# Scoutleader looking for understanding of fuel burn for getting away from earth gravity Vs. fuel expended when traveling from A-B in space

I am a layman scoutleader and like to discuss the amount of fuel needed to get from earths gravity to the thrust needed in space to get from A-B. Is there a spreadsheet that would give course calculations that could be a start or other means? Thank you!!

• I don't know my way around this so I can't point you to a specific page, but I think you'll find it interesting: hopsblog-hop.blogspot.com For a one-stage rocket, the things you'll need to look into (Wikipedia, search this stack exchange site, and that blog) are 1) your payload mass, 2) Tsiolkovsky rocket equation, and 3) your rocket engine's Isp. – uhoh Feb 9 '19 at 13:54
• @Hobbes posted an answer to a recent question that I think has what you need in it. It shows a nice chart of how much velocity is needed to travel between any 2 points in the solar system. It shows well the relative difficulty of getting to low Earth orbit vs traveling elsewhere. Re: Heinlein's quote something like "Once you are in low Earth orbit you are halfway to anywhere." The question is here: space.stackexchange.com/questions/34085/… As uhoh says you also need payload and engine information. – Organic Marble Feb 9 '19 at 15:53

The difficulty of traveling between two points in space is measured by "delta-V", i.e. the change in speed of your spaceship, or how much you need to accelerate it.

Once you're out of the atmosphere, you can coast endlessly as there is no friction. So to travel from here to Mars, you burn lots of fuel to get into Earth orbit, then you burn some more to leave Earth's orbit on a trajectory to Mars, and then you coast for 3-6 months until you get near Mars.

Here is a map of the Solar system that shows the delta-V to get to various places:

To calculate the amount of fuel you need from a delta-V figure, you need the Tsiolkovsky rocket equation:

$$\Delta v = I_{sp} \ g \ \ln\left(\frac{m_i}{m_f}\right)$$

$$\Delta v$$ is delta-v – the maximum change of velocity of the vehicle (with no external forces acting).
$$m_0$$ is the initial total mass, including propellant, also known as wet mass.
$$m_f$$ is the final total mass without propellant, also known as dry mass.
$$I_{sp}$$ is specific impulse, a measure of how efficient the rocket engine is. $$g_0$$ is standard gravity = 9.80665 m/s2
ln is the natural logarithm function.

In your case, $$\Delta v$$ and $$m_f$$ are known, you have to choose an engine and find its $$I_{sp}$$ and then you can calculate $$m_0$$. The difference between $$m_0$$ and $$m_f$$ is the amount of fuel you need to burn.