Download Unit I – The Size, Shape and Motion of the Earth

Unit I – The Size, Shape and
Motion of the Earth
ASTR 101
Prof. Dave Hanes
Aristotle Knew the World to be Round
1. The behaviour of stars (say, Athens vs Khartoum)
2. The behaviour of sea-going ships
3. The Earth’s Shadow in a Lunar Eclipse
Easier in Modern Times!
The Ancient Greeks Knew the Earth’s
Size, Too!
Eratosthenes, 250 BC
Do It Yourself!
Some Numbers
No Need to Remember These!
From Google Maps: it’s a 3362 km drive
(an overestimate, because it’s not a straight road!)
From Tucson, the Sun is ~24o higher in the sky
Since 24/360 = 1/15th of a full circle, conclude
Earth’s circumference ~ 15 x 3362 km
- about 49,000 km
Even Before Columbus
The Behaim
Globe
The flat-earth
myth is thanks
to Washington
Irving
Is the Earth Spinning?
Reasons to think not (all were used, all are incorrect!):
n 
We’d feel the ‘rumble’under our feet.
n 
There would be a wind in our faces.
n 
The Earth would be torn to pieces.
n 
If we shot an arrow vertically, it would come back down ‘behind us’
n 
We’d be thrown off, like stones from a slingshot.
n 
Even if it were, it would quickly slow to a halt.
Proof No 1: Earth’s Figure
…much exaggerated!
By the Way, the Flattening
is Measured Astronomically
A Small Effect on Earth
- Bigger Elsewhere!
Earth is only 41 km longer through the Equator than from
North Pole to South Pole, in a total of ~12,700 km.
But consider
Saturn:
Proof 2: Foucault Pendulum
Stirling Hall Foyer
Physics Dept, Queen’s
Notice the changed direction of the pendulum swing
at three different times of day!
http://www.youtube.com/watch?v=8rhqh1hZd8Y&feature=em-upload_owner
http://www.youtube.com/watch?v=ZTTTKyiWUWg&feature=em-upload_owner
http://www.youtube.com/watch?v=JKSyxsd5BF8&feature=em-upload_owner
Proof No 3: The Coriolis Effect
Shoot a Rocket from the NP to LA
You miss! (The missile appears to veer off to the
right, landing in the Pacific.) Why?
Less Obviously:
Objects fired north from
the equator appear to
veer off to the right
because they are already
moving quite quickly
Eastward, thanks to the
spin of the Earth.
Explaining Hurricanes
like Ivan (2004)
Irrelevant on Small Scales
(like toilets and bathroom sinks)
https://www.youtube.com/watch?v=Ct_17xYGNz8
Does the Earth Move Through Space
- say, Orbiting the Sun?
There were reasons to think not (all wrong!)
n 
Wouldn’t we feel the motion?
n 
Wouldn’t it ‘naturally’ slow down and come to rest?
n 
n 
It’s clear that the moon orbits us. Then how can the Earth orbit the
Sun? Surely there can be only one ‘centre!’
If we’re moving around the Sun, why doesn’t the moon get left
behind? How can it keep up with us?
Four Potential Tests
1. 
2. 
3. 
4. 
Do various stars change in apparent brightness as we
move around?
Can we measure our speed through space, rather as a
traffic cop measures the speed of moving cars?
Can we appeal to an analogy about walking through
falling rain: stellar aberration?
Do the positions of (some) stars seem to shift as we
move around: parallax?
1. Varying Stellar Brightnesses?
Correct in Principle, but
Immeasurably Small Effects
As we move, our distance changes by less than 0.0004%
for the closest stars -- even less for more remote stars
Moreover, the changes are slow, spread over months
2. Can We Measure
Our Speed?
Can We Use a‘Radar Gun’?
In the Solar System, yes! We send radar signals to the
moon, planets, asteroids, etc, to work out their distances
and speeds.
The stars are much too distant! (Any return signal would
take years!)
Moreover, the return signal would be much too feeble to
detect.
NO NEED for Radar!
The light emitted by the star itself actually
contains information that allows us to
work out its state of relative motion.
(Details later in the course…)
A Preliminary Glimpse
Example: The Star Arcturus
Its spectrum in June
Its spectrum in December
The “Doppler Shift”
(Features are displaced towards the red or blue at
different times of year)
At one time of year, Arcturus is apparently receding from
us (at a speed of ~30 km/sec)
Six months later, it seems to be approaching us at a
comparable speed.
The Enforced Conclusion
The Earth is in motion!
Sometimes we are moving towards Arcturus (and other
stars in its vicinity, not just this one!) at a speed of ~30
km/sec;
and six months later we are moving the opposite direction!
Of course it is because we are orbiting the Sun.
3. Stellar Aberration
Historical Note
This was the very first
definitive proof that the
Earth actually moves
through space!
Discovered by Bradley
in 1725.
4. Stellar ‘Parallax’
Suppose there was
n  one moderately nearby star, and
n  a host of very remote background stars.
Then as the Earth moves from place to place in its
orbit around the Sun, we should see the nearby
star appear to shift relative to the background
To Determine Distances:
Use Parallax Measurements
Alternative word: triangulation. (Consider
the word “triangle.” )
Think of a surveyor.
Determining Distances
Parallax Exemplified
Try it with your two eyes and an upraised finger!
Wide Eyes
Widen the Separation
Creating 3-D Images
Ensuring that Each Eye
Sees a Different Image
Heliocentric parallax
Supremely important: it allows us to
determine the distances of the stars!
Stellar Parallax Visualization
http://www.astro.washington.edu/users/jrad/plx.gif
To the lower left of this visualization, we see an animation
of the Earth going around and around the Sun. From our
perspective on Earth, we then expect to see nearby stars
shifting back and forth much more dramatically than the
more remote stars. Very distant stars will scarcely budge.
(In reality, the stars are so remote that the annual shifts
are barely detectable, even for the very nearest stars of all.)
Unrealistically Idealized
Compare the “January view” and the “July view”
The Practical Reality
Even the very nearest star is very remote (indeed, 100
million times as far away as the moon).
The actual parallactic shifts are barely detectable
Success only came in 1837, fully 240 years after
Galileo’s first telescope!
Still, it’s additional proof that the Earth moves!