1. Welcometo GEEN 2850 / 4850 ASTR 2840 Independent Study Colorado Space Grant Consortium March 19, 2001

2. Today - Announcements - Discussion on Orbits

3. Announcements: - Status reports due last Friday -Don’t forget about outreach requirement -I won’t be here on Wednesday -Andrew Busbee and Steve Wichman will be speaking

4. Orbits: A Brief Historical Look Arthur C. Clark Discovered This Orbit

5. Ancient Orbit History: “ORBIT” from Latin word “orbita” orbitus = circularorbis = orb 1800 B.C. Stonehenge - Study of the vernal equinox 1500 B.C. Egyptians and Babylonians - Written evidence of stellar observations - Time divided into 60 even units

6. Ancient Orbit History: 350 B.C. Aristotle - Said earth is center of the universe - Dominated scientific thought for 1800 years Aristarchus - Said that is B.S.

7. Kinda Old Orbit History: 1543 A.D. Nicholas Copernicus - Said Sun-centered rotations - Measurements crude but thinking shifts 1580 A.D. Tycho Brahe - Accurate measurements of planets as a function of time - Even though telescope had not been invented

8. Orbit History : 1610 A.D. Galileo Galilei - Good friends with Copernicus - Observations with TELESCOPE reinforced Copernicus - The wrath of the Catholic Church

9. Orbit History: 1600 A.D. Johannes Kepler - Used Tycho’s careful observations to smash Aristotle theories - Presented 3 laws of planetary motion - Basis of understanding of spacecraft motion - However, “Why was not understood” - Calculus?

10. Orbit History: Kepler’s 3 Laws of Planetary Motion 1. All planets move in elliptical orbits, sun at one focus 2.A line joining any planet to the sun, sweeps out equal areas in equal times 3.The square of the period of any planet about the sun is proportional to the cube of the of the planet’s mean distance from the sun.

11. Orbit History: 1665 A.D. Isaac Newton - At 23, plague while at Cambridge - Went to be one with nature - He studied gravity - Discovered “Newton’s Laws of Motion” F = m a - 1666, he understood planetary motion - Did zip for 20 years until Edmund Halley

12. Newton’s Laws: 1st Law..... Body at rest stays at rest, a body in motion stay in motion 2nd Law.... F = m * a 3rd Law... For every action, there is an equal and opposite reaction

13. Newton’s Laws: Newton Continued... - 1687, Principia Published - Law of Universal Gravitation (Attraction)

14. Universal Gravitation, Applied: - When in space why do you float? i.e. Weightlessness

15. Types of Orbits:

18. Earth, the Moon, Mars, and the Stars Beyond A Brief Discussion on Mission Design

19. Kepler: Kepler’s Laws...Orbits described by conic sections Velocity of an orbit described by following equation For a circle (a=r): For a ellipse (a>0): For a parabola (a=  ):

21. Circular Orbit: For a 250 km circular Earth Orbit Orbital Velocity Orbital Period

22. Circular Orbit: For a 500 km circular Earth Orbit Orbital Velocity Orbital Period Conclusions???

23. Changing Orbits: How about 250 km to 500 km How would you do it?

24. Changing Orbits: Changing orbits usually involves an elliptical orbit Perigee = close Apogee = far Since orbit is elliptical a > 0, so where

25. Changing Orbits: Here’s what you need: 1) Velocity of initial orbit 2) Velocity of final orbit 3) Velocity at perigee 4) Velocity at apogee Then figure out your  V’s

26. Changing Orbits: Therefore:  V 1 is to start transfer  V 2 is to circularize orbit Time to do transfer is

27. How well do you understand Hohmann Transfers? 123 1 to 2? 2 to 3? 3 to 1? 1 to 3?

28. Changing Orbits: Also something called “Fast Transfer” It is more direct and quicker However it takes more fuel  V 1 and  V 2 are much bigger

30. From Earth Orbit to the Moon: Same as changing orbits but.... - At apogee you don’t have empty space - Instead, you have a large and massive object Gravity from this object can act as a  V against your spacecraft When going to the Moon the following could happen: 1) Gravity will cause your spacecraft to crash into the surface 2) Gravity will cause your spacecraft to zip off into space for a long time

31. Getting to the Moon:  Gravity Assist

32. Apollo XIII:

36. To the Moon for Money:

40. Earth to L1:

42. Earth to Mars: Mars Orbit Earth Orbit Transfer Orbit Initial Orbit Final Orbit

44. Earth to Beyond: Say you are in a 250 km orbit... Orbital Velocity: Velocity on parabolic (a=  escape trajectory:  V needed:  V will not put you in a orbit, you will escape the Earth’s gravity never to come back

45. Questions