A Newton is the SI measure of force. It is defined as the force required to move $1$ kg at a rate of $1$ m$/$s$\mathrm{²}($so $1$N$=1$kg$.$m$/$s$\mathrm{²}).$ The core stage of NASAs Artemis $1$ rocket uses $4$ RS$-25$D engines, each of which produces $10$x$10\mathrm{³}$ kN of thrust $(=$force$).$ Artemis $1$ has a mass of $5\mathrm{.}75$ million pounds, and is $322$ ft tall. Artemis $1$ reaches earth orbit after $8$ minutes and $30$ seconds at which time it ejects its core engines:

a$.$ What velocity, in m$/$s$,$ is Artemis $1$ traveling when it reaches orbit? $($ignore earths gravity since its effect is negligible$)$

b$.$ Assume that no further force is applied after ejection of the core engines and that Artemis $1$s velocity therefore remains constant. The circumference of the earth at orbit altitude is $25,000$ miles. How long will Artemis $1$ take to orbit the earth?