$($a$)$ Explain the concept of ablative cooling and its application to solid$-$fuelled rockets, giving

examples of ablative materials suitable for $($i$)$ nozzles and $($ii$)$ seals.

$($b$)$ The International Space Station has a mass of $420{10}^{3}kg$ and orbits at a speed of

$7\mathrm{.}6km{s}^{-1}$ relative to the Earth. A change in speed of $V=3m{s}^{-1}$ is required to

boost the altitude of the station, and a solid$-$fuelled rocket motor is to be used. Using

the data in the table below, and assuming negligible casing mass and constant burning

rate exponent, calculate:

i$.$ The mass of propellant required to achieve this velocity change, assuming $V=$

$v_{e}ln(\frac{M_0}{M_f}),$ where $M_0$ is the initial mass and $M_f$ is the final mass of the spacecraft.

ii$.$ The burning rate of propellant in $mm{s}^{-1}.$

iii. The chamber pressure during the burn, in $Pa.$

Table $2$: Table for Question $4$

$($c$)$ What is meant by a plateau burning propellant? Can plateau burning characteristics

be achieved in practice?