Transcript GEEN2850_15_Orbits - Colorado Space Grant Consortium

Welcome
to
GEEN 2850 / 4850
ASTR 2840
Independent Study
Colorado Space Grant Consortium
March 19, 2001
Today
- Announcements
- Discussion on Orbits
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
Orbits:
A Brief Historical Look
Arthur C. Clark
Discovered This Orbit
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
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.
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
Orbit History :
• 1610 A.D.
Galileo Galilei
- Good friends with Copernicus
- Observations with TELESCOPE reinforced
Copernicus
- The wrath of the Catholic Church
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?
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.
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=ma
- 1666, he understood planetary motion
- Did zip for 20 years until Edmund Halley
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
Newton’s Laws:
Newton Continued...
- 1687, Principia Published
- Law of Universal Gravitation (Attraction)
MmG
mV
F
F
2
r
r
2
Universal Gravitation, Applied:
- When in space why do you float? i.e. Weightlessness
mV
r
2
MmG

2
r
Types of Orbits:
Types of Orbits:
Types of Orbits:
Earth, the Moon, Mars, and the
Stars Beyond
A Brief Discussion on Mission Design
Kepler:
Kepler’s Laws...Orbits described by conic sections
Velocity of an orbit described by following equation
v
2  
r

  
a 
For a circle (a=r):
v
For a ellipse (a>0):
v
For a parabola (a=):
v
GM

r
2  
r

  
a 
2  
r
Circular Orbit:
For a 250 km circular Earth Orbit
Orbital Velocity
v
v

r
398600.4
(250  6378.14)
v7.75
km
 17,347 mph
sec
Orbital Period
P 
circumference
velocity
P  2
r3

(250  6378.14)3
P  2
398600.4
P  5,370 sec  89.5 min
Circular Orbit:
For a 500 km circular Earth Orbit
Orbital Velocity
v
v

r
398600.4
(500  6378.14)
v7.61
km
 17,028 mph
sec
Orbital Period
P  2
r3

(500  6378.14)3
398600.4
P  5,676 sec  94.6 min
P  2
Conclusions???
Changing Orbits:
How about 250 km to 500 km
How would you do it?
Changing Orbits:
Changing orbits usually involves an elliptical orbit
Perigee = close
Apogee = far
Since orbit is elliptical a > 0, so
2    
v
where
a 
r
  
a
r1  r2 
2
(250  6378.14)  (500  6378.14)
a 
2
a  6753 km
Changing Orbits:
Here’s what you need:
1) Velocity of initial orbit
vi  7.75
km
sec
v f  7.61
km
sec
2) Velocity of final orbit
3) Velocity at perigee
v per 
v per 
2     
r
a 
2* 398600.4
(250  6378.14)
v per  7.83

398600.4 
 6753 
km
sec
4) Velocity at apogee
v apo  7.54
km
sec
Then figure out your DV’s
Dv1  v per  vi
Dv2  v apo  v f
Changing Orbits:
Therefore:
DV1 is to start transfer
Dv1  v per  vi
Dv1  7.83  7.75
km
Dv1  .08
sec
DV2 is to circularize orbit
Dv2  v apo  v f
Dv2  7.54  7.61
km
Dv2  .07
sec
Time to do transfer is
P  2
a3

*.5
(6753)3
* .5
398600.4
P  2,761 sec  46 min
P  2
Dv1
Dv2
How well do you understand Hohmann Transfers?
• 1 to 2?
• 2 to 3?
• 3 to 1?
3
• 1 to 3?
2
1
Changing Orbits:
Also something called
“Fast Transfer”
• It is more direct and quicker
• However it takes more fuel
• DV1 and DV2 are much bigger
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 DV 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
Getting to the Moon:
Dv2
Dv1
 Gravity Assist
Apollo XIII:
Apollo XIII:
Apollo XIII:
Apollo XIII:
To the Moon for Money:
To the Moon for Money:
To the Moon for Money:
Earth to L1:
Earth to Mars:
Final Orbit
Initial Orbit
Dv2
Dv1
Earth Orbit
Transfer Orbit
Mars Orbit
Earth to Beyond:
Say you are in a 250 km orbit...
Orbital Velocity:
km
vi  7.75
sec
Velocity on parabolic
(a=escape trajectory:
v
2  
r
DV needed:
vesc 
2 * 398600.4
(250  6378.14)
vesc  10.97
km
sec
Dvesc  3.22
km
sec
DV will not put you in a orbit,
you will escape the Earth’s
gravity never to come back
Questions