1. Determining the Distances to Astronomical Objects
parallax

2. Parallax
Parallax view: the variation in angle that occurs when viewing a nearby object from different places.
Importance of parallax: Danish astronomer Tycho Brahe reasoned that the distance of the object may be determined by measuring the amount of parallax. A smaller parallax angle meant the object was further away.

3. The apparent change in the location of an object due to the difference in location of the observer is called parallax.
Their views differ because of a change in position relative to the mountain

4. Because the parallax of the “star” was too small to measure, Tycho knew that it had to be among the other stars, thus disproving the ancient belief that the “heavens” were fixed and unchangeable.

5. Limitation to using parallax
Eventually, the parallax shift will no longer be measurable.
This is because the distance is too great for the effect to be observed.

6. Astronomical Unit
Distances in space are so great that millions of miles has little meaning.
An astronomical unit (1 AU) is the distance from Earth to the Sun.

7. Calculating using Parallax.
Distance-x (parsecs) = 1 AU/ P (arcsecs)

8. Calculating using Parallax.
Distance = r/ tan (angle P)
d = r / tan P (r in km and P in degrees)
1 arcsec = degrees
1 AU = 150,000,000 km
D = 1/ P if P is in arcseconds
So,
find D, If P= .25 arcseconds
Distance = 1 / P
= 1/ .25
= 4 parsecs
If P is 1 second of arc:  d = / tan 1" = 30 million million km  This distance is called one parsec and is a basic unit for measuring astronomical distances.  Distance in parsecs = 1 / P in seconds of arc

9. Convert Parsec to Light Years
1Parsecs is 3.26 Light Years
So,
D = 1/ P if P is in arcseconds find D, If P= .25 arcseconds
Distance = 1 / P
= 1/ .25
= 4 parsecs
How many Light Years?
4 parsec x 3.26 LY = light years
parsec