Angular Size & Parallax

• Fig. 1

Appearance and position of pin-hole protractor

• Figure 2

The pattern for pin-hole protractor

• Fig. 3

Fold on dashed lines

Cut along solid black line to make a strip. Fold on dashed.

Cut object template and “Paper Mate Sharpwriter” holder from part of an 8 ½ x 11 inch sheet of paper as shown here.

Fig. 5 lower. Assembled ang. Size object and parallax target

• Tape pencil to middle of 10 cm wide object.

• Make object which holds pencil 4 cm high.

• Dashed line divides triangle symmetrically.

• Example: d=115 cm angular size= 6o. Phy.size th.=115cm(6o/57.3o) = 12 cmActual size =13 cm

=100(13-12)/13=8%

• Aristarchus example• Thought Sun distance 840x diameter Earth• About 0.5o angular size• Physical size =840(0.5/57.3)= 7xdiameter Earth. => Earth orbits Sun, Was

ignored.Modern distance ≈ 12000 diameter Determined by parallax

• Aristarchus’ ideas were rejected. Why?

• Common sense AND failure to observe stars’ parallax.

Parallax used to get distances of solar system objects and stars.

• Fig. 6 Geometry of parallax experiment set-up

Layout for parallax observation versus theory

Layout for parallax observation versus theory

Viewing parallax target with pinhole protractor

• Nearby pencil relative to distant star along dashed line.

• From each of two baseline points 10 cm from “Sun.”

• Figure 9-Protractor views of nearby star (red) vs distant star (blue).

• View of angular scale as seen through protractor.• Lower example: p = (50-24)/2= 13o.• Upper: p= (25+25)/2= 25o.

• Lower example previous page: p= 13o. R= 10 cm• d = 57.3 o (10/13 o) = 44.1 cm• Actual d = 43.3 cm• % error=100(44.1-43.1)/43.3 ≈ 2%

Finding the Distance of our Sun)

• Recall Copernicus found relative distances of planets in solar system wrt Earth-Sun 1 AU.

• Measure parallax of Earth-Sun, Earth-Planets etc

• Observe from one side of Earth to other

• 93 million miles=150 million km.

The Long Quest for Stellar Parallax

• Not until 1800’s.

• German astronomer Karl Bessel

• First accurate measurement of parallax of star 61 Cygni in 1838.

• Tiny, p = 0.3 seconds of arc. One arc sec= 1/3600 o

Distance pc=1/p parallax in arc sec1 arc sec = 1/3600 degree

1 pc=200,000 AU=3.26 LY. 1 LY = 6trillion miles

Even the nearest stars are amazingly far away.

• Nearest star parallax,

• p ~0.7725 arc sec

• 1/0.7725=1.3 pc away, about four light years travel time.

• > 200,000 times Earth-Sun distance

• The double star, Alpha & Proxima Centaurus.

Example calculation of distance with parallax.

• A star’s Π = 0.5 sec of arc.

• Distance in parsec = 1/Π in arc sec.

• Distance = 1/0.5 = 2 parsecs

= 6.52 light years or about 400,000 AU

= 39 trillion miles.

Progress in Measuring Parallax

• Limited by atmosphere “seeing.” and instrument.

• Bessel could measure distances to ~8 pc, ~25 ly, only a few neighboring stars.

• 1989 Hipparchus satellite, to 0.001 arc sec; d=1000pc= 3000 ly.

• Still only 3% of our Galaxy.

• 2011 Gaia space probe, will cover our whole Galaxy.

End of Presentation