Planet $\backslash ($ X $\backslash )$ rotates in the same manner as the earth, around an axis through its north and south poles, and is perfectly spherical. An astronaut who weighs $943\mathrm{.}0$ N on the earth weighs $910\mathrm{.}0$ N at the north pole of Planet X and only $840\mathrm{.}0$ N at its equator. The distance from the north pole to the equator is $\backslash (18,850\backslash$mathrm$\{$~km$\}\backslash ),$ measured along the surface of Planet $\backslash ($ X $\backslash ).$

If a $\backslash (45,000\backslash$mathrm$\{$~kg$\}\backslash )$ satellite is placed in a circular orbit $1000$ km above the surface of Planet X $,$ what will be its orbital period?

Express your answer in seconds.