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Celestial Sphere

Celestial Sphere. Greek geocentric model ( c . 400 B.C.). What was once so mysterious about the movement of planets in our sky?. Planets usually move slightly eastward from night to night relative to the stars.

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Celestial Sphere

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  1. Celestial Sphere Greek geocentric model (c. 400 B.C.)

  2. What was once so mysterious about the movement of planets in our sky? • Planets usually move slightly eastwardfrom night to night relative to the stars. • But, sometimes they go westward relative to the stars for a few weeks: apparent retrograde motion.

  3. Geocentric Universe - the Earth at the center The most sophisticated geocentric model was that of Ptolemy (A.D. 100–170) — the Ptolemaic model: • Sufficiently accurate to remain in use for 1,500 years • Arabic translation of Ptolemy’s work named Almagest (“the greatest compilation”) Ptolemy

  4. So how does the Ptolemaic model explain retrograde motion? Planets really do go backward in this model. In the Ptolemaic model, the planets orbit the Earth. They travel around on epicycles while the epicycle moves around on a deferent that is centered on the Earth. To predict the orbits of the planets correctly, there were further complications to this basic model. epicycle deferent Ptolemaic Model

  5. We see apparent retrograde motion when we pass by a planet in its orbit. Mars Retrograde Motion

  6. Nicolaus Copernicus - Heliocentric Model Copernicus (1473–1543): • He proposed the Sun-centered model (published 1543 - after his death!). • He used the model to determine the layout of the solar system (planetary distances in AU). But . . . • The model was no more accurate than Ptolemaic model in predicting planetary positions, because it still used perfect circles.

  7. Tycho Brahe (1546–1601) • Lots of data! • Brahe compiled the most accurate (one arcminute) naked eye measurements ever made of planetary positions. • He still could not detect stellar parallax, and thus still thought Earth must be at the center of the solar system (but recognized that other planets go around the Sun). The Earth is not moving! • He hired Kepler, who used Tycho’s observations to discover the nature of planetary motion.

  8. Johannes Kepler (1571–1630) • Kepler succeeded Tycho as Imperial Mathematician to the Austrian Emperor • Kepler first tried to match Tycho’s observations with circular orbits. • But an 8-arcminute discrepancy led him eventually to ellipses and his 3 Laws of Planetary Motion • 1627 published the Rudolphine Tables predicting planetary positions • Died in 1630, a year before his prediction of a transit of Mercury occurred. www.kepler.arc.nasa.gov/johannes.html More on Thursday… “If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy.”

  9. Celestial SphereOur Modern View

  10. Defining a Coordinate System The Equatorial System- observer independent α: right ascension δ: declination

  11. ClassAction demos • The Earth moves • Daily • LST changes – objects rise and set • Monthly – lunar phases • Yearly – seasons, seasonal stars • Precession – coordinate system zero point moves • Wobble – yikes! • Through the Galaxy • Etc….

  12. Defining a Coordinate System • The zero of δ is the celestial equator. • The zero of α is the Vernal equinox. • While observer independent, it does change with time as the equinoxes precess. Problem 1.4: VE: α = 0, δ = 0 SS: 6 hr = 0, δ = 23.5° AE: α = 12 hr, δ = 0 WS: α = 18 hr, δ = -23.5° Problem 1.5: let’s work it now

  13. Figure 12a for problem 1.6 1.6 (a) Circumpolar stars are stars that never set below the horizon of the local observer or stars that are never visible above the horizon. After sketching a diagram similar to Fig. 1.12(a), calculate the range of declinations for these two groups of stars for an observer at the latitude L. (b) At what latitude(s) on Earth will the Sun never set when it is at the summer solstice? (c) Is there any latitude on Earth where the Sun will never set when it is at the vernal equinox? If so, where?

  14. Group Work • Problem 1.6 • Form into two groups • Work the problem together • I’ll call on someone to explain it at the board. • Actually, do for homework…

  15. Local Sidereal Time (LST) • Sidereal – with respect to background stars, not the Sun. So the LST at any given time (say midnight) at a particular place changes over the course of the year. • LST – the amount of time that has elapsed since the vernal equinox point (where the ecliptic and celestial equator cross) last traversed the local meridian. • To an observer, this really means, “Objects of what RA (α) are overhead right now.”

  16. Precession • Although the axis seems fixed on human time scales, it actually precesses over about 26,000 years. — Polaris won’t always be the North Star. — Positions of equinoxes shift around orbit; for example, the spring equinox, once in Aries, is now in Pisces!

  17. Other Stuff Moves, too. Proper Motion

  18. Stellar Parallax 1 parsec = 206265 AU (the number of arcsec in a radian) 1 degree contains 3600" Tycho could measure differeneces of about 120" The largest p is about 0.77” (2 cm at a distance of about 5 km) Parallax Applet

  19. Parallax - Hipparcos In 1989, ESA launched Hipparcos: High Precision Parallax Collecting Satellite - to measure the parallaxes of 120,000 stars with an accuracy of about 2 milli-arcsecs. Data was collected until 1993. Catalogs were published in 1997. Also useful for measuring proper motion…

  20. Highest proper motion stars from Hipparcos[25]# Star Proper motion Radial velocity(km/s) Parallax(mas) μα(mas/yr) μδ(mas/yr) 1 Barnard's star -798.71 10337.77 -106.8 549.30 2 Kapteyn's star 6500.34 -5723.17 +245.5 255.12 3 Groombridge 1830 4003.69 -5814.64 -98.0 109.22 4 Lacaille 9352 6766.63 1327.99 +9.7 303.89 5 Gliese 1 (CD -37 15492) (GJ 1) 5633.95 -2336.69 +23.6 229.32 6 HIP 67593 2282.15 5369.33 — 76.20 7 61 Cygni A & B 4133.05 3201.78 -64.3 287.18 8 Lalande 21185 -580.46 -4769.95 -85.0 392.52 9 Epsilon Indi 3961.41 -2538.33 -40.4 275.79

  21. Stars in Stereo Ursa Major Ursa Major + 60000 years Scorpius Cassiopeia

  22. Homework • Problems 1.6 and 1.9 • Due next Tuesday in class (along with more problems assigned on Thursday).

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