THE ARTEMIS PROJECT PRIVATE ENTERPRISE ON THE MOON Mission Design Tech Committee Section 6.7.3.1.
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## How to Calculate Mass Ratio for Flight from LEO to Lunar Surface

When you're designing a moon mission, you'll need look at how you're going to get your stuff to the moon. Let's assume you've figured out what you want to have on the lunar surface and how much that weighs. Given that starting point, here's how to calculate the amount of fuel you'll need to get it there from low earth orbit.

Once you know how much mass you need in LEO, you can review the list of launchers and figure out how you're going to get your payload up to orbit in the first place.

The tables below do this calculation for a simple mission example, flying one rocket from LEO all the way to the moon, to deliver a 100-lb payload the lunar surface, for three different rocket engines. See the notes and definitions for more details about how to use this information.

Rocket Equation Calculations

 Isp sec 460 444.4 260 Mf lbs 100 100 100 delta_V ft/sec 0 0 0 g ft/sec/sec 32.174 32.174 32.174 Mo lbs 386 405 1092 Delta_M lbs 286 305 992 Mass Ratio - 3.86 4.05 10.92

Rocket Motor Burns

 TLI 10000 ft/sec LOI 2800 ft/sec DOI 200 ft/sec Landing 7000 ft/sec Total 20000 ft/sec

To make it easy for you to import these numbers into your own spreadsheet program, I've included two versions of the file on line: leo-luna-example.csv and leo-luna-formulas.csv. The first file has the numbers from the tables above; the second one has the formulas.

You can open these files in your web browser and save them as text files. (If you click on the links, the files show show up in a new window in your browser.) Then start up your spreadsheet program and open them as a CSV (comma-delimited) files. The numbers and labels should show up in nice, neat columns. You're on your own for formatting.

The Rocket Equation

The real key to this calculation is the formula for the inverse rocket equation. It shows up in cells that look like this:

=D3*EXP(D4/(D5*D2))

If you look at which cells it's pointing at, you'll see that the formula is

Mo = Mf * EXP( delta_v / ( g * Isp ))

Definitions