The gravitational force F between two bodies of respective masses M and m and distance R is
[tex]F = G\dfrac{Mm}{R^2}[/tex]
where G ≈ 6.7 × 10⁻¹¹ m³/(kg•s) is the universal gravitational constant.
8.1.1. Let M = mass of Earth, m = mass of person, and R = radius of Earth. At point C, the distance between the center of the Earth and the person is 3R, so the gravitational force has magnitude
[tex]F = G \dfrac{\left(6.0\times10^{24}\,\mathrm{kg}\right) \left(50\,\mathrm{kg}\right)}{3\times6.4\times10^6\,\mathrm m} \approx \boxed{1.0\times10^9 \,\mathrm{N}}[/tex]
8.1.2. Using the same values for M and m, now take R = radius of Earth + 10³ m. Then the gravitational force is
[tex]F = G \dfrac{\left(6.0\times10^{24}\,\mathrm{kg}\right) \left(50\,\mathrm{kg}\right)}{\left(6.4\times10^6+10^3\right)\,\mathrm m} \approx \boxed{3.1\times10^9 \,\mathrm{N}}[/tex]
