Scales of the Universe in space, time, and motion

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General Astronomy
Instructor:
Prof. Kaaret
702 Van Allen Hall
E-mail: philip-kaaret [at] uiowa.edu
Phone: 335-1985
Class website:
http://astro.physics.uiowa.edu/~kaaret/2014s_29c62
Course topics
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Sun, stars
Black holes, neutron stars
Galaxies
Cosmology
Course elements
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Lecture
Homework
In-class exams
Final exam
Laboratory (must pass lab to pass course)
Lectures and Homework
Lectures: MWF 1:30 pm – 2:20 pm, LR70 VAN
Textbook: Foundations of Astrophysics, Ryden and
Peterson
Homework: About once per week, usually due on
Mondays, do in groups of 2-3 if that helps.
Help: Help is available during office hours
Help: Astronomy tutorial in 310 VAN. Hours
posted at
http://www.physics.uiowa.edu/academics/astron_tutorial_sched.html
Laboratory
Lab: T 7:00 pm – 9:00 pm, 665 VAN
Lab will consist of several `canned’ labs and a
research project. Get started on the research
project early.
Grading
One-hour exams (3 exams, each 100 points)
300
Final exam
200
Homework (some extra credit available)
100
Laboratory
200
Total
800
Scales in length, time, and motion
• Astrophysics requires knowledge of the
Universe on the entire range of length scales
from sub-nuclear to cosmological.
• Knowing the typical size and time scales of a
system gives significant insight into that
system.
• Astronomical time scales can be extremely
long.
Sizes are in meters
People
Height of (small) person is about 1 m
People
• If the small person spins around, she can make
one revolution in about 1 second.
• The typical time scale for people, i.e. how fast
they react to some event (how long does it take
you to slam on the brakes if the car in front of
you stops), is of order seconds.
• The typical velocity scale for people is
Velocity = length/time ~ 1 m/1 s = 1 m/s
Typical walking speed is 3 mph = 1.3 m/s
Earth to Moon
Image taken by Galileo spacecraft
Distance Earth to Moon is 3.8108 m
Moon’s Orbit
• The Moon makes one revolution about the Earth in
one month, or about 2.4106 seconds.
• A month is the time scale of the Moon’s orbit.
• The velocity scale for the Moon’s orbital motion is
Velocity = 2  3.8108 m/2.4106 s = 1000 m/s
= 1 km/s = 2000 mph
• This is comparable to the fastest Earth bound speeds
A `speeding bullet’ travels at about 1000 m/s = 2000 mph.
Earth to Sun
Distance from Earth to Sun is 1.51011 m
This is one “Astronomical Unit” = 1 A.U.
Earth’s Orbit
• The Earth makes one revolution about the Sun in one
year, or about 3107 seconds.
• A year is the time scale of the Earth’s orbit.
• The velocity scale for the Earth’s orbital motion is
Velocity = 2  1.51011 m/3107 s = 3104 m/s
= 30 km/s = 70,000 mph
• This is much faster than Earth bound speeds.
A `speeding bullet’ travels at about 1000 m/s = 2000 mph.
• This is faster than the orbital speed of the Moon.
to Center of Milky Way
Distance to Center of our galaxy is 2.61020 m
or 28,000 ly
Sun’s Orbit
• The Sun makes one revolution about the center of the
Milky Way in 230 million years, or about 71015
seconds.
• This is the `time scale’ of the Sun’s orbit and a reasonable
time scale for interactions of galaxies (how long does a
galaxy take to react to an event like a collision with
another galaxy).
• The velocity scale for the Sun’s orbital motion is
Velocity = 2  2.61020 m/71015 s = 2105 m/s
= 200 km/s
• This is an order of magnitude faster than the orbit of the
Earth around the Sun.
to Nearest (big) Galaxy
Distance to nearest (big) galaxy is 2.41022 m or 2.6 106 ly
to edge of Observable Universe
Distance to edge of observable universe is
1.31026 m or 1.4 1010 ly
Scale models
Use scale models to gain some sense of the
(relative) scales of physical objects or systems.
What is a scale model?
1. made out of plastic?
2. corresponds to a real object?
3. has the same proportions as a real object?
4. has the same colors as a real object?
Scale models
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A scale model is a representation
of a real object or set of objects
in which all of the different parts
of the model have sizes in the
correct proportions to the real
thing.
• For scale factor s, real dimension D, then model dimension d = sD
• For example, with a scale factor s = 1:50 = 1/50 = 0.02, an
airplane with a length of D = 36 feet becomes a model with a
length of d = 0.02*36 feet = 8.64 inches.
Scale models
• In a scale model of Earth-Moon-Sun system that
could fit into this room (5 meters), how large
would Earth be?
• Need measurements of real system:
– Distance from Earth to Sun is 1.51011 m
– Diameter of Earth is 1.3107 m
• Find scale factor s = 5/1.51011 = 3.310-11
• Model Earth diameter = sD = 3.310-111.3107 m
= 4.310-4 m = 0.43 mm
'Cosmic Calendar' by Carl
Sagan
If the age of the
Universe were
compressed into
one year, your
life to date
would be about
0.046 seconds,
or 1/10 a blink
of an eye.
Review Questions
• How long does it take light to travel from the
Sun to the Earth?
• Find Earth’s rotational speed at the equator from
the Earth’s diameter and the length of a day.
• If you make a scale model of the Universe that
can fit into your bedroom, how large is the
Earth? Is there a physical object of about that
size?
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