Perhaps the most$-$common gravitational calculation is to determine the "weight" of an object of mass $m_0$ sitting on the surface of the earth $($i$.$e$.,$ the magnitude of the gravitational attraction between the earth and the object$).$ According to Newton's law of universal gravitation, the gravitational force on the object is

$F_g=G(\frac{m_e{m}_o}{r_e^2})=(\frac{G{m}_e}{r_e^2})m_o$

where $m_e$ is the mass of the earth and $r_e$ is the distance between the object and the center of the earth $($i$.$e$.,r_e=$ radius of the earth $=6\mathrm{.}38{10}^{3}km).$

Part F

What is the value of the composite constant $(\frac{G{m}_e}{r_e^2}),$ to be multiplied by the mass of the object $m_o$ in the equation above?

Express your answer numerically in meters per second per second.