Announcements Wednesday Sept 13

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AnnouncementsWednesday Sept 13

• Observing tonight
• Meet at 730pm loading dock (across street from
  Breuggers, Iowa Ave.
• Meet at Field campus (Zack will lead)
• Bring jacket

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Lecture today (lots of equations!

• Escape speed
• Keplers 3rd law derived
• Galileos observations heliocentric model
• Tidal forces, Roche limit

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Escape speed Derivation using energy balance
Gravitational potential energy
Kinetic energy (energy of motion)
When KE gt Egrav object can escape (ignoring air
friction!)
Example Earth, Vesc 11.2 km/s 24,000 mph
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PRS EC question If the escape speed of Earth
is 11.2 km/s, and Mars is 1/10 Earths Mass and ½
its radius, what is Mars escape speed (km/s)?
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Keplers 3rd Law Derived

• 1. Equate gravitational, centripetal forces

• Notes
• Mass of object (m) cancels
• M is mass of central object
• For elliptical orbits, r is replaced by a, the
  semi-major axis

2. Write orbital velocity in terms of radius r,
period P
3. Substitute for V, solve
For solar system only
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Keplers 3rd law example calculations

• Sun-centered Use simplified law Pyr2 aAU3
• Suppose new planet is discovered with an orbital
  period of 6 yrs. What is the semi-major axis of
  the orbit?

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Non-Sun centered example

• Use Keplers 3rd law with full constants
• What is the orbital period of the Marss moon
  Phobos? It has a semi-major axis a 9,400 km
  The mass of Mars is 6.4E23 kg.

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PRS EC question (60 sec) What is the orbital
period (in Earth years) of the Kuiper-belt object
Sedna, which has a semi-major axis of 530 AU?
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Keplers 2nd Law and Vis-Viva EquationHow
velocity changes with distance from focus
(central body)
Use conservation of total Energy
Where kinetic, potential, and total energies are
given by
Solve for V(r) (vis-viva equation)
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• Galileos key astronomical discoveries
• First astronomical telescopic observations
• All confirmed heliocentric model
• Galilean (4 largest) Moons of Jupiter
• Sunspots
• Phases of Venus (falsified geocentric model)

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Galileos discoveries of Jupiters moons with his
telescope showed that Earth was not the center of
all orbits strongly supported a heliocentric
model.
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Galileo also observed blemishes on the Sun
(sunspots) This contradicted perfect spheres
idea of Aristotle. This was an important example
of scientific method Observations can test (and
disprove) hypotheses
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Galileos discoveries of Venus phases with his
telescope showed that Venus must orbit the Sun
Strongly supports a heliocentric model

• Venus is clearly smallest when it is at superior
  conjunction and largest when it is close to
  inferior conjunction.

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• Venus can only go through phases if it orbits the
  Sun.

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Galileo and the Roman Inquisition

• 1610-1616 First telescopic observations support
  heliocentric hypothesis. Galileo publishes
  results in the book De Revolutionibus Orbium
  Coelestium and several letters.
• 1616 After formal complaints from friars to
  Rome, Galileo first reports to Office of
  Inquisition. De Revolutionibus put on Index of
  Forbidden Books, Galileo ordered silent about
  heliocentric theory.
• 1630. After receiving permission from the Pope
  (Urban II) to discuss heliocentric hypothesis as
  a theory, not a fact, he publishes Dialogue
  Concerning the Two Chief World Systems, or
  Diologio.
• 1633 Charged with heresy, retried by Office of
  Inquisitor. Galileo, age 68, formally recanted,
  was sentenced to house arrest in his home near
  Florence (Arcetri), where he died in 1642.
• 1966 Roman Church abolishes Index of Banned
  Books, admits Galileo trial was a mistake.

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The Unfortunate Case of Giordano Bruno (1548-1600)

• 1548 Born near Naples. Italian polymath
  (theologian, mathematician, astronomer,
  Dominican friar)
• 1576-1590 Flees Italy after threat of
  Inquisition. Lives in France, England, Germany,
  Hungary
• 1584 pubishes De l'Infinito, Universo e Mondi
  ("On the Infinite Universe and Worlds") in
  London.
• 1591 arrested in Venice, recanted under threat of
  torture.
• 1591-1600 imprisoned in Rome, frequently
  questioned about beliefs
• 1600 refuses to recant again, burned at the
  stake.
• Statue of Bruno is presently at site of his
  execution in Rome (Plaza Navona)