$($a$)$ Explain the concept of gravity loss in the context of electric propulsion

missions.

$($b$)$ Explain $($in general terms$)$ why there is an optimum exhaust velocity for

a given electric propulsion mission.

$($c$)$ The mass of the electrical power system, $M_E,$ is related to the power

output $P,$ the thruster efficiency $,$ and the power$-$to$-$mass ratio of the

power system, $,$ by the expression

$M_E=\frac{P}{}.$

Beginning with this relationship, show that the ratio of the mass of the

electric power supply to the mass of propellant $(\frac{M_E}{M_P})$ can be ex$-$

pressed as

$\frac{M_E}{M_P}=\frac{v_e^2}{2t},$

where $v_e$ is the exhaust velocity and $t$ is the burn time.

$($d$)$ An interplanetary mission with a payload mass of $1800kg,$ requires a

$V$ of $4km{s}^{-1}$ for a post$-$launch manoeuvre. Mission designers are

considering either a chemical rocket engine using storable propellant, or

solar electric propulsion using a Hall thruster powered by solar panels and

using Xenon as the propellant. The dry mass of the two propulsion units

$($excluding power supply in the case of the Hall thruster$)$ is the same.

Using the data provided in Table $1($overleaf$),$ calculate:

i$.$ the total $($wet$)$ mass of the rocket propulsion system versus that of

the electric propulsion system

ii$.$ the burn line for the rocket propulsion system versus that of the

electric propulsion system