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WelcomeWelcometoto
GEEN 2850 / 4850GEEN 2850 / 4850ASTR 2840 ASTR 2840
Independent StudyIndependent Study
Colorado Space Grant ConsortiumColorado Space Grant ConsortiumMarch 19, 2001March 19, 2001
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TodayToday
- Announcements- Announcements
- Discussion on Orbits- Discussion on Orbits
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Announcements:Announcements:
- Status reports due last Friday- Status reports due last Friday
- Don’t forget about outreach requirementDon’t forget about outreach requirement
- I won’t be here on WednesdayI won’t be here on Wednesday
- Andrew Busbee and Steve Wichman will be Andrew Busbee and Steve Wichman will be speakingspeaking
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Orbits:A Brief Historical Look
Arthur C. Clark
Discovered This Orbit
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Ancient Orbit History:
“ORBIT” from Latin word “orbita” orbitus = circular orbis = 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
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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.
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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
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Orbit History :
• 1610 A.D. Galileo Galilei
- Good friends with Copernicus- Observations with TELESCOPE reinforced Copernicus- The wrath of the Catholic Church
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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?
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Orbit History:
Kepler’s 3 Laws of Planetary Motion1. 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 theplanet’s mean distance from the sun.
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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
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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
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Newton’s Laws:
Newton Continued... - 1687, Principia Published
- Law of Universal Gravitation (Attraction)
FMmG
r 2 F
mV
r
2
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Universal Gravitation, Applied:
- When in space why do you float? i.e. Weightlessness
mV
r
MmG
r
2
2
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Types of Orbits:
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Types of Orbits:
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Types of Orbits:
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Earth, the Moon, Mars, and the Stars Beyond
A Brief Discussion on Mission Design
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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=):
v2 r
a
GM
v r
v2 r
a
v2 r
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Circular Orbit:
For a 250 km circular Earth Orbit
Orbital Velocity
Orbital Period
v r
v398600.4
(250 6378.14)
v7.75 km
sec 17,347 mph
P circumference
velocity
P 2r3
P 2 (250 6378.14)3
398600.4
P 5,370 sec 89.5 min
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Circular Orbit:
For a 500 km circular Earth Orbit
Orbital Velocity
Orbital Period
Conclusions???
v r
v398600.4
(500 6378.14)
v7.61 km
sec 17,028 mph
P 2 r3
P 2(500 6378.14)3
398600.4P 5,676 sec 94.6 min
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Changing Orbits:
How about 250 km to 500 km
How would you do it?
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Changing Orbits:
Changing orbits usually involves an elliptical orbit
Perigee = closeApogee = far
Since orbit is elliptical a > 0, so
where
v2 r
a
a r1 r2
2
a (250 6378.14) (500 6378.14)
2a 6753 km
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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
v f 7.61 km
sec
vi 7.75 km
sec
vper 2 r
a
vper 2* 398600.4
(250 6378.14)
398600.4
6753
vper 7.83 km
sec
vapo 7.54 km
sec v1 vper vi
v2 vapo v f
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Changing Orbits:
Therefore:V1 is to start transfer
V2 is to circularize orbit
Time to do transfer is
v1 vper vi
v1 7.83 7.75
v1 .08 km
sec
v2 vapo v f
v2 7.54 7.61
v2 .07 km
sec
P 2 a3
*.5
P 2(6753)3
398600.4* .5
P 2,761 sec 46 min
v2v1
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How well do you understand Hohmann Transfers?
123
• 1 to 2?
• 2 to 3?
• 3 to 1?
• 1 to 3?
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Changing Orbits:
Also something called “Fast Transfer”
• It is more direct and quicker
• However it takes more fuel
• V1 and V2 are much bigger
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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 surface2) Gravity will cause your spacecraft to zip off into space for a
long time
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Getting to the Moon:
Gravity Assist
v2
v1
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Apollo XIII:
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Apollo XIII:
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Apollo XIII:
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Apollo XIII:
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To the Moon for Money:
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To the Moon for Money:
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To the Moon for Money:
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Earth to L1:
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Earth to Mars:
Mars Orbit
Earth Orbit
Transfer Orbit
Initial Orbit
Final Orbit
v2v1
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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
sec 75.7 km
vi
v2 r
vesc 2 * 398600.4
(250 6378.14)
vesc 10.97 km
sec
vesc 3.22 km
sec
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QuestionsQuestions