)/(9,500 kg + 8 kg))
- For a 1,800 kg payload: Δv1 = 255 s * 9.81 m/s² * ln((115,000 kg + 9,500 kg + 1,800 kg)/(9,500 kg + 1,800 kg))
For the second stage, we need to add the final mass of the first stage to the initial mass of the second stage, and then perform a similar calculation:
- For a 8 kg payload: Δv2 = 345 s * 9.81 m/s² * ln((31,000 kg + 3,500 kg + 8 kg + the final mass of the first stage)/(3,500 kg + 8 kg + the final mass of the first stage))
- For a 1,800 kg payload: Δv2 = 345 s * 9.81 m/s² * ln((31,000 kg + 3,500 kg + 1,800 kg + the final mass of the first stage)/(3,500 kg + 1,800 kg + the final mass of the first stage))
Finally, to get the total Δv for the entire system, simply add Δv1 and Δv2 for each payload scenario.
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