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Unformatted text preview: Ast 307 - Aug. 31, 2010 Positions and Sizes in Angular Units
Angular measure & the small-angle formula Conditions for eclipses (angular diameter) Locating things on the Sky The Night Sky - September 2010
Jupiter is bright in the evening sky, with the Great Square of Pegasus lying to the upper left. Ast 307 Ast 307 Tuesday evening, Spica lies a little above Venus, with Mars off to the right. By Saturday, Mars will be closer to Spica than Venus is. Light-travel Time
Light travels at 3 !105 km/s, fast but not infinite. It takes a while to reach us from distant objects.
Destination Moon Sun Sirius Andromeda Galaxy Light travel time 1 second 8 minutes 8 years 2.5 million years “Look-back” Time The farther we look in distance, the further back we look in time.
8/31/10 Ast 307 3 You can think of light as a “time machine;” the time it takes light to reach us is the “look-back time.” If we know the distance in light years, we also know how long ago the light was sent to us.
8/31/10 Ast 307 4 Angular Measure
PlacesMoonizes on the sky are specified in angles. &s Units of Angular Measure
• Full circle = 360º = 2! radians • 1º = 60" (arc minutes) • 1" = 60# (arc seconds) 1/2° 90° The angular diameter of the full moon in the sky is about 1/2°. Complete circle = 360° Horizontal Fig. 1-11
Ast 307 8/31/10 Ast 307 6 “Handy” Rules for Measuring Angles
The angular distance between the two pointer stars at the front of the Big Dipper is about 5°, roughly 10 times the angular diameter of the Moon. Angular vs. Linear Size Which quantities are directly proportional to each other? Which quantities are inversely proportional to each other?
8/31/10 Ast 307 7 8/31/10 Ast 307 8 The “Small-Angle” Formula
Your textbook gives this equation in Box 1-1 on page 9, but does not derive it. The derivation is straightforward, and involves converting units from radians to arc sec.
$ Diam ' " (") = 206,265 # & ) % dist ( An Urban Legend What are the units of D (diameter) and d (distance)? !
8/31/10 Ast 307 9 An anonymous e-mail first circulated in August 2003 claimed that during the close approach of Mars to Earth that summer, Mars would look as large as the Moon. Do you think this prediction was accurate? (Yes/No)
8/31/10 Ast 307 10 An Urban Legend
At that time, Mars was only 0.52 A.U from the Earth; its physical diameter is 6800 km. Use the small-angle formula to calculate the angular diameter of Mars at this time (rounding off to just one significant digit if you don’t have a calculator). Which of these, if any, is close to your answer? (a) 18# (b) 180# = 3" (c) 1800# = 30"= 0.5 °
! An Urban Legend
Here is the calculation, to 2 - 3 significant figures: ' $ Diam ' $ 6800 km " (") = 206,265 # & ) = 206,265 # & ) % dist ( % 0.52 A.U . # 1.5 # 10 8 km / A.U .(
# 6.8 & #10 3 km & 5 )5 = 2.06 " 10 5 " % ( "% ( = 18 " 10 " 10 = 18.0 arc sec $ 0.78 ' $10 8 km ' 8/31/10 Ast 307 11 ! 8/31/10 Ast 307 12 Close Approaches of Mars
Mars is closest to Earth when they are aligned with respect to the Sun, an arrangement called “opposition” because Mars is then in the opposite direction from the Sun (as seen from Earth). Because Mars has a rather elliptical orbit, its angular size at opposition varies by a modest factor. Total Solar Eclipse of July 11
There was a solar eclipse last month, visible from the south Pacific (including Easter Island and Tahiti) and southern S. America, including Patagonia. Ast 307 8/31/10 Ast 307 14 Annular Solar Eclipse of Jan 15
There was a rare, so-called “annular” solar eclipse earlier in the year. The Moon did not cover the Sun completely; instead, an annulus (ring) of sunlight was seen. Condition for a Total Eclipse
In order for a nearer object to fully eclipse a more distant object, the angular size of the nearer one must be at least as large as the angular size of the more distant one:
$ Diam ' $ Diam ' " near (") = 206,265 # & ) * " far (") = 206,265 # & ) % dist ( near % dist ( far ! This phenomenon doesn’t apply to just the Earth, Moon, and Sun, but these are the most familiar examples. 8/31/10 Ast 307 15 8/31/10 Ast 307 16 The Parsec: another useful unit
Astronomers cite distances to objects outside the Solar System in parsecs (pc), not light-years. 1 pc = 206,265 A.U., as you can figure out using the definition (right) and the smallangle equation.
8/31/10 Ast 307 17 8/31/10 The Celestial (Hemi)sphere
• The sky above us looks like a dome (hemisphere). • If (in our imagination) we extend the sky all the way around the Earth, we call this the celestial sphere. • …but, of course, we only see the “top half” • In this picture, the Earth is located in the center of the celestial sphere. Ast 307 18 Locating Objects on the Sky
Zenith: The point directly overhead Horizon: Great circle 90° from the zenith Meridian: The great circle passing through the zenith, connecting the north and south points on horizon
19 The location of an object can be specified by its altitude above the horizon and direction or azimuth relative to the cardinal directions.
8/31/10 Ast 307 ...
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This note was uploaded on 04/30/2011 for the course AST 317 taught by Professor Dinerstein during the Fall '10 term at University of Texas.
- Fall '10