# How do I calculate the characteristic energy for a rocket to near rectilinear halo orbit where the Deep Space Gateway is going to orbit the Moon?

How do I calculate the characteristic energy for a rocket to near rectilinear halo orbit (NRHO) where the LOP-G or the Deep Space Gateway is going to be orbiting the Moon? Or if someone already has a number, it would be appreciated!!

I am trying to find the payloads different rockets can take to the NRHO. I already have the C3 vs payload mass plots for the rockets I want. I just need the exact amount of C3 required to get there. I know it will be negative, since we are not leaving Earth SOI. Thank you for any and all help. Sources are appreciated.

Reading the linked questions, answers, and references (thanks @uhoh), particularly R. Whitley and R. Martinez, 2015, Options for Staging Orbits in Cis-Lunar Space and this figure: Leads me to believe that getting to a NRHO is much like an 'Apollo-style' lunar transfer (i.e., in plane, Hohmann-ish transfer orbit). The only difference comes in targeting the lunar flyby over one of the poles to displace the spacecraft out of the Earth-Moon plane (hence the term 'halo') and the 'capture' burn into the NRHO is slowing the spacecraft down (from its lunar escape trajectory). This removes a lot of 3-body dynamics shenanigans from the problem.

A good, quick way to calculate the required C3 is to pretend your rocket is performing a Hohmann transfer to the Moon's (average) orbital distance, 384400 km. From a 250 km low Earth parking orbit:

$$C3=-\frac{GM}{a}, a=\frac{6378km+250km+384400km}{2}=195514km$$ $$C3=-2.0\frac{km^2}{s^2}$$

I recall a professor (whose graduate research was designing lunar landers) saying a C3 value of $$-1\frac{km^2}{s^2}$$ is commonly used in early analyses.

This Apollo By the Numbers archived webpage (linked from the TLI Wikipedia) has the Apollo C3 data (converted to nice units):

Mission C3 ($$\frac{km^2}{s^2}$$)
Apollo 8 -1.5
Apollo 10 -1.3
Apollo 11 -1.4
Apollo 12 -1.8
Apollo 13 -1.4
Apollo 14 -1.7
Apollo 15 -1.5
Apollo 16 -1.6
Apollo 17 -1.7

I don't know where you got the performance information but I hope it is NASA Launch Services Program Launch Vehicle Performance Website and the SLS mission planner's guide. Side note, New Glenn and Vulcan are now on the NLSP performance website!

• Cool, so that's how they'll enter orbit.
– uhoh
Jun 16, 2021 at 14:25