Newton’s Law of Universal Gravitation

AP Physics C

Isaac Newton

• 1666, England (45 years after Kepler).

Questions• If the planets are orbiting the sun , what force is

keeping them in orbit?• What force keeps the moon in its orbit?• Could the force of gravity be universal?

Newton’s Law of Universal Gravitation

• Any two objects attract each other with a gravitational force, proportional to the product of their masses and inversely proportional to the square of the distance between them.

• The force acts in the direction of the line connecting the centers of the masses.

Note

• Newton’s Law is universal, it acts between any two masses regardless of how large (planets, stars) or how small (particles, atoms, neutrons) they are.

• The gravitational force is weaker than the electrical force.

• The gravitational force is one of the 4 fundamental forces in nature.

Newton’s Law of Universal Gravitation

http://scienceblogs.com/startswithabang/upload/2009/07/meet_our_second_moon/400px-NewtonsLawOfUniversalGravitation.svg.png

The Value of G.

G= 6.67 x 10-11 N m2 / kg2

Vector Form of Newton’s Law of Universal Gravitation

1 212 122

ˆmm

Gr

F r

Note

• F12 = -F21 Action-reaction pair.

• Gravitation is a field force.

• Masses are considered point masses.

Henry Cavendish’s

experiment determined the proportionality

constant G

in 1798.

http://www.newscientist.com/data/images/archive/1639/16390101.jpg

Change of Gravitational

Force with Distance

• Law of universal gravitation is known as an inverse square law.

Why does the moon not fall straight down onto the earth?

2

MM

vF

rThe gravitational force place

the role of the centripetal force.

Example Problem

• Two spheres of equal mass m are a distance d apart.

a)If the mass of one is doubled and the distance between them is reduced to ½d, how does the force change?b) If both masses are doubled and the distance is also doubled how does the force change?

Example

• An object that of mass 5kg is located at a planet that has 3 times the mass of the earth and half its radius. What is its weight on this planet.

The Gravitational Force Inside the Earth

• Varies linearly with the distance from the center of the Earth. geff = g r/ REarth

Ex: #3

• A 200kg object and a 500kg object are separated by 0.400m.a) Find the net gravitational force exerted by these

objects on a 50.0kg object placed midway between them.

b) At what position (other than an infinitely remote one ) can the 50kg object be be placed so as to experience a zero force?

Ans: a)2.50x10-5 N towards the 500kg object, b)0.245m

Ex: #5• Three uniform spheres are 2 kg, 4kg, 6 kg are

located as shown:

• Calculate the resultant gravitational force acting on the 4kg object.

• Ans: (-10i + 5.93j) x10-11 N

2kg

6kg

4kg

4m

3m