A spacecraft transfers from a circular orbit with a radius of $r_a$ to another circular orbit with a radius of $r_b,$ taking $5$ hours and $15$ minutes for the transfer. The semi

$x$

minor axis of the transfer orbit was $16,639km.$ For the two tangential burns, the total velocity increment required was $3,936\frac{m}{s}.$ Before the transfer, its original velocity was $7,791\frac{m}{s}.$ Find:

$(1)$ The eccentricity of the transfer orbit

$(2)$ The velocity increment required for the second burn

$(3)$ The radius of orbit $B$

The gravitational constant G is $6\mathrm{.}67430{10}^{-11}{m}^{3}k{g}^{-1}s,$ the mass of Earth is $5\mathrm{.}972{10}^{24}kg,$ and the standard gravitational parameter,

Ans: e$=0\mathrm{.}730,$ delta V$=1478\mathrm{.}43$m$/$s$,$ rb$=42160$ km