# How can I calculate the Characteristic Energy to Sun-Earth L1?

Alternatively, does anyone know it?

I'm asking in regards to the upcoming DSCOVR (Deep Space Climate Observatory) mission scheduled to launch aboard a Falcon 9 v1.1 rocket in January 2015. DSCOVR is 507 kg in mass and will be headed to the Sun-Earth L1 (SEL1).

I'm trying to calculate the payload fraction of the rocket based off the C3 (characteristic energy) involved. I'm assuming it'll be greater than 0 km2/s2 and less than 12.2 km2/s2, which is the C3 of MAVEN to Mars.

## 1 Answer

Actually, it's less than zero. The Lagrange points are still effectively captured by the Earth, so you have not escaped. This paper states the required $C_3$ as $-0.7\,\mathrm{km^2/s^2}$.

If we ignore the Sun, the $C_3$ required to get to the altitude of the S-E L1 point is:

$$C_3=-{2\mu\over{r_a+r_p}}$$

where $\mu$ is the $G M$ of the Earth and the Moon, and $r_a$ and $r_p$ are the apoapsis (L1) and periapsis (LEO). The result is $C_3=-0.54\,\mathrm{km^2/s^2}$. However the Sun is there and helps, hence the $C_3$ of $-0.7\,\mathrm{km^2/s^2}$.