what is the gravitational constant

Question

we are doing a science fair project with gravitational potential energy and are wondering what exactly is the gravitational constant

Answer 1

The force of gravity between two objects is:

 

F = G*m₁m₂/r²

 

Where F is the force, m₁ and m₂ are the masses of the two objects, r is the distance between the two objects, and G is the gravitational constant.  The value of G is:

 

G = 6.67384 x 10^-11 m³/kg*sec²

 

At the surface of the Earth, the force on any object due to Earth's gravity can be approximated by the equation:

 

F = mg

 

Where m is the object's mass and g is the acceleration due to gravity at the Earth's surface:

 

g = (G*M_earth)/Radius_earth) = -9.8 meters/sec² = -32 feet/sec²

 

The potential energy of any object near the surface of the earth is given by:

 

Potential Energy = mgh

 

Where m is the object's mass, g is the acceleration due to gravity (-9.8 m/sec²) and h is the object's height above the surface (in meters).  So an 80 kg man standing on a ladder 2 meters above the surface has a potential energy of:

 

P.E. = (80 kg)(-9.8 m/sec²)(2 m) = -1568 joules

 

Where joules is the unit of energy in the mks (meters-kilograms-seconds) system of units.