$($Section $3\mathrm{.}7)$ Consider a satellite which is presently in a circular LEO with a radius of $6563$ km

and an inclination of $45.$ This satellite is to be delivered to a high circular equatorial orbit

with a radius of $12,756km($i$.$e$.r=2*r_e)$ using a combined Hohmann transfer and inclination

change maneuver. $($a$)$ Determine the first, second, and total velocity increments if the

inclination change at low orbit $($i$.$e$.i_1)$ is $0.$ Then, repeat for $i_1$ of $1$ to $45$ in $1$ increments.

Present your results in both tabular and graphical forms. Remember to justify your work by

showing the relevant equations which were used. $($b$)$ Determine the optimum inclination change

angle which minimizes the total velocity increment.Consider a satellite which $is$ presently $in$ a circular LEO with a radius $of6563km$ and $an$ inclination $of45.$ This satellite $istobe$ delivered $to$ a high circular equatorial orbit with a radius $of12,756km(i.e.r=2(re))$ using a combined Hohmann transfer and inclination change maneuver.

$(a)$ Determine the first, second, and total velocity increments $if$ the inclination change $at$ low orbit $(i.e.[Delta]i1)is0.$ Then, repeat for $[Delta]i1of1to45in1$ increments. Present your results $in$ both tabular and graphical forms. Remember $to$ justify your work $by$ showing the relevant equations which were used.

$(b)$ Determine the optimum inclination change angle which minimizes the total velocity increment.