When the center of Earth is 2 × 1011 meters from the center of Mars, the force of gravity between the two planets is about 64.32 × 1014 newtons. The mass of Earth is about 6 × 1024 kilograms, and the mass of Mars is about 6.4 × 1023 kilograms. Using these values, estimate the gravitational constant.
+33616 $${\mathtt{G}} = {\frac{{\mathtt{64.32}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{14}}\right)}{\mathtt{\,\times\,}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{11}}\right)}\right)}^{{\mathtt{2}}}}{\left({\mathtt{6}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{24}}\right)}{\mathtt{\,\times\,}}{\mathtt{6.4}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{23}}\right)}\right)}} \Rightarrow {\mathtt{G}} = {\mathtt{0.000\: \!000\: \!000\: \!067}}$$
G ≈6.7*10-11 m3/(kg.sec2)
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+33616 $${\mathtt{G}} = {\frac{{\mathtt{64.32}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{14}}\right)}{\mathtt{\,\times\,}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{11}}\right)}\right)}^{{\mathtt{2}}}}{\left({\mathtt{6}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{24}}\right)}{\mathtt{\,\times\,}}{\mathtt{6.4}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{23}}\right)}\right)}} \Rightarrow {\mathtt{G}} = {\mathtt{0.000\: \!000\: \!000\: \!067}}$$
G ≈6.7*10-11 m3/(kg.sec2)
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