Problem $4$: rocket equation $(10$ pts$).$ A spacecraft in low earth orbit is subjected to very small dragforces due to the low density remnants of the atmosphere at those altitudes. Over time, these forces canlower the orbital altitude of the spacecraft such that it needs to re$-$boost itself on a regular basis. Thespacecraft mass is $500$ kg$,$ and its thrusters have an exhaust velocity of $2900$ m$/$s$.$ If the spacecraft needs toraise its apogee every $3$ months with a V impulse of $5$ m$/$s$,$ and the desired spacecraft lifetime is $20$ years,how much propellant must it carry to perform these regular re$-$boost operations? Note that the spacecraftis already at the orbit when using these propellant.