Newtons Law of Universal Gravitation

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Newtons Law of Universal Gravitation

• If one of the masses doubles the force doubles
• If the distance doubles the force decreases to
  1/4

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What does the gravitational force look like as a
function of distance?
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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
  

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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.

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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.

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Keplers Laws

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

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Johannes Kepler

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

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Drawing an ellipse

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

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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.

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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

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Halleys comet
planet will move from East to West across the sky
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• 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

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An edge on view of the solar system
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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.

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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

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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,

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Semi-major axis

• The arrow represents the semi-major axis.

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Keplers Third Law
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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

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Does Keplers 3rd Law Work? T2 R3
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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.