Download Unit 3 - Section 9.1 2011 Distances in Space

Grade 9 Academic Science – Space
Measuring Distance in Space
Section 9.1 Pages 365-369
Our Sun is about 1.5 X 108 km away…or 150,000,000 km. The next nearest star is Proxima Centauri at 4.01 X 10 13
km away (about 40 trillion km).
These distances are very hard to imagine. What does 40 trillion km look like?
To bring it into the realm of our reality, we measure the vast distances in space by other methods.
 Astronomical Unit (AU) is a relative measure. The distance from Earth to the Sun is 1 AU. If Neptune is
30 AUs from the Sun, Neptune is 30X further from the Sun than Earth. An AU is a practical measuring
unit inside our Solar System.
 Outside our Solar System, Light Years (ly) are the measurement unit.
 A ly is not a measurement of time; rather, it is a measurement of distance.
 A ly is the distance that light travels in a vacuum (i.e., empty space) in one year.
 Light travels at a constant speed of about 300,000 km/s. Thus, light can travel 9.46 X 10 12 km in one
year (300,000 km X 31,558,464 s/yr). The formula is 1 ly = 9.46 X 1012 km
Examples
The Andromeda Galaxy is 2.4596 X 1019 km from Earth. How many ly is the Andromeda Galaxy away?
Distance is 2.4596 X 1017 km
One ly = 9.46 X 1012 km
2.4596 X 1017 / 9.46 X 1012 = 2.6 X 106
The Andromeda Galaxy is 2.6 X 106 or 2,600,000 ly from Earth
The star Polaris is 400 ly from Earth. What is the distance in kilometers?
Distance is 400 ly
One ly = 9.46 X 1012 km
400 X 9.46 X 1012 = 3.784 X 1015
The star Polaris is 3.784 X 1015 km from Earth


It makes intuitive sense that the farther a star is from Earth, the longer it takes light from the star to
reach Earth. The star Polaris is 400 ly from Earth. In other words, it takes light from Polaris 400 years
to reach Earth. The light that we see when we look at Polaris is 400 years old. We are actually
looking back in time.
For ease of understanding, a ly can be converted into a light-second (ls)
1 ly = (60 X 60 X 24 X 364.26) ls = 3.15 X 10 7 ls
Challenge – How many kilometers are there in 1 ls?

Parallax – The apparent change in position of an object as viewed from two different locations that are not
on a line with the object.

To determine the distance to a star,
you measure the apparent change
of the star’s position over one
year. As the Earth orbits the Sun,
you take measurements at the
opposite sides of the Earth's orbit.
You will observe an apparent
movement of the star compared to
more distant stars. The closer a
star is to the Earth the greater the
observed parallax.
As shown in the diagram, the lines
of sight and the line connecting the
observer's position form a triangle
with the star at the apex. NOTE:
Star A and Star B in the diagram are the same star. The difference is the apparent movement of the
star due to the movement of the viewer on Earth.
The parallax of the star is equal to the angular radius of the Earth's orbit as seen from the star. The
distance to the star (D) is equal to the reciprocal of the parallax angle (measurement units are arcseconds). The formula is TanӨ = R/D


A little fun…
Star
Proxima Centauri
Sirius
Parallax Angle
Distance
(parseconds)
Light Years
0.77233
1.29478
4.233
0.379
2.6385
8.606
This is one of the basic problems in trigonometry: Determining the distance of some far away point C given the
direction that C appears from two ends of a baseline AB (see illustration). The problem is simplified by three ideas.
1. The baseline is perpendicular (i.e., 90O) to a line draw from the middle of AB to point C. Thus, the
triangle ABC is symmetric. If we call the drawn line r, then AC = BC = r
2. The length of AB is less than r. This means that the angle between AC and AB is small. This is the
parallax of C as viewed from AB
3. We do not require great accuracy (i.e., within 1% of the approximate distance).
Return to the diagram above
 The diameter of the Earth’s orbit around the Sun is 300,000,000 kilometers. (Question: How do I know
that distance?) On dates separated by half-a-year, the Earth position…and where you are relative to the star
between viewed…is 300,00,000 kilometers apart.
 The stars do not shift very little when viewed from 300,000,000 kilometers apart
 A circle has 360O and each degree can be divided into 60 minutes…called “minutes of arc” so they are
distinguished from a minute of time. Moreover, each minute of arc contains 60 “seconds of arc.” A
parsecond (…or parsec…) is the distance to a star whose yearly parallax is 1 second of arc. One parsecond
equals 3.26 light years.
Practice Questions / Homework
 Page 369, Questions 2, 3, 5,7,10,11
Determining Locations in Space
Laboratory
Distances in space are immense. Our nearest star is Proxima Centauri at 4.24 LY, while the brightest star in the
night sky, Sirius, is about 8.58 LY away. Our Milky Way galaxy, which contains between 100 and 400 billion star,
is a spiral galaxy about 100,000 LYs in diameter. (For interest, our solar system is located about 27,000 LYs from
the centre of the Milky Way). Recall: 1 LY = 9.46 X 1012 km.
Traveling those distances, an error of less than one degree would mean missing your desired destination by many,
many light years.
Challenge
 You want to travel to Proxima Centauri. As you know, the star is 4.24 LY…a relatively short distance in
space. You are told to travel directly at 90 O, but the coordinates are wrong. You should have traveled at
91O. You miss the star. If you went 4.24 LY, what distance lies between you and Proxima Centauri? That
is, how much did you miss the star by?
Task
You want to determine how determine correct distance over the immense distances of space
Materials
 Protractor
 Meter stick
 One (1) ball of string
 Masking or duct tape
Methods
1. In a long hallway, place the protractor along the edge of one floor tile.
2. Using tape, mark 90O and 91O on the tile
3. Using one ball of string, walk off 30 tiles, stretch the string at 90 O and mark the location at 30 tiles using
the tape
4. Repeat using the ball of string, stretch the string at 91O and mark the location at 30 tiles using the tape
5. Using the meter stick, measure the separation distance between the 90O and 91O at 30 tiles
6. Using the meter stick, measure one tile on the floor
7. For every tile, what was the separation distance between 90 O and 91O?
8. Assuming each tile on the floor is 1 LY, what is the separation distance in light years?
9. Locate at point randomly between 90O and 91O at 30 tiles
10. What is the coordinate degree you would assign to the new coordinate to exactly reach this point on the
floor? NOTE: You cannot guess….you must be precise. Recall if this were light years, you would not
want to miss your destination (i.e., you would not be coming back). Provide your ideas how to set the
exact coordinate degree location.
Table of Results