Unit I The Size, Shape and Motion of the Earth

Transcription

1 Unit I The Size, Shape and Motion of the Earth ASTR 101 Prof. Dave Hanes

2 Aristotle Knew the World to be Round 1. The behaviour of stars (say, Athens vs Khartoum)

3 2. The behaviour of sea-going ships

4 3. The Earth s Shadow in a Lunar Eclipse

5 Easier in Modern Times!

6 The Ancient Greeks Knew the Earth s Size, Too! Eratosthenes, 250 BC

7 Do It Yourself!

8 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 ~24 o higher in the sky Since 24/360 = 1/15 th of a full circle, conclude Earth s circumference ~ 15 x 3362 km - about 49,000 km

9 Even Before Columbus The Behaim Globe The flat-earth myth is thanks to Washington Irving

10 Is the Earth Spinning? Reasons to think not (all were used, all are incorrect!): n n n n n n We d feel the rumble under our feet. There would be a wind in our faces. The Earth would be torn to pieces. If we shot an arrow vertically, it would come back down behind us We d be thrown off, like stones from a slingshot. Even if it were, it would quickly slow to a halt.

11 Proof No 1: Earth s Figure much exaggerated!

12 By the Way, the Flattening is Measured Astronomically

13 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:

14 Proof 2: Foucault Pendulum

15 Stirling Hall Foyer Physics Dept, Queen s Notice the changed direction of the pendulum swing at three different times of day!

16 Proof No 3: The Coriolis Effect

17 Shoot a Rocket from the NP to LA You miss! (The missile appears to veer off to the right, landing in the Pacific.) Why?

18 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.

19 Explaining Hurricanes like Ivan (2004)

20 Irrelevant on Small Scales (like toilets and bathroom sinks)

21 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 It s clear that the moon orbits us. Then how can the Earth orbit the Sun? Surely there can be only one centre! n If we re moving around the Sun, why doesn t the moon get left behind? How can it keep up with us?

22 Four Potential Tests 1. Do various stars change in apparent brightness as we move around? 2. Can we measure our speed through space, rather as a traffic cop measures the speed of moving cars? 3. Can we appeal to an analogy about walking through falling rain: stellar aberration? 4. Do the positions of (some) stars seem to shift as we move around: parallax?

23 1. Varying Stellar Brightnesses?

24 Correct in Principle, but Immeasurably Small Effects As we move, our distance changes by less than % for the closest stars -- even less for more remote stars Moreover, the changes are slow, spread over months

25 2. Can We Measure Our Speed?

26 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.

27 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 )

28 A Preliminary Glimpse

29 Example: The Star Arcturus Its spectrum in June Its spectrum in December

30 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.

31 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.

32 3. Stellar Aberration

33 Historical Note This was the very first definitive proof that the Earth actually moves through space! Discovered by Bradley in 1725.

34 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

35 To Determine Distances: Use Parallax Measurements Alternative word: triangulation. (Consider the word triangle. ) Think of a surveyor.

36 Determining Distances

37 Parallax Exemplified Try it with your two eyes and an upraised finger!

38 Wide Eyes

39 Widen the Separation

40 Creating 3-D Images

41 Ensuring that Each Eye Sees a Different Image

42 Heliocentric parallax Supremely important: it allows us to determine the distances of the stars!

43 Stellar Parallax Visualization 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.)

44 Unrealistically Idealized Compare the January view and the July view

45 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!