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= 6 o. Phy.size th.=115cm(6 o /57.3 o ) = 12 cm Actual size =13 cm =100(13-12)/13=8%

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

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= 13 o. Upper: p= (25+25)/2= 25 o.

Lower example previous page: p= 13 o. R= 10 cm d = 57.3 o (10/13 o ) = 44.1 cm Actual d = 43.3 cm % error=100( )/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 Tiny, p = 0.3 seconds of arc. One arc sec= 1/3600 o

Distance pc=1/p parallax in arc sec 1 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 ~ 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 Hipparchus satellite, to arc sec; d=1000pc= 3000 ly. Still only 3% of our Galaxy Gaia space probe, will cover our whole Galaxy.

End of Presentation