1. ASTROPHYSICS Yr 2 Session 3 – Orbits & the Solar System 1

2. Solar System Contents One star

3. Inner planets (not to scale) Mercury Mars Earth Venus

4. Asteroids

5. Outer (gas giant) planets Jupiter Saturn Uranus Neptune

6. Kuiper Belts objects Pluto & Charon

7. Comets

8. Meteoroids

9. The whole Solar System

10. L  =3.826×10 26 Watts r L  /4  r 2 Wm -2 1 A.U. 1.36×10 3 Wm -2 The Solar constant Solar radiation

11. Apparent brightness of the Planets Albedo A = Fraction of solar radiation reflected by planet Venus & crescent Moon

12. Example: Saturn’s moon Iapetus High albedo Low albedo

13. r (A.U.’s) R Cross sectional Area =  R 2 S 0 = Solar constant. S mars = ‘solar constant’ for Mars S mars = S 0 /r 2 Wm -2 Total radiation reflected by Mars = A × S mars ×  R 2

14. Planet positions & motion

15. Principal planet positions  ° = elongation

16. Retrograde motion

18. Eclipses

19. Moon at perigee & apogee

21. Lunar eclipses

22.  Earth’s orbit as seen from the Sun  Sun’s apparent orbit as seen from the Earth The Ecliptic (again) Celestial Equator

23. North pole of the ecliptic North celestial pole is here

24. Ecliptic coordinates

25. Johannes Kepler 1571 - 1630 Kepler’s laws of planetary motion

26. The Epicycle Planetary motion problems

27. Tycho Brahe 1546 - 1601

28. Kepler’s Laws First Law: The orbit of each planet is an ellipse with the Sun at one focus. Second Law: The rate at which the radius vector sweeps out an area on the ellipse is a constant. Third Law: The ratio of the semi-major axis cubed to the orbital period squared is the same constant for all the planets. i.e. is a constant, where P is the planet’s orbital period.

29. The Ellipse Directrix Area =  ab GF 1 /GZ 1 = GF 2 /GZ 2 = e e = eccentricity (<1) Cartesian equation

30. F 1 PA = Periapsis r 1 F 1 AA = Apapsis r 2 Line of apsides For an orbiting body at P

31. r = Radius vector  = True anomaly For an orbiting body at P

32. Important ellipse properties Polar form of Ellipse equation

33. Example: Proof of OF 1 = ae OF1F1 P1P1 P2P2 Z P 1 P 2 = 2a P 1 F 1 = eP 1 Z: P 2 F 1 = eP 2 Z P 2 F 1 – P 1 F 1 = e(P 2 Z - P 1 Z) = e × 2a Also: P 2 F 1 = a + OF 1 & P 1 F 1 = a – OF 1  P 2 F 1 – P 1 F 1 = 2OF 1 = e × 2a: Hence OF 1 = ea aa

34. Kepler’s Third Law = 1 if… a is in A.U.’s P in sidereal years (365.257 days) We need to determine a for the Earth.

35. Finding the Astronomical Unit Jeremiah Horrocks 1619 - 1641

36. The 2004 transit of Venus

38. The Asteroid Eros

39. Venus

40. Next time – Orbits & the Solar System 2

41. Logarithms Quick Notes

44. The number ‘e’ = 2.718 Same basic properties as for logs to base 10

46. See ‘Serious Logarithm Notes’ on Blackboard for full details