Download Unit 3 - Section 9.1 2011 Distances in Space0

Grade 9 Academic Science – Unit 3 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 1013 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) is 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 107 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 arc-seconds). 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