What is the Difference between gravitational constant and acceleration due to gravity?

Answer 1

The acceleration due to gravity in the neighborhood of some mass is:

A = G m/R2

A = the acceleration of gravity
m = the mass of the mass
R = your distance from its center

==> G is the "gravitational constant".

Without it, you would know that the acceleration is 'proportional' to the mass of the mass, and 'inversely proportional' to the square of your distance from it. But you couldn't calculate an actual number without a 'proportionality constant'. That's what 'G' is.

A More Complete Answer:

The gravitational constant is a universal number that applies equally in all places, at all times, and upon all objects. It is expressed as:

• 6.67300 × 10-11 m3 kg-1 s-2

Acceleration due to gravity is the phenomenom in which all masses are attracted to all other masses. The force due to gravity is expressed as:

• Fg = Gm1m2/R2

where:

• Fg is the force due to gravity;
• G is the universal gravitational constant, above;
• m1 is the mass of the first object;
• m2 is the mass of the second object; and
• R is the distance from the centers of the two objects.

Acceleration is expressed as

• Ag = Fg/m1

where:

• Ag is the acceleration due to gravity;
• Fg is the Force due to gravity, from the equation above; and
• m1 is the mass of the object being accelerated.

Subsituting the equation for the force due to gravity (Fg) in the above equation for acceleration due to gravity (Ag), we get:

• Ag = Gm2/R2

Remember that m2 is the mass of the other object (say, planet Earth). Notice, too, that m1 (your mass) cancels out completely. So the acceleration of your body due to gravity depends on the mass of planet Earth, but does not at all depend upon you own mass, or weight. That means that all things, regardless of how heavy or light, experience the same acceleration due to gravity at sea level on planet Earth.