Question

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

Answer 1

`g=G(m_E)/(r^2)`

Step-by-step explanation:

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

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