Gat ew ay T o S pace AS EN / AS TR Class # 19. Colorado S pace Grant Consortium

Gat ew ay T o S pace AS EN / AS TR 2500 Class # 19 Colorado S pace Grant Consortium

Announcements: - Launch Readiness Review Cards - 11 days to launch

Announcements:

Orbits: A Brief Historical Look

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

Universal Gravitation, Applied: When in space why do you float? i.e. Weightlessness 2 mv MmG = 2 r r MG V= r

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

Orbits: A Brief Historical Look Arthur C. Clarke 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 Solar Calendar of 365 days Time divided into 60 even units

350 B.C.: Greek Thoughts Aristotle Said earth is center of the universe Dominated scientific thought for 1800 years Ptolemy Geocentric (Earth centered) theory

Start of the Heliocentric Model: 350 B.C Aristarchus of Samos Said Geocentric model was B.S Heliocentric Figured out distance to sun and moon Why didn t objects fly off the spinning Earth? Why didn t the motion of the Earth around the sun leave behind the birds flying in the air?

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

Orbit History : 1580 A.D. Tycho Brahe Accurate measurements of planets (Mars) 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 Discovered Venus has phases

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?

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

Orbit History: Kepler s 3 Laws of Planetary Motion: 2. A line joining any planet to the sun, sweeps out equal areas in equal times

Orbit History: Kepler s 3 Laws of Planetary Motion: 2. 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. Planet P (yr) a (AU) T2 R3 Mercury 0.24 0.39 0.06 0.06 Venus 0.62 0.72 0.39 0.37 2 3 Earth 1.00 1.00 1.00 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 T =R If you can observe the period of rotation, you can determine the distance

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

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) m1m 2 G F= 2 r

Newton s Laws: Newton Continued... 1687, Principia Published Law of Universal Gravitation (Attraction) F= m1m 2G r2 m1m 2 G F= = m1 g 2 r

Newton s Laws: Newton Continued... 1687, Principia Published Law of Universal Gravitation (Attraction) m2v F= ma = r 2 m1m 2 G F= 2 r

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

Universal Gravitation, Applied: When in space why do you float? i.e. Weightlessness 2 mv MmG = 2 r r MG V= r

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 V= 2 MG MG r a

Kepler: Kepler s Laws...Orbits described by conic sections Velocity of an orbit described by following equation v= (2 µ ) r For a circle (a=r): µ a v= For a ellipse (a>0): v= For a parabola (a= ): v= µ= G M (µ ) r (2 µ ) r (2 µ ) r µ a

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?

Questions: Let s figure it out v = GM R v is velocity G is Universal Gravitational Constant M is mass of planet or satellite R is radius of planet of satellite

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

Atmosphere: Let s figure it out v = GM R v is velocity G is Universal Gravitational Constant M is mass of planet or satellite R is radius of planet of satellite G = 6.6 7 x 1 0 M M 1 1 ( m 3 kg s2 24 E a r th = 5.9 7 4 x 1 0 = 7.3 5 0 x 1 0 22 M oon ) kg R E a r th = 6367000 m kg R M oon = 1738000 m

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

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

Types of Orbits:

Circular Orbit: For a 250 km circular Earth Orbit Orbital Velocity (µ ) v= r (3 9 8 6 0 0. 4 ) v= ( 2 5 0 + 6 3 7 8.1 4 ) km v =7.7 5 = 1 7,3 4 7 m p h sec Orbital Period P P = c ir c u m f e r e n c e v e lo c ity = 2π r3 µ ( 2 5 0 + 6 3 7 8.1 4 ) = 2π 3 9 8 6 0 0.4 = 5, 3 7 0 s e c = 8 9. 5 m in 3 P P

Circular Orbit: For a 500 km circular Earth Orbit Orbital Velocity (µ ) v= r v= (3 9 8 6 0 0. 4 ) ( 5 0 0 + 6 3 7 8.1 4 ) km v =7.6 1 = 17,028 m p h sec Orbital Period P = 2π r3 µ ( 5 0 0 + 6 3 7 8.1 4 ) 3 P = 2π 3 9 8 6 0 0.4 P = 5, 6 7 6 s e c = 9 4. 6 m in 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 µ ) µ v= where a = r a (r 1 + r 2 ) 2 (( 2 5 0 + 6 3 7 8. 1 4 ) + ( 5 0 0 + 6 3 7 8. 1 4 ) ) a = 2 a = 6753 k m

Changing Orbits: Here s what you need: 1) Velocity of initial orbit v i = 7.7 5 km sec = 7.6 1 km sec 2) Velocity of final orbit v f 3) Velocity at perigee (2 µ ) µ = v per v per = v per = a r ( 2 * 3 9 8 6 0 0.4 ) ( 2 5 0 + 6 3 7 8.1 4 ) 7.8 3 3 9 8 6 0 0.4 6753 km sec 4) Velocity at apogee km v apo = 7.5 4 sec Then figure out your V s v1 = v per vi v2 = v f vapo

Changing Orbits: Therefore: V1 is to start transfer v1 = v p er vi v1 = 7.8 3 7.7 5 km v1 =.0 8 sec V2 is to circularize orbit v2 = v f vapo v2 = 7.61 7.54 v2 =.07 km sec Time to do transfer is P = 2π a3 *.5 µ (67 5 3 )3 *.5 3 9 8 6 0 0.4 P = 2, 7 6 1 s e c = 4 6 m in P = 2π v1 v2

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

Changing Orbits: Also something called Fast Transfer It is more direct and quicker However it takes more fuel V1 and V2 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 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

Getting to the Moon: v2 v1 Gravity Assist

Apollo XIII:

So... One switch controls the light bulb Light bulb is on 2nd floor Can t see it unless you go upstairs Can flip switches as many times Can go upstairs once Which switch is it? If you could go up twice, how would you do it? What does a light bulb do? Besides light? What about heat?

To the Moon for Money:

Earth to L1:

Earth to Mars: Final Orbit Initial Orbit v2 v1 Earth Orbit Mars Orbit Transfer Orbit

Earth to Beyond: Say you are in a 250 km orbit... km Orbital Velocity: vi = 7.75 sec Velocity on parabolic (a= ) escape trajectory: v= (2 µ ) v esc = r v esc V needed: (2 * 3 9 8 6 0 0. 4 ) ( 2 5 0 + 6 3 7 8.1 4 ) km = 1 0.9 7 sec v esc = 3.2 2 km sec V will not put you in a orbit, you will escape the Earth s gravity never to come back

Questions

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