# Question 05a3c

Jan 15, 2018

Acceleration due to gravity, g is defined as being the rate of change in potential per unit distance or g = (dV)/(dr

#### Explanation:

Equally you can call it the force per unit mass, so $g = \frac{F}{m}$ where force, F requires vector notation & spherical geometry so vec(F) = -G(m_1m_2)/vec(r^2

Thus vec(g) = -G(m_1)/vec(r^2#

So $g = - 6.67 \times {10}^{-} 11 \frac{319 \times 6 \times {10}^{24}}{11.2 \times 6.37 \times {10}^{6}} ^ 2$

Giving $g = 25.1 \frac{m}{s} ^ 2$

Another way of saying it is that the greater mass will increase g by 319 times and the increased radius will decrease it by ${11.2}^{2}$ times. $\frac{319}{11.2} ^ 2 = 2.54$ and $2.54 g = 24.9 \frac{m}{s} ^ 2$ so about correct!