Module 2: Star Gazing

1. Module 2: Star Gazing Activity 2:Earth’s Seasons

2. Summary: • In this Activity, we will investigate: • (a) the Earth’s orbit around the Sun, • (b) the origin of the seasons on Earth, and • (c) the Earth’s precession.

3. Remember that the plane of the ecliptic is an imaginary surface in space containing the Earth’s orbit around the Sun. The Ecliptic At the end of the last Activity we introduced the ecliptic, which is the apparent path of the Sun across the sky. The Earth takes one year to make a complete orbit around the Sun. What else do you know about the Earth’s orbit around the Sun besides how long it takes?

4. (a) The Earth’s orbit around the Sun You might think that the Earth travels around the Sun in a circular orbit ... … but actually the shape of the Earth’s orbit is an ellipse. You can think of an ellipse as a “squashed” circle(but note that this one is quite exaggerated!).

5. Elliptic orbits can have various shapes, from: “squashed”, or more technically, orbits of higheccentricity to: nearly or completely circular, or more technically, orbits of low or zero eccentricity.

6. A circle is in fact a special case of an ellipse. • Ellipses are characterised by their eccentricity e, which varies from: e = 0.99999... e = 0 e  0.8 Circles are ellipses with zero eccentricity.

7. The Earth’s orbit is nearly circular, with e = 0.0167. Its average distance from the Sun is 149,597,900 km. We write large numbers like this in a mathematical shorthand called scientific notation, where 149,597,900 km = 1.49597900 x 108 km where the 108 is 1 followed by 8 zeros. This is the same as multiplying 1.49597900 by 10 eight times.

8. In astronomy, however, we have more convenient way of representing the average distance from the Earthto the Sun: it’s defined as one Astronomical Unit, where 1 AU = 1.495979 x 108 km 1 AU We’ll find Astronomical Units (AU) convenient whenwe compare distances between the Sun and other planets in our Solar System.

9. * * The factor of 2 is here is because the eccentric orbit can take the Earth to a distance of 1AU  0.0167AU The small eccentricity of the Earth’s orbit (0.0167) means that its distance from the Sun varies by 0.0167 x 2 x 1.495979 x 108 km, or about 5.00 x 106 km during the course of a year. This is a variation of only about 3% in the overall orbital radius, but represents a distance of about 400 times the Earth’s diameter. For more information about elliptic orbits, click here.

10. The Sun The Earth (b) The origin of the seasons on Earth • As we saw in the last Activity, one (Earth) year is the time it takes for Earth to make a complete orbit around the Sun.

11. However, we can’t really feel that the Earth is orbiting the Sun (even though the Earth is travelling 30 km/s!), and these days not many people take notice of the Earth’s orbital position (that is, people don’t take much notice of the changing of the constellations in the night sky). We primarily notice the passing of a year by the cycle of the seasons. Other planets have seasons too. Investigating the reasons for Earth’s seasons will help us understand the conditions on other planets also.

12. Clearly the seasons have something to do with the Earth’s orbit around the Sun. Yet many people are confused about why the Earth has seasons. • So what is the cause of the seasons? Before going on to the next slide, have a think about it yourself: what is the cause of the seasons?

13. “The seasons are caused by the changing distance between the Earth and the Sun, and it is warmer in summer because the Earth is closer to the Sun at summer time.” This is a very common response - and it is true that the Earth-Sun distance does charge. As we just saw, the Earth’s distance from the Sun varies by about 3% during its orbit. So could summer occur when the Earth is closest to the Sun? The problem with this idea is that when it’s summer in the northern hemisphere, it’s winter in the southern hemisphere, and vice versa. So if this were the correct answer, it would be the same season in both hemispheres at the same time - which is not the case.

14. Earth’s rotation axis plane of the ecliptic The Earth’s rotational axis is tilted by 23.5° with respect to a line drawn perpendicular to the plane of the ecliptic. 23.5° The seasons result from this tilt of the Earth’s axis of rotation. This is true not only of the Earth, but all other planets with tilted rotation axes, as we shall see.

15. The direction of the rotational axis stays (nearly) fixed in space while the Earth orbits the Sun and the hemisphere that seems to “lean into” the Sun experiences summer, while the hemisphere that “leans away” from the Sun experiences winter. northern hemisphere “leans away” from Sun winter in NH summer in NH (leans into Sun) winter in SH (leans away from Sun) southern hemisphere “leans into” Sun summer in SH And six months later the opposite is true: Thus the tilt of the Earth’s rotation axis naturally explains why the seasons are opposite in the northern and southern hemispheres.

16. N Sun S In December, when the southern hemisphere is tilted towards the Sun, the southern part of the Earth receives more sunlight and experiences long summer days. At the same time, the northern hemisphere is tilted away from the Sun and receives less sunlight, experiencing short winter days. If you live near the Equator, there is not much difference between the seasons all year round. equator

17. rotation axis equator If we take the case when the northern hemisphere is in summer ... sunlight not only does the northern hemisphere receive more sunlight, but it receives more direct sunlight because the Sun is higher in the daytime sky. This helps heat the atmosphere in summer.

18. When the Sun is higher in the summer sky, the sunlight is more concentrated …. … than in winter, when the Sun is lower in the sky, and the sunlight is more diffuse. Concentrated beamof Summer sunlight Diffuse, “spread-out” beam of Winter sunlight

19. … so for the hemisphere experiencing Summer, sunlight striking the Earth is more concentrated and this helps to raise the average temperature. The reverse is true for the hemisphere experiencing Winter. During spring and autumn, the two hemispheres receive approximately equal amounts of sunlight.

20. northern spring northern summer northern hemisphere winter southern autumn southern winter northern autumn southern hemisphere summer southern spring Let’s have a look how it works during the course of a year:

21. As we’ve already mentioned, if you live near the Equator, you don’t really notice the changing seasons during the course of a year. Generally you just have two seasons: “dry” and “wet”! If you are at the North or South Pole, then also experience two very long seasons: in summer, the South Pole is leaning towards the Sun and there is “daylight” for nearly six months. In winter, the South Pole is leaning away from the Sun and it is “nighttime” for nearly six months.

22. If we take the case when the northern hemisphere is in midsummer ... then the north pole has continuous daylight and locations in the northern hemisphere have long periods of daylight, sunlight equator whereas locations in the southern hemisphere have long nights. the south pole is in continuous darkness

23. 23.5° plane of the ecliptic So in summary, the cause of the seasons is the tilt of the Earth’s rotational axis, and as a consequence of this tilt: the Sun is higher in the sky for longer during summer days (and lower in the sky for a shorter number of hours on winter days); and because the Sun in higher in the summer sky, the heating of the Earth’s surface is more direct (whereas the low winter Sun‘s heating is more diffuse).

24. As we will see, whether the rotational axis is tilted or notdetermines whether other planets experience seasonstoo.

25. 23.5° plane of the ecliptic (c) The Earth’s precession During its yearly orbit around the Sun, the Earth’s rotation axis is fixed in space. However, if we could watch the orientation of the Earth’s rotation axis over a very long period of time (about 26,000 years!), we would see that it in fact precesses.

26. Not to scale! The Earth’s rotation creates an “equatorial bulge” (meaning the Earth is fatter at the equator than at the poles). • The precession of the Earth is due to the gravitational “tug of war” on the Earth by the Sun and the Moon. • The Earth’s tilt means the Sun and Moon are not aligned with the equator, and both the Sun and Moon try to pulls the Earth’s equatorial bulge closer to it. • The combined pull of the Sun and Moon, along with the Earth’s own rotation, result in the observed precession.

27. Over a period of 26,000 years, the Earth’s rotational axis “precesses” through a complete cycle. Click here to see an animation of precession. It is this precession which has gradually shifted the positions of the constellations in the sky, and, in particular, the periods of the year which correspond to each zodiacal constellation. * * See the previous Activity, Star Patterns

28. Precession also changes the locations at which seasons occur in the Earth’s orbit. The Earth is currently closest to the Sun during southern summers, but in about 13,000 years it will occur duringnorthern summers. This may cause southern summers to become more mild, and northern winters to become more severe.

29. Image Credits • NASA: View of the Mid-Pacific Oceanhttp://nssdc.gsfc.nasa.gov/image/planetary/earth/gal_mid-pacific.jpg

30. Now return to the Module home page, and read more about the Earth’s seasons and precession in the Textbook Readings. Hit the Esc key (escape) to return to the Module 2 Home Page

32. b a y x Elliptic Orbits • The Cartesian (i.e (x,y) coordinates) equation for an ellipse is given by: • where a is the semi-major axis • and bis the semi-minor axis. • If a = b, then the ellipse becomes a circle. The larger a is than b, the more “squashed” the ellipse is.

33. r  y x • We can also write the equation for an ellipse in polar coordinates (i.e (r,) coordinates): • where r is the radius • and  is the angle (from the x-axis). r and  are measured from the focus of the ellipse. • The eccentricity e, which is given by: describes how “squashed” the ellipse is, with circles having e = 0.

34. For a circle, the radius remains constant with angle, and hence our Cartesian plot: • will look pretty boring in polar coordinates: y r x r y   x Cartesian Polar • If we use polar coordinates to plot the ellipse, we need to run from  = 0 to  = 2 (or  = 0 to 360°). • An ellipse, however, will look like a sine wave:

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