# Energy use of Asteroid Redirect Robotic Mission (ARRM)?

In the ARRM feasibility Study Table 4, parameters of four different options (three different launchers and different trajectories) are gathered. What would be the total energy use of a mission like this (if I would choose for example "the Direct drive 1" with Falcon Heavy)?

Is it possible to just use the specific energy of hydrazine and then also calculate the energy use during launch? But what about SEP? Where do I get a exhaust velocity ($v_e$) for a ion thruster? And could I then still use the Energy equation:

$$E = 0.5 \times m_1 \times (e^{\Delta v/v_e}-1) \times v_e^2$$

$m_1$ would then be the ARRV and the whole asteroid (ARRV having negligible mass compared to the 400 000 kg chunk of an asteroid).

$\Delta v$ would just be summed up?

I'm well aware of the fact that "energy use" is a bit vague and not very practical to look at in space exploration, but to tell you the truth, this is what my thesis supervisor expects from me... Luckily in "order of magnitude" level though as whole space exploration is far from my own studies. ] This whole question was a spin off from (How much energy is required to send a payload of 40 t from Earth's surface to LEO?)

Thanks if someone has some tips to throw. :)

• From the paper: "An Isp of 3000 s with a 60% efficiency for the electric propulsion (EP) system was used". The exhaust velocity is $g I_{sp}$. Table 4 gives you all the masses and $\Delta V$'s you need. – Mark Adler Oct 22 '14 at 2:38
• So I would get Ve = 0.6 * 3000 s * 9.81 m/s ? Am I supposed to use g0 even though the system is in space and not on sea level? (This is probably a silly question...) – Nina K Oct 22 '14 at 6:42
• No, the 60% allows you to compute the input energy from the output energy. The exhaust velocity is what I said. Yes, you use Earth g. It is simply a conversion factor from English to Metric units. – Mark Adler Oct 22 '14 at 6:49