UNIVERSAL GRAVITATION

THE PHYSICS OF GRAVITY FOR OUR UNIVERSE

 

"Every particle in the universe attracts every other material particle with a force that is proportional to the product of the masses of the two particles, and inversely proportional to the square of distance between their centers. The force is directed along a line joining their centers."
Seven Ideas that Shook the Universe-- Spielberg & Anderson

 

So far we have learned that...

  • Gravitational forces attract objects with mass & the bigger the mass the greater the attraction!
  • The gravitational forces are action/reaction pairs. The Earth pulls on the moon and the moon pulls on the Earth with an equal but opposite force!
  • Gravity pulls from the Center of Gravity of an object that is not a point mass!
  • The weight of an object on the earth is the gravitational force that the Earth exerts on the object. Scales measure normal force. The scale reading is often is the same as weight but will not be the same as weight if the scale is accelerating.
  • Weight pulls downward from the object toward the center of the Earth.
  • Weight varies for an object while mass does not change.
  • GPE = mgh (gravitational Potential Energy = mass x g x height above Earth's surface.

WHAT IS NEW! ... LEARN MORE

We introduce a concept of weight not confined to the planet Earth where weight = mg (g has a value of  9.81 m/s^2 at our location on this planet--Raleigh, NC). Weight may still equal mg BUT "g" has changed.
        Now we use the Universal Law of Gravitation.  Note the unit vector (with the hat)!    
  • Weight varies depending upon the mass of the planet and the distance to the center of the planet. This means "g" changes! "G" does NOT change and is always                       .
  • "G" was measured by Sir Henry Cavendish.

 
  • The unit vector for R is along the line connecting the two masses, pointing away from "pulling" mass toward the "pulled" mass, and has a magnitude of one!
  • GPE (or U) changes because the force of gravity is no longer constant (as with mgh). So we integrate:

       ORBITS

  • Centripetal force is the key here. Just replace F with centripetal force in the Universal Law of Gravity. Orbits are a direct result of the Universal Law of Gravitation!

       KEPLER'S LAWS

  • PLEASE NOTE THEIR IMPORTANCE! THEY ARE THE SHOULDERS OF THE GIANT UPON WHOM NEWTON CLIMBED!  LEARN ABOUT THE HISTORY!

    ESCAPE VELOCITY

  • To escape a planet of mass M a rocket of mass m must move very, very far away so that U becomes zero. Remember that energy is conserved so that Total Energy E = PE + KE = a constant.    
  • The minimum escape speed means that the final kinetic energy must also be zero! So the following equations describe the concept of escape velocity for a mass "m" from a planet of mass "M"
  • When we solve for the escape velocity we obtain the escape velocity equation.                        

Updated 02/05/06