Astronomical Units of distance Astronomical units a u

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Astronomical Units of distance • Astronomical units (a. u. ) • Parsecs (pc) •

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 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

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?

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

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,

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”

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

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

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

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?

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?

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

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

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

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 =

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?

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,

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