Question

Demonstrate how you can derive our 9.8m/s^2 from Newton's general law of gravity.

Answer 1

Answer:

$g=G\frac{m_E}{r^2}$

Explanation:

Using Newton's Law of Universal Gravitation, we can write:

$F=G\frac{m_E}{r^2}$, where $G$ is gravitational constant $6.67\cdot 10^{-11}$, $m_E$ is Earth's mass, and $r$ is Earth's radius.

Using these measured values, we have:

$F=6.67\cdot 10^{-11}\frac{5.97\cdot 10^{24}}{(6.38\cdot10^6)^2},\\g\approx \fbox{ 9.8\:\mathrm{m/s^2} }$.