PLANETARY ORBITS

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PLANETARY ORBITS

• Chapter 2

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CONIC SECTIONS
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PLANETARY GEOMETRY

• Definition of a Circle
• A Circle is a figure for which all points on it
  are the same distance from the centre.
• Definition of an Ellipse
• An Ellipse is a figure for which the sum of the
  distances from any point on the figure to two
  points inside the figure is always the same

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HOW to DRAW an ELLIPSE
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HOW to DRAW an ELLIPSE

• (ellipticity e distance between foci / major
  axis eEarth 0.02, eJupiter 0.05, eMercury 0.21)

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KEPLERS THREE LAWS
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KEPLERS THREE LAWS

• First Law
• The orbit of each planet is an ellipse with the
  Sun at one focus

Foci
Planet
Sun
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PLANETARY ORBITS
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KEPLERS THREE LAWS

• First Law
• The orbit of each planet is an ellipse with the
  Sun at one focus

• Second Law
• The line joining the planet and the Sun sweeps
  out equal areas in equal times.

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KEPLERS SECOND LAW
Area 1 Area 2
Area 2
Area 1
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FLASHCARD
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KEPLERS THREE LAWS

• First Law
• The orbit of each planet is an ellipse with the
  Sun at one focus

• Second Law
• The line joining the planet and the Sun sweeps
  out equal areas in equal times.

• Third Law
• The squares of the planets periods of
  revolution are in proportion to the cubes of the
  semimajor axes of their orbits

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KEPLERS THIRD LAW
(period)2 (distance)3
Eg. Mars p 1.88 year, d 1.52 AU
(1.88)2 (1.52)3
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KEPLERS THIRD LAW
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COMET HALLEYS ORBIT
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FLASHCARD
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FLASHCARD
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ORBITAL DATA
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KEPLERS THREE LAWS

• First Law
• The orbit of each planet is an ellipse with the
  Sun at one focus

• Second Law
• The line joining the planet and the Sun sweeps
  out equal areas in equal times.

• Third Law
• The squares of the planets periods of
  revolution are in proportion to the cubes of the
  semimajor axes of their orbits

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NEWTONS THREE LAWS
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NEWTONS THREE LAWS

• First Law
• Every body continues what it is doing (at rest
  or in motion in a straight line) unless acted
  upon by an outside force. (Note break here with
  tradition)

• Second Law
• Change in motion of a body is proportional to
  the force acting on it and is in the direction
  that the force is acting.

• Third Law
• For every action there is an equal and opposite
  reaction.

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NEWTONS UNIVERSAL LAW of GRAVITATION

• Force GM1M2/D2
• M1 and M2 are the masses of the two objects
• D is the distance between them
• G is a constant called the Gravitational Constant
• Newton found that the orbits derived from this
  force were exactly those found by Kepler
• Keplers 3rd Law becomes D3 (M1 M2) x P2