$3)$ Two atomic clocks are synchronized on the ground. One is placed on a jet and sent around the Earth above the equator at an altitude of $30,000$ m and speed of $700$ m$/$s $($Mach $2).$ a$)$ Approximately how long does it take the jet to circle the Earth once? $($Show work$)\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ b$)$ What is the numerical value of the Lorentz factor $$ for the velocity of the jet? $($include at least $15$ significant digits!$)$ Note that your calculator probably does not have $15$ digits, so use the trick given in Example $37\mathrm{.}2$ in your text book. $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ c$)$ According to Special Relativity and assuming the jet moves while the ground clock is stationary, what is the difference in time between the two clocks when the jet arrives back at the take off point? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$s d$)$ Is there a significant difference between the watches for a globe$-$trotting politician and her spouse who stays behind after she has circled the globe $20$ times at Mach $2?($Consider anything less than $1$ second to be negligible.$)$