Figure $1$: Geocentric Elliptical Orbit

Problem $2(30$ points$)$: The geocentric elliptical orbit shown in Fig $1$ has eccentricity $e$ and period $T.$

$($a$)$ In terms of $e,T,$ and the angles $$ and $($in radians$),$ show that the time to fly point $1$ to point $2$ on the ellipse is

$t=\frac{T}{2}(--2$ecos$(\frac{+}{2})sin(\frac{-}{2})).$

$($b$)$ Calculate the time to fly from perigee to $B,$ located on the minor axis $($answer in terms of $e$ and $T).$