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.
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 $-0.7\,\mathrm{km^2/s^2}$.
