1. Gateway To Space T-18 ASEN / ASTR 2500 Class #15
Colorado Space Grant Consortium

2. Gateway To Space T-18 ASEN / ASTR 2500 Class #15
Colorado Space Grant Consortium

3. Gateway To Space T-18 ASEN / ASTR 2500 Class #17
Colorado Space Grant Consortium

4. Student Hands On Training Workshop (SHOT 2007)
Today…
- Announcements
- One Minute Reports
- Project Q/A and Orbits and Mission Design – Part I
Thursday
- Orbits and Mission Design – Part II (15 minutes)
- Spider
June , 2007

5. Student Hands On Training Workshop (SHOT 2007)
Announcements…
June , 2007

6. Student Hands On Training Workshop (SHOT 2007)
Announcements…
June , 2007

7. Student Hands On Training Workshop (SHOT 2007)
Announcements…
June , 2007

8. Student Hands On Training Workshop (SHOT 2007)
Announcements…
June , 2007

9. Student Hands On Training Workshop (SHOT 2007)
Announcements…
June , 2007

10. Student Hands On Training Workshop (SHOT 2007)
Announcements…
- DD Rev C is due
- Don’t forget about HW #7 due
- Don’t forget about community service
- Updated grades will be posted this week
- Spacecraft Communications lecture?
- Spacecraft Propulsion lecture?
June , 2007

11. Student Hands On Training Workshop (SHOT 2007)
One Minute Report…
- Can satellites that remain in the same spot in the sky be seen with a telescope?
- How long after landing do we get our payloads?
- What role does congress have in deciding what NASA is and is not allowed to do?
- How do this year’s experiments compare to previous years?
- Does the mass of the satellite include the flight tube?
- What do we have to talk about when we do our community service?
June , 2007

12. Student Hands On Training Workshop (SHOT 2007)
One Minute Report…
- If we are overweight can we use margin of other teams?
- How is the camera programming coming along?
June , 2007

13. A Brief Historical Look
Orbits:
A Brief Historical Look

14. Earth, the Moon, Mars, and the Stars Beyond
A Brief Discussion on Mission Design
Chris: Everything from here on looked ok to me. I don’t know how to better explain it, your numbers and equations look fine to me, and I don’t know how to use STK well enough to do an animation for you of the interplanetary stuff, sorry.

15. Universal Gravitation, Applied:
When in space why do you float? i.e. Weightlessness
Chris- I still wasn’t quite sure what you wanted to illustrate with this slide, so I left it as was. Sorry.

16. Universal Gravitation, Applied:
How does this apply to orbits?
Chris- I still wasn’t quite sure what you wanted to illustrate with this slide, so I left it as was. Sorry.

17. Questions: • How fast can you throw a snowball? - A baseball?
- A shot put?
- A Subway sandwich out a moving car?
• Could you throw any of these in to an orbit?
- How fast would it have to be going?

18. Questions: • Let’s figure it out… v is velocity
G is Universal Gravitational Constant
M is mass of planet or satellite
R is radius of planet of satellite

19. Atmosphere: • How about throwing something into orbit on the moon?
golf ball

20. Atmosphere: • Let’s figure it out… v is velocity
G is Universal Gravitational Constant
M is mass of planet or satellite
R is radius of planet of satellite

21. A Brief Historical Look
Orbits:
A Brief Historical Look
Arthur C. Clarke
Discovered This Orbit

22. Ancient Orbit History:
“ORBIT” from Latin word “orbita”
orbitus = circular; orbis = orb
• 1800 B.C.
Stonehenge
- Study of the vernal equinox

23. 1500 B.C.: Egyptians and Babylonians
Written evidence of stellar observations
Solar Calendar of 365 days
Time divided into 60 even units

24. Said earth is center of the universe
350 B.C.: Greek Thoughts
Aristotle
Said earth is center of the universe
Dominated scientific thought for years

25. Start of the Heliocentric Model:
1543 A.D.
Nicholas Copernicus
Said Sun-centered rotations
Measurements crude but thinking shifts
Didn’t release findings until the end of his life

26. Orbit History :
• 1580 A.D.
Tycho Brahe
Accurate measurements of planets (Mars) as a function of time
Even though telescope had not been invented

27. Good friends with Copernicus Observations with TELESCOPE reinforced
Orbit History :
• 1610 A.D.
Galileo Galilei
Good friends with Copernicus
Observations with TELESCOPE reinforced
Discovered Venus has phases

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

29. Orbit History: Kepler’s 3 Laws of Planetary Motion:
All planets move in elliptical orbits, sun at one focus

30. Orbit History: Kepler’s 3 Laws of Planetary Motion:
All planets move in elliptical orbits, sun at one focus

31. Orbit History: Kepler’s 3 Laws of Planetary Motion:
A line joining any planet to the sun, sweeps out equal areas in equal times

32. Orbit History: Kepler’s 3 Laws of Planetary Motion:
A line joining any planet to the sun, sweeps out equal areas in equal times

33. T2 = R3 Orbit History: Kepler’s 3 Laws of Planetary Motion:
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.
If you can observe the period of rotation, you can determine the distance
Planet
P (yr)
a (AU) T2 R3
Mercury
0.24
0.39
0.06
Venus
0.62
0.72
0.37
Earth
1.00
Mars
1.88
1.52
3.53
3.51
Jupiter
11.9
5.20
142
141
Saturn
29.5
9.54
870
868
T2 = R3

34. 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”
1666, he understood planetary motion
Did zip for 20 years until Edmund Halley

35. Body at rest stays at rest, a body in motion stay in motion
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
Chris: I couldn’t find any really useful pictures for this slide.

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

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

38. Universal Gravitation, Applied:
When in space why do you float? i.e. Weightlessness
Chris- I still wasn’t quite sure what you wanted to illustrate with this slide, so I left it as was. Sorry.

39. Types of Orbits: Orbits are conic sections: Circle Ellipse Parabola
Hyperbola
From Kepler’s Law, the central body is at a focus of the conic section

40. 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=):

41. Questions: • Let’s figure it out… v is velocity
G is Universal Gravitational Constant
M is mass of planet or satellite
R is radius of planet of satellite

42. Earth, the Moon, Mars, and the Stars Beyond
A Brief Discussion on Mission Design
Chris: Everything from here on looked ok to me. I don’t know how to better explain it, your numbers and equations look fine to me, and I don’t know how to use STK well enough to do an animation for you of the interplanetary stuff, sorry.

43. Orbit Introduction: What is an orbit?
- The path of a satellite around the Earth
(or any central body)
What shape is it?
- Orbits are conic sections
- Circles, Ellipses, Parabolas, Hyperbolas
How are orbits described?
- Position and Velocity at any one time
- Keplerian Elements (from Kepler’s Laws)

44. Orbit Definition: - Velocity & Position
- Given position and velocity of a satellite at
time t, you can calculate the position and
velocity at any other time

45. Keplerian Elements Orbit Definition: - Semi major axis (a) - Size
- Eccentricity (e)
- Shape

46. Keplerian Elements Orbit Definition: - Inclination (i)
- Angle to the Equator

47. Keplerian Elements Orbit Definition:
- Right Ascension of Ascending Node (RAAN, Ω)
- Rotation about the Earth’s Spin Axis

48. Keplerian Elements Orbit Definition: - Argument of Perigee (ω)
- Rotation of the conic section in the plane
- True Anomaly (θ)
- Angle between the Position Vector and
the vector to Perigee

49. Orbital Elements:
Used to determine a satellite’s location in orbit:

50. Types of Orbits:

51. Types of Orbits:

52. Types of Orbits (cont.) Geosynchronous/ Geostationary
Satellite remains over same spot on earth

53. Types of Orbits (cont.) Critical Inclination
Pass repeats the longitude

54. Types of Orbits (cont.) Repeating Ground Trace
Satellite covers same territory over and over

55. Types of Orbits (cont.) Polar/ Sun Synchronous
Sun sync precesses at the same rate as the sun, so it stays in the sun more per orbit than a normal polar orbit

56. Types of Orbits (cont.) Molniya
A very elliptical polar orbit, designed by the Russians to be used for their spy and communication satellites because it stays over the northern hemisphere for 75% of its orbit.

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

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

60. Changing Orbits: How about 250 km to 500 km How would you do it?
Chris: I would recommend referring back and forth to the picture and the video clip, so people can get an idea of what the pictures translate to in 3-D and so that they can get a fixed reference view on the video (since it’s kinda hard to see). So you know, the satellite doesn’t do the first burn when the lower half of the orbit changes to blue, it does the first burn when the “satellite” gets to the perigee of the elliptical orbit (so when green turns to blue). The second burn is easier to see, and happens when the satellite passes the apogee of the elliptical (blue) orbit for the second time- the second circular orbit (in red) shows up. –Kendra

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

62. 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 DV’s

63. Changing Orbits: Therefore: DV1 is to start transfer
DV2 is to circularize orbit
Time to do transfer is

64. How well do you understand Hohmann Transfers?
• 1 to 2?
• 2 to 3?
• 3 to 1?
• 1 to 3? 3 2 1

65. Circular Orbit: