Answer to Question #204475 in Physics for Ronrick

Question

What is the acceleration due to gravity at a distance from the center of the earth which is equal to diameter of the earth

Answer 1

The acceleration due to gravity is given as follows:

$$g = G\dfrac{M}{R^2}$$

where $G \approx 6.67\times 10^{-11} \dfrac{m^3}{kg\cdot s^2}$ is the gravitational constant, $M \approx 5.97\times 10^{24}kg$ is the mass of the Earth, $R$ is the distance from the center of the Earth. Substituting $R = 2\cdot 6.37\times 10^{6}m$ (diameter of the Earth), obtain:

$$g = G\dfrac{M}{R^2}\\ g = 6.67\times 10^{-11}\cdot \dfrac{5.97\times 10^{24}}{(2\cdot 6.37\times 10^{6})^2} \approx 2.45\space m/s^2$$

Answer. $2.45\space m/s^2$.