ASTRONOMY 330

1
ASTRONOMY 330

• Lecture 2

2
Astronomy 330 Planetary Motions

• Ancients noticed some stars not fixed wrt. the
  background stars.
• They called them planets which comes for the
  Greek word for wanderer.
• They also noticed that the planets move in paths
  through the stars which is very close to the
  ecliptic, giving the zodiac constellations even
  more significanceAstrology was born

3
Astronomy 330 Planetary Motions

• The planets became associated with gods.
  Different cultures named them differently.
• The names we use for the planets come from the
  Roman pantheon.
• There are 5 planets easily visible to the naked
  eye Mercury, Venus, Mars, Jupiter and Saturn.

4
Astronomy 330 Planetary Motions (Mercury, Venus)

• Mercury is the fastest moving planet.
• Venus and Mercury are only seen in the morning
  and evening sky and not too far from the location
  of the sun on the celestial sphere.
• These planets reach a point called greatest
  eastern or western elongationThe maximum angle
  east or west of the location of the sun on the
  celestial sphere.
• 28 degrees for Mercury, 45 degrees for Venus

5
Astronomy 330 Greatest Eastward Elongation
6
Astronomy 330 Motions of Mars, Jupiter, and
Saturn

• Mars Jupiter and Saturn can have any elongation
  angle
• These planets undergo strange motions relative to
  the starsThey appear to reverse their directions
  and to undergo retrograde motions

7
Astronomy 330 Retrograde Motions
8
Astronomy 330Ptolemaic System

• Ptolemy lived 85 - 165 C.E.
• Geocentric system used for next 1,400 years
• Epicycles used to explain retrograde motions

Images on this page were copied from Nick
Strobel's Astronomy Notes. Go to his site at
www.astronomynotes.com for the updated and
corrected version.
9
Astronomy 330 Epicycles
Images on this page were copied from Nick
Strobel's Astronomy Notes. Go to his site at
www.astronomynotes.com for the updated and
corrected version.
10
Astronomy 330Copernicus

• Nicholaus Copernicus (1473-1543)
• Modern Originator of Heliocentric Sytem
• Sun at the center and planets go around it,
  explains retrograde motions more easily than
  Ptolemaic system

Images on this page were copied from Nick
Strobel's Astronomy Notes. Go to his site at
www.astronomynotes.com for the updated and
corrected version
11
Astronomy 330 Heliocentric System
Images on this page were copied from Nick
Strobel's Astronomy Notes. Go to his site at
www.astronomynotes.com for the updated and
corrected version
12
Astronomy 330Tycho Brahe

• Tycho Brahe (1546-1601)
• Made careful observations of planets
• Believed in geocentric system.
• Needed epicycle on top of epicycle to explain his
  observations

Images on this page were copied from Nick
Strobel's Astronomy Notes. Go to his site at
www.astronomynotes.com for the updated and
corrected version
13
Astronomy 330Kepler

• Johaness Kepler (1571-1630)
• Got access to Tycho Brahes data on his death bed
• Discovered Keplers laws of Planetary Motion

Images on this page were copied from Nick
Strobel's Astronomy Notes. Go to his site at
www.astronomynotes.com for the updated and
corrected version
14
Astronomy 330 Keplers Laws

• Law 1 -- The orbits of the planets are in the
  shape of ellipses with the sun at one focus.

15
Astronomy 330 The Ellipse
b
a
focus
d
a semimajor axis b semiminor axis e
eccentricity d/a
16
Astronomy 330 Keplers Laws

• Law 2 -- The planets sweep out equal areas in
  equal times as they execute their orbitsPlanet
  moves fast near the sun, slowly when its farther
  away.

Slow
Fast
17
Astronomy 330 Keplers Laws

• Law 3 -- The square of a planets Period is
  proportional to the cube of the semi-major axis
  of its elliptical orbit.
• P2 const. x a3
• Period -- The time it takes a planet to execute 1
  orbit

18
Astronomy 330 Properties of Orbits
Aphelion
Perihelion
1 Astronomical Unit Average distance of Earth
to Sun 1.5 x 1013 cm
19
Astronomy 330 Galileo

• Galileo
• With telescope provided proof of heliocentric
  hypothesis
• Discovered phases of Venus
• Discovered 4 moons of Jupiter

Images on this page were copied from Nick
Strobel's Astronomy Notes. Go to his site at
www.astronomynotes.com for the updated and
corrected version
20
Astronomy 330 Discussion Question

• If you were confronted with scientific evidence
  that one of your deeply held beliefs was
  incorrect or inconsistent, would you be able to
  give up that belief ?

21
Astronomy 330Special Positions of Inferior
Planet Orbits

• Mercury and Venus are inferior planetsthey orbit
  the sun inside the orbit of the earth
• Full phase is impossible in the geocentric
  system.
• Also, Galileo noted the crescent phases are
  brighter.

Superior Conjunction Appears full
Greatest Eastern Elongation Appears as a crescent
Inferior Conjunction Invisible or appears as spot
on the sun
Greatest Western Elongation Appears as a crescent
22
Astronomy 330Special Positions of Superior
Planets Orbits
Quadrature

• Planets which orbit the sun outside the Earths
  orbit are called superior planets

Conjunction
Opposition
23
Astronomy 330 But why do the planets move this
way ?

• We need some kind of theory to explain planetary
  motions, Keplers laws
• There must be some force which keeps planets on
  their curved paths, otherwise they would fly off
  into space, continue on straight lines.
• What is the nature of this force ?

24
Astronomy 330 Newton

• Issac Newton (1642-1727)
• Formulated laws of motion
• Formulated universal gravitation
• Invented the Calculus (along with Leibnitz)

Images on this page were copied from Nick
Strobel's Astronomy Notes. Go to his site at
www.astronomynotes.com for the updated and
corrected version
25
Astronomy 330 Newtons laws of motion

• Every body continues in its state of rest or
  uniform motion in a straight line unless it is
  acted on by an external force (Law of Inertia)
• The acceleration of a body is proportional to the
  force and is inversely proportional to the mass
  (F/m a or F ma)
• To every action there is an equal and opposite
  reaction (Forces come in pairs).

26
Astronomy 330 Universal Gravitation

• The gravitational force between two objects is
  proportional to the product of their masses and
  inversely proportional to the square of the
  distance between them.
• Fgrav GM1M2/R2
• G is Newtons gravitational constant Force is
  attractive

27
Astronomy 330 Keplers Laws explained

• How did Newton come up with this law of universal
  gravitation ?
• Notice that the force of the sun (M1) is equal
  but in an opposite direction to the force of the
  Earth (M2) the Sun.
• Newton was able to solve for the motion of a
  planet around the sun using Fma formula where F
  is the force of gravity. He was able to prove
  that only if the force falls off as the square of
  the distance does one get elliptical orbits !

28
Astronomy 330 Keplers laws explained
Change in Velocity acceleration
Velocity
Force of Gravity
29
Astronomy 330 Keplers 1st law modifiedAll
orbits are conic sections
30
Astronomy 330 Ellipses

• Circles have eccentricities of zero
• Ellipses have eccentricities less than 1
• Parabolas have eccentricities equal to 1
• Hyperbolae have eccentricities gt 1
• Circles and Ellipses are bound orbits
• Parabolas are bound, but at infinity
• Hyperbolae are unbound

31
Astronomy 330 Launching a satellite into Earth
Orbit
32
Astronomy 330 Launching a probe to Mars
Orbit of Mars
Orbit of Earth
Least energy orbit
Probe is launched with a velocity taking
advantage of velocity of earth least energy
orbit around sunReaches Mars roughly 6 months
after launch
33
Astronomy 330 Discussion Question

• How would we travel to Venus using the least
  energy ?

34
Astronomy 330Reading

• Read the rest of Chapter 1, Morrison and Owen
• Extra Optional Reading http//www.astronomynotes.
  com/history/s1.htm