Course content > Kinds of Forces > Gravitational Forces

Prerequisites

• Formulation of Newton's Laws as foothold principles
• Gravity
• Flat-earth gravity

In our discussion of flat-earth gravity we learned that the reason all objects accelerate the same (as long as air resistance doesn't have a significant effect) when they are unsupported --dropped or thrown-- near the surface of the earth is that the force of gravity is proportional to the object's mass. It seems like the earth is pulling down on each piece of the object with the same force, so bigger objects are pulled down with a bigger force.  If we can ignore air resistance then the only force on an unsupported object is its weight so

a = F^net/m = -mg/m = g

Since the force of the earth pulling on the object is mg, then g = W/m has units of N/kg, which conveniently for describing falling bodies, turns out to be the same as the units of acceleration, m/s².

If we are going to restrict all our considerations to motion near the surface of the earth, the above discussion is sufficient. We can just leave "g" as a fixed number associated with the force of gravity. But if we are going to do rocket science and do interplanetary travel, then we have to take into account the idea that the force of gravity changes with position. We would have to allow g to be a function of position: g(x,y,z), where (x,y,z) represents the point in space where we are measuring a gravitational effect. Since the gravitational force have a direction, we should really write these as vectors:

This is a funny kind of mathematical object -- a vector function of a vector. We call it a field and we refer to the vector function, g, as the gravitational field.

What it means mathematically is that we have three functions: the x component of g, the y component of g, and the z component of g, and they are each functions of the three variables that determine the position we are looking at:

What it means physically is:

If we have a gravitational field  it means that if we put an object of mass m at the position labeled by the vector, r, then the object feels a gravitational force equal to mg.

One way of representing this is to put an arrow at every point in space pointing in the direction of the gravitational force an object would feel if it were placed there. This allow us to focus not only on the object t