what is the importance of measuring the acceleration due to gravity

Question

Why is is important to measure the acceleration due to gravity and why does the value for  the acceleration due to gravity change in different places?

Answer 1

Just to expand on Asad's answer, remember that weight is a type of gravitational force. The general equation for a gravitational force between two masses is given by

 

Fg= (GM₁M₂)/R²

 

Where M1 and M2 are the two different masses, G is called the gravitational constant (this is different from g=9.8), and R is the distance between the two centers of mass of M1 and M2.

 

For instance, suppose you were M1 in outer space, and M2 was the mass of Earth. R would be the distance from your center of mass and the center of mass of the Earth (which is effectively the center of the planet). Now think of what would happen as you traveled from outer space to land on Earth's surface. M1 and M2 remain the same, but R will decrease until you land. Once you're on the surface, R has to stay fixed as the Earth's radius.

 

At this point, we can lump together some of the terms in the gravitational force--everything that pertains to YOU, and everything else that pertains to EARTH

 

Fg= [G*(M_earth/R²_earth)]*M_you. 

 

The first two products in [...] in the above equation are what get lumped together into gravitational acceleration g. It's "constant" insofar as the mass and radius of Earth tend not to change, but it is possible to affect R slightly by traveling to very high/low altitudes, or going to the poles or equator where the Earth flattens or bulges out because of its spin.

 

In general, this is also how you calculate the relative g for other planets (common question for AP, at least).

Answer 2

Since weight is m g, changing the acceleration due to gravity in various places would effect the apparent weight of objects and peoples. g is the indication of existing gravitational force on things.....