The centripetal acceleration:
[tex]a\text{ = 6 }\times10^{-3}m\text{/s}^2[/tex]The mass of the Earth:
[tex]m\text{ = }5.972\times10^{24}\operatorname{kg}[/tex]The Force needed for the earth to stay in the orbit is given as:
F = ma
[tex]\begin{gathered} F\text{ = }5.972\times10^{24}\times\text{ 6 }\times10^{-3} \\ F\text{ = }35.832\times10^{24-3} \\ F\text{ = 35.832 }\times10^{21} \\ F\text{ = 3.5832}\times10^{22}N \end{gathered}[/tex]Therefore, the force (F) needed for the earth to stay in the orbit is:
[tex]F\text{ = 3.5832}\times10^{22}N[/tex]