Astronomical Units of distance

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Presentation transcript:

Astronomical Units of distance Astronomical units (a.u.) Parsecs (pc) Light Years (ly)

The Astronomical Unit - The Earth - Sun distance. First, we knew Kepler’s Period/Radius relationship for the orbit of Mars and Earth around the Sun: RE3 = RM3 TE2 TM2 Second, we knew the distance to Mars:

Measuring Earth-Mars: Paris This angle was measured simultaneously Ø Cayenne (in French Guiana)

The Astronomical Unit - The Earth - Sun distance. Using Kepler’s Period/Radius relationship for the Orbit of Mars and Earth around the Sun: RE3 = RM3 TE2 TM2 And a triangulation of Mars to find how far Earth was from Mars (RM - RE) since the periods were well known, they now had two equations, and two unknowns. RE is of course, 1 A.U. 1 A.U. is 1.496 x 108 km = 1.5 x 108 km

An astronomical unit (AU) is 1.5 x 108 km Concept -1: An astronomical unit (AU) is 1.5 x 108 km 3.2*3600=11520

Neptune is 4500 million kilometers from the sun. How far is this in AUs? 4500x106 km/(1.5x108km/AU) = 30AU 4500E6/1.5E8 = 30 30AU

Parsecs - Parallax Seconds The distance in parsecs is defined as 1/Ø where Ø is the parallax angle in seconds (1 second - 1/3600 of a degree) From Douglas Giancoli’s Physics

Which star is the closest? Toggle between images Which star is the closest? 3.2*3600=11520

Concept 0: There are 3600 seconds to a degree. (Parallax angles are really small, and measured in seconds) 3.2*3600=11520

How many arc seconds are there in 3.2 degrees? 3.2o*3600”/o=11520” 3.2*3600=11520 11520”

45 arc seconds is how many degrees? 45”/3600”/o=.0125o .0125o

The distance in parsecs is defined as 1/Ø where Ø is Concept 1: The distance in parsecs is defined as 1/Ø where Ø is the parallax angle in seconds 3.2*3600=11520

If a star has a parallax of .12”, what is its distance in parsecs? Parsecs = 1/arcseconds = 1/.12 = 8.3 pc Parsecs = 1/arcseconds = 1/.12 = 8.3 pc 8.3 pc

If a star is 89 parsecs away, what is its parallax in arc seconds? Parsecs = 1/arcseconds so 89 = 1/arseconds, arseconds = 1/89 = .0112” Parsecs = 1/arcseconds so 89 = 1/arseconds, arseconds = 1/89 = .0112” .0112”

the kilometers to the star. Suppose Ø = 1” so parsecs = 1/1 = 1 pc Since d is 1 AU, if we know Ø – the parallax Angle we can find D – the kilometers to the star. You know that Tan(Ø ) = d/D, so D = 1.5 x 108 km/Tan(1/3600o) = 3.1 x 1013 km So 1 pc = 3.1 x 1013 km From Douglas Giancoli’s Physics

Light Year - The distance traveled by light in a year 1 ly = (2.998x108m/s)(365.2499d/y)(24h/d)(3600s/h) 1 ly = 9.46x1012 km = 1013 km 1 parsec = 1.496 x 108/Tan(1/3600) = 3.086 x 1013 km = (3.086 x 1013 km)/(9.46x1012 km/ly) = 3.26 ly

All together: 1 ly = 9.46x1012 km 1 parsec = 3.26 ly = 3.086 x 1013 km 1 A.U. is 1.5 x 108 km 1 ly = 9.46x1012 km 1 parsec = 3.26 ly = 3.086 x 1013 km

How many meters wide is it? Our Galaxy is 100,000 ly wide. How many meters wide is it? (100,000ly)(9.46x1012*km/ly)(1000m/km) = 9.46x1020m 100,000x9.46E12*1000 = 9.46E20m 9.46x1020m

A star is 4.3 light years from Earth. How many parsecs is this? = 4.3 ly/(3.26 ly/pc) = 1.3 pc = ly/3.26 = 1.3 pc 1.3 pc