Peoples Physics Concepts

http://www.ck12.org Chapter 6. Gravity

6.1 Universal Law of Gravity

• Use Newton’s Universal Law of Gravity equation to solve problems.


• Explain how the acceleration of gravity on Earth is calculated.

Students will learn to use Newton’s Universal Law of Gravity equation to solve problems. They will also learn how
the acceleration of gravity on Earth is calculated and a bit about gravitational fields in general.

Key Equations

• FG=Gmr^12 m^2 ; the force of gravity between an object with massm 1 and another object of massm 2 and a distance
  between them ofr.


• G= 6. 67 × 10 −^11 Nm^2 /kg^2 ; the universal constant of gravity


• g=Gmr 2 ; gravitational field strength or gravitational acceleration of a planet with massmand radiusr. Note
  that this is not really a separate equation but comes from Newton’s second law and the law of universal
  gravitation.


• Some data needed for the problems:

The radius of Earth is 6. 4 × 106 m

The mass of Earth is about 6. 0 × 1024 kg

The mass of Sun is about 2. 0 × 1030 kg

The Earth-Sun distance is about 1. 5 × 1011 m

The Earth-Moon distance is about 3. 8 × 108 m

Guidance

• When using the Universal Law of Gravity formula and the constantGabove, make sure to use units of meters
  and kilograms.


• The direction of the force of gravity is in a straight line between two objects. It is always attractive.


• Newton invented calculus in order to prove that for a spherical object (like Earth) one can assume all of its
  mass is at the center of the sphere (thus in his formula, one can use the radius of Earth for the distance between
  a falling rock and Earth).


• Newton’s Laws apply to all forces; but when he developed them only one was known: gravity. Newton’s
  major insight — and one of the greatest in the history of science — was that the same force that causes objects
  to fall when released is also responsible for keeping the planets in orbit.

Universal Gravity

Any two objects in the universe, with massesm 1 andm 2 with their centers of mass at a distancerapart will experience
a force of mutual attraction along the line joining their centers of mass equal to:

F~G=Gm^1 m^2

r^2

Universal Gravitation,