Day 5 notes Parallax measurements Small angular measurements Units of large distances

We have been describing the position of stars, the sun, and the orientation of the Earth using the celestial sphere and coordinates. These coordinates are described in terms of angles (declination and right ascension). To fully understand the position of the sun and stars, we need to also know the DISTANCE to these objects. This is similar to saying that Chicago is northeast of here; we need to also say how far it is, to know its location.

Question ? How do we measure the distance to an object if we cannot reach it? For example, we look across a river and see an object. We can walk around on our side of the river, and make measurements of directions.

The method is called Triangulation, since there is a triangle involved in obtaining the distance. Notice that angles are also needed to estimate the size of the sides of the triangle.

Parallax is an angle that describes the change in your “line of sight” when you look at a distant object from TWO points of view, or from TWO positions.

Parallax Geometry can be illustrated by using two pencils. Look at some distant object with one eye, then the other.

More on parallax Motion parallax is seen when you travel. (link)(link) The measurement of parallax can be used to estimate the distance to the Moon if observations are made from different parts of the Earth.

Parallax can also be used to estimate the distance to relatively near-by stars by observing at opposite points in the Earth’s orbit (of course, you have to wait 6 months between measurements). We will mention this again when we study stars in Ch. 9.

Notice that the parallax angle is larger for stars that are closer.

This simulation shows what the sky might look like if the orbit of the Earth were huge, say 16 light-years. The stars close to us would appear to wobble back and forth during the year. The actual motion is much smaller and requires careful measurement with telescopes or similar instruments.

Proper motion of the stars Over very long periods of time, even the constellations will change shape, since the stars have REAL motion, called “proper motion”, but this is difficult to see in one lifetime because there is little relative movement. Here is a drawing of what the Big Dipper would look like if you went back 100,000 years from the present.

Measuring Distances with Geometry and angular diameter

Very small angles are used in Astronomy

Small angles are defined using the number 60 A full circle has 360 degrees. One degree has 60 arc minutes. One arc minute has 60 arc seconds. So, one arc minute is 1/60 of a degree. One arc second is 1/60 of an arc minute and it is also 1/3600 of a degree. An example would be 5 o 23’ 45”

Units of Astronomical Distance Astronomical Unit – AU 1 AU = 1.5 x 10 8 km = 9.3 x 10 7 miles This is the distance from Earth to Sun. Light Year is abbreviated ly 1 ly = 9.46 x km = 63,000 AU The nearest star is 4.2 ly away (over 265,000 AU).

Units of Astronomical Distance Parsec – defined as the distance at which 1 AU perpendicular to the observer’s line of sight make an angle of 1 arcsec 1 pc = 3.09 x km = 3.26 ly The nearest star is 1.3 pc away (over 265,000 AU).

Astronomical Distances are huge compared to the size of the solar system Make a model using a golf ball to represent the Sun. The Earth is a grain of sand 1 m away. One meter represents one A.U. The nearest star is over 265,000 AU away so this would be 265,000 meters or 265 kilometers in our model. This is about the distance from Macomb to a big city like St. Louis or Chicago.

The first exam is on Thursday, Feb. 4 (this week!) We will have about 30 minutes of class before the exam. Then you will take the exam (which uses a Scantron). The exam is multiple choice and true/false questions. Coverage is Chapters 1 and 2 in your textbook. To review, look at the chapter summaries, day notes, and a study guide that I posted over the weekend.

2009 was a special year for Astronomy because we celebrated the 400 th anniversary of the first use of the telescope to look at the sky (by Galileo). We will see some short movies that were made to celebrate that year. Eyes on the Skies is an mp4-coded HD1080p movie in several parts. It is also available on DVD.