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I have some problems about Tsiolkovsky's Rocket Equation and some graphs.

Firstly, I didn't get what I can do with Rocket Equation formulas as seen below,

equations

Also, what these three graphs try to mean? Can someone explain the relations between these values?

Mass Ratio(∆v)/∆v and Mass Ratio(Isp)/Isp graphs

Time of the burn(Mass ratio)/Mass Ratio graph

Thanks!

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These graphs show different visualizations of the Tsiolkovsky rocket equation:

enter image description here

(source: wikipedia article)

The equation relates change in velocity to engine efficiency and the propellant mass consumed.

For example the first graph shows that to achieve a delta-v of 30,000 m/s with an engine that has an $I_{sp}$ of 1000, you will need a mass ratio of 21. Tripling the $I_{sp}$ to 3000 hugely reduces the mass ratio required for the same delta-v to ~ 2.77.

enter image description here

The second graph just swaps the placement of specific impulse and delta-v but uses the same equation.

Update: After looking into it, I am dubious about Equation 3.37. See discussion in my answer to Some exercise questions about Tsiolkovsky's Rocket Equation and Thrust Equation There are good burn time equations in answers to this question How do I calculate a rockets burn time from required velocity? .

Finally, the first equation in your question is derived from the rocket equation by dividing through by $I_{sp} * g_0$, taking the inverse natural log of both sides, and multiplying the result by $m_f$ (equivalent to your $M_{empty}$).

The second equation in your question is derived from the burn time equation 3.37 in the same manner. Update: But I am still dubious about equation 3.37.

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    $\begingroup$ Hey! This answer is fit to my question perfectly. I have another question. I could not understand the meaning of specific impulse. It's an efficiency measurement of a rocket engine, that's ok, but in the description of it and where to use it, it confuses my head. Can you give me a brief explanation of specific impulse, please? $\endgroup$
    – M. Çağlar TUFAN
    Commented Apr 30, 2019 at 15:18
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    $\begingroup$ Glad it helped! That's already been asked, and you can read about it here: space.stackexchange.com/questions/9344/… $\endgroup$
    – Organic Marble
    Commented Apr 30, 2019 at 16:07
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    $\begingroup$ Alright, thanks so much @Organic Marble. I will not forget to giving positive feedback your answer and comments, I need 15 reputations to do it. Have a good day! $\endgroup$
    – M. Çağlar TUFAN
    Commented Apr 30, 2019 at 18:13
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    $\begingroup$ You are welcome and welcome to space stack exchange. $\endgroup$
    – Organic Marble
    Commented Apr 30, 2019 at 18:26

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