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Newtons Law of Universal Gravitation

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Newton's Law of Universal Gravitation. If one of the masses doubles the force doubles. If the ... Comets have the most elliptical orbits. Halley's comet ... – PowerPoint PPT presentation

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Title: Newtons Law of Universal Gravitation


1
Newtons Law of Universal Gravitation
  • If one of the masses doubles the force doubles
  • If the distance doubles the force decreases to
    1/4

2
What does the gravitational force look like as a
function of distance?
3
What is a year and a day? (write this down!!)
  • A year time to travel an orbit (measured in
    Earth years)
  • A day- how long it takes a planet to rotate on
    its axis
  • A.U. - Astronomical Unit -
    distance from Earth to sun

4
Satellites
  • Satellites are bodies in orbit around a central
    point.
  • The moon is a satellite of Earth and Earth is a
    satellite of the Sun.
  • Most satellites are the result of passing objects
    that get caught by the pull of a larger body and
    are not moving fast enough to get away.

5
Speed life or death
  • Too slow, the satellite will get pulled into the
    planet and crash into it. This is how planets
    are able to clear their orbital path.
  • Just right, it enters into an elliptical orbit
    around the body.
  • Too fast, it just shoots on by with a change in
    its path.

6
Keplers Laws
  • How can we describe how the planets move?
  • Decades of observations Math SUCCESS

7
Johannes Kepler
  • 1571-1630
  • Made many observations of the motions Mars
  • Supported Galileo
  • Kepler didnt know why his Laws workeda law
    summarizes observations

8
Drawing an ellipse
  • The black line is a piece of string
  • The thumb tacks are the foci of the ellipse

9
Keplers First Law
  • Planets travel in elliptical orbits about the sun
  • The sun is at one foci of the ellipse
  • Eccentricity (e) is used to describe the shape.

10
Orbits in the Solar System
  • The planets have nearly circular orbits
  • Icarus, an asteroid, has a very elliptical orbit
  • Comets have the most elliptical orbits

11
Halleys comet
planet will move from East to West across the sky
12
  • Retrograde motion planet will move from East to
    West across the sky but occasionally move West to
    East- caused by differences in speed of orbit

13
An edge on view of the solar system
14
First Law
  • Keplers First Law was developed from the data he
    collected.
  • It explained the Retrograde motion observed for
    planets in the sky.
  • It was the first relationship that did not have
    special conditions for various times of the year.

15
Keplers Second Law
  • The planets sweep out equal areas in equal times
  • The planets move faster on the side of the orbit
    closer to the sun
  • The planets slow as they get further from the sun

16
Keplers Third Law
  • The square of the period of the rotation is
    proportional to the cube of the semi-major axis
    of the ellipse.
  • For every body orbiting the same foci, the ratios
    of T2/R3 are equal to each other.
  • For all bodies in orbit around the sun,

17
Semi-major axis
  • The arrow represents the semi-major axis.

18
Keplers Third Law
19
Does Keplers 3rd Law Work?
  • Astronomical unit A.U. average distance
    between the earth and the sun
  • A.U. 150 million km or 93 million miles
  • 1 year period of Earths orbit
  • T2 R3 if T is in years and R is in A.U.
  • ALSO written as P2 D3 , P period, and D
    distance from sun

20
Does Keplers 3rd Law Work? T2 R3
21
So What?
  • Kepler didnt know why his laws worked! Remember
    a law just describes a relationship, it does not
    tell you why.
  • Newton was able to show that he could derive
    Keplers Laws from Newtons three laws and the
    theory of universal gravitation.
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