Astronomical Units of distance Astronomical units a u
- Slides: 18
Astronomical Units of distance • Astronomical units (a. u. ) • Parsecs (pc) • Light Years (ly)
The Astronomical Unit - The Earth - Sun distance. Using Kepler’s Period/Radius relationship for the Orbit of Mars and Earth around the Sun: R E 3 = R M 3 T E 2 T M 2 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. is 1. 496 x 108 km = 1. 5 x 108 km
Concept -1: An astronomical unit (AU) is 8 1. 5 x 10 km
Neptune is 4500 million kilometers from the sun. How far is this in AUs? 4500 x 106 km/(1. 5 x 108 km/AU) = 30 AU
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
Concept 0: There are 3600 seconds to a degree. (Parallax angles are really small, and measured in seconds)
How many arc seconds are there in 3. 2 degrees? 3. 2 o*3600”/o=11520”
45 arc seconds is how many degrees? o 45”/3600”/o=. 0125 o
Suppose Ø = 1. 45 x 10 -5 o x 3600 =. 0522” so parsecs = 1/. 0522 = 19. 2 pc Since d is 1 AU, if we know Ø – the parallax Angle we can find D – The distance to the star. You know that Tan(Ø ) = d/D, so D = 1. 5 x 108 km/Tan(1. 45 x 10 -5 o) = 5. 9 x 1014 km From Douglas Giancoli’s Physics
Concept 1: The distance in parsecs is defined as 1/Ø where Ø is the parallax angle in seconds
If a star has a parallax of. 12”, what is its distance in parsecs? Parsecs = 1/arcseconds = 1/. 12 = 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”
Concept 2: You know that Tan(Ø ) = d/D (Where d = 1. 5 x 108 km)
A star has a parallax of. 015” what is its distance in parsecs and km? Parsecs = 1/arcseconds = 1/. 015 = 66. 666 pc Tan(angle) = 1. 5 E 8 km/D, so D = 1. 5 E 8 km/ Tan(angle) = 1. 5 E 8/tan(. 015/3600) 15 = 2. 06 x 10 km 2. 06 x 1015 km
A star is 6. 14 x 1014 km away. What is its parallax in arc seconds? How many parsecs is it away? -1 Angle = tan (d/D) = tan-1(1. 5 E 8/6. 14 E 14) = 1. 4 E-5 degrees x 3600 =. 0504 arcseconds Parsecs = 1/. 0504 = 19. 8 pc
Light Year - The distance traveled by light in a year 1 ly = (2. 998 x 108 m/s)(365. 2499 d/y)(24 h/d)(3600 s/h) 1 ly = 9. 46 x 1012 km = 1013 km 1 parsec = 1. 496 x 108/Tan(1/3600) = 3. 086 x 1013 km = (3. 086 x 1013 km)/(9. 46 x 1012 km/ly) = 3. 26 ly
A star is 4. 3 light years from Earth. How many parsecs is this? = 4. 3 ly/(3. 26 ly/pc) = 1. 3 pc
Our Galaxy is 100, 000 ly wide. How many meters wide is it? (100, 000 ly)(9. 46 x 1012*km/ly)(1000 m/km) = 9. 46 x 1020 m
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