Answer to Question #247607 in Physics for Tithi

Question

What is meant by acceleration due to gravity? Discuss the variation of acceleration due to gravity with (i) altitude, (ii) depth, and (iii) rotation of the earth. Define the escape velocity. Calculate the expression of the escape velocity.

Answer 1

The acceleration due to gravity is a property of massive objects that defines how quickly other bodies bodies will accelerate falling in the vicinity of the massive object (for example, Earth).

The acceleration due to gravity decreases with altitude, increased with depth, it is smaller near the equator and slowly increases to the maximum value at the poles because the speed of rotation there is zero.

The escape velocity is the initial velocity that a body needs to have to escape the gravitational attraction of the Earth and become a satellite of the Sun:

$$v=\sqrt{\frac{2GM}R}=\sqrt{\frac{2(6.673·10^{-11})(6·10^{24})}{6378000}}=11205\text{ m/s}.$$