NEWTONIAN GRAVITYPHYSICS GRADE 112016

Basic CompetencyDapat menginterpretasikan hukum-hukum Newton tentang gerak dan gravitasi serta penerapannya, dan menyadari adanya keteraturan gerak planet dalam tata surya.

Law of Falling BodiesAll falling bodies experience the same gravitational acceleration

Law of Universal GravitationGravity is an attractive force between all pairs of massive objects Gravitational force is proportional to the masses, and inversely proportional to the square of the distance between them.

(The Law of Ellipses)(The Law of Equal Areas)(The Law of Harmonies)

The Law of Falling Bodies• Prior to his telescopic work, Galileo performed

fundamental research on motion. Explored the rate of falling bodies by dropping different weights, or sliding them down inclined planes.

• Law of Falling Bodies • In the absence of air, heavy objects and light

objects fall at the same, constant rate of acceleration

GarvitationIsaac Newton, in his Principia, formulated the Law of Universal Mutual Gravitation: • Gravity is an Attractive force: It draws massive

objects closer together • Gravity is a Universal force: It operates

everywhere in the Universe. • Gravity is a Mutual force: It works between pairs

of massive objects.

Gravitational Force The Force of Gravity between any two objects depends only upon: • The masses of the two objects: • More massive objects exert a stronger the

gravitational force. • The distance between them: • The force gets stronger as the two objects move

closer together. • The force gets weaker as the two objects move

farther apart. • It does not depend on the shapes, colors, or

compositions of the objects.

General Equation

The Law of Universal Gravitation

Determine the constant G

Cavendish Balance

Resultant of Gravity Force

Gravity Fielda gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body

The Fall of an Apple.

Stand on the Earth and drop an apple. • What is the force of the Earth on the apple? • F = GMearth Mapple/Rearth

2 What is the apple's acceleration (Newton's 2nd Law of Motion):

• aapple = F/Mapple = GMearth/Rearth2 = 9.8 meters/sec2

Note that the mass of the apple (Mapple) had divided out of the equation. This means that the acceleration due to gravity is independent of the mass of the apple, just like Galileo had shown earlier.

Strength of Gravity FieldGravity force over mass for a testing

mass m.

Equal and Opposite ReactionsNewton's Third Law of Motion states that all forces come in equal yet opposite pairs • What force does the the apple apply in return upon the

Earth? • F = GMearth Mapple/Rearth

2 How much does the Earth accelerate towards the apple?

• aearth = F/Mearth = GMapple/Rearth2 This can be rewritten to give

the acceleration of the Earth in terms of the acceleration of the apple towards the Earth as aearth = aapple x (Mapple/Mearth) where aapple=9.8 meters/sec2, and the ratio of the Mass of the apple to the Mass of the Earth is very small number. For a typical 200g apple, this works out to be about 10-25 meters/sec2, a very tiny acceleration.

What is the strength of gravity field on the earth surface?

Earth Surface

Earth center

rA = R and rB = (R + h)

Comparison the strength of gravity field between two planets

Speed to orbit

Geostationary Orbit

The Mass of the Earth• We can directly measure the acceleration of

gravity at the surface of the Earth by dropping objects and timing their fall (e.g., like was done by Galileo). We find a = 9.8 meters/sec2 We can also measure the radius of the Earth using geometry (Eratosthenes):

• Rearth=6378 kilometers = 6,378,000 meters

• Combining these together using Newton's formula for the Gravitational Force allows us to estimate the mass of the Earth, as follows:

• This is an example of one of the powerful implications of Newton's Law of Gravity: It gives us a way to use the motions of objects under the influence of their mutual gravitation to measure the masses of planets, stars, galaxies, etc.

Kepler’s LawFirst Law

Second Law

Third Law

(1) Planets move around the Sun in ellipses, with the Sun at one focus

(2) The line connecting the Sun to a planet sweeps equal areas in equal times.

(3) The square of the orbital period of a planet is proportional to the cube of the mean distance from the Sun

Correlation between Kepler’s Law and Newtonian Gravity

k = 2.97 x 10-19 s2/m3 

Fnet = (Mplanet * v2) / R Fgrav = (G* Mplanet * MSun ) / R2

(Mplanet * v2) / R = (G* Mplanet * MSun ) / R2

(Mplanet * 4 * pi2 * R2) / (R • T2) = (G* Mplanet * MSun ) / R2

T2 / R3 = (Mplanet * 4 * pi2) / (G* Mplanet * MSun )

T2 / R3 = (4 * pi2) / (G * MSun )

HW:1. A 15 kg object orbits the planet Mars at an

altitude of 200 km. What is the weight of the object if Mars has radius of 3,430 km and a mass of 6.34 x 1023 kg ?

2. If a planet's orbital period is 10 years, what is its average distance from the sun?

3. The average orbital distance of Mars is 1.52 times the average orbital distance of the Earth. Knowing that the Earth orbits the sun in approximately 365 days, use Kepler's law of harmonies to predict the time for Mars to orbit the sun.

ObjectivesDetermine the gravity force of some masses

Order:1. Make 6 groups2. Discuss the problem in some position of the

masses

12

3

45

6Choose your position

Position 1

EQUILATERAL TRIANGLE

R = 1 m

F exerted on C ?

A B

CMass of :A = 30 KgB = 25 KgC = 10 Kg

Position 2

R = 2 m

F exerted on A and B ?

A B

Mass of :A = 20 KgB = 10 Kg

Position 3

R = 7 m

Position of C ?

A

B

Mass of :A = 12.5 KgB = 2 KgC

FC = 0 N

Position 4

ISOSCELES TRIANGLE

R = 2 m

F exerted on C ?

A B

CMass of :A = 90 KgB = 75 KgC = 50 Kg

R = 2 m

Position 5

R = 1.2 m

F exerted on C ?

A

B

Mass of :A = 8 KgB = 2 KgC = 1 KgC

R = 0.4 m

R = 0.8 m

C

A B

D

Mass of :A = 25 KgB = 36 KgC = 3 KgD = 16 Kg

F exerted on C ?

( 0 ; 5 )( 4 ; 5 )

( 4 ; 0 )

Position 6