Gateway To Space ASEN ASTR 2500 Class 15
- Slides: 65
Gateway To Space ASEN / ASTR 2500 Class #15 Colorado Space Grant Consortium T-18
Gateway To Space ASEN / ASTR 2500 Class #15 Colorado Space Grant Consortium T-18
Gateway To Space ASEN / ASTR 2500 Class #17 Colorado Space Grant Consortium T-18
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 4
Announcements… 5
Announcements… 6
Announcements… 7
Announcements… 8
Announcements… 9
Announcements… - DD Rev C is due 11 -02 -10 - Don’t forget about HW #7 due 11 -18 -10 - Don’t forget about community service - Updated grades will be posted this week - Spacecraft Communications lecture? - Spacecraft Propulsion lecture? 10
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? 11
One Minute Report… - If we are overweight can we use margin of other teams? - How is the camera programming coming along? 12
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
Universal Gravitation, Applied: • How does this apply to orbits?
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 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 is velocity G is Universal Gravitational Constant M is mass of planet or satellite R is radius of planet of satellite
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
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: 1. All planets move in elliptical orbits, sun at one focus
Orbit History: Kepler’s 3 Laws of Planetary Motion: 1. 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. A line joining any planet to the sun, sweeps out equal areas in equal times
Orbit History: Kepler’s 3 Laws of Planetary Motion: 3. The square of the period of any planet about the sun is proportional to the cube of the planet’s mean distance from the sun. Planet P (yr) a (AU) T 2 R 3 Mercury 0. 24 0. 39 0. 06 Venus 0. 62 0. 72 0. 39 0. 37 Earth 1. 00 2 T = 3 R Mars Jupiter Saturn 1. 88 11. 9 29. 5 1. 52 5. 20 9. 54 3. 53 3. 51 142 141 870 868 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: 1 st Law. . . Body at rest stays at rest, a body in motion stay in motion 2 nd Law. . F=m*a 3 rd Law. . . For every action, there is an equal and opposite reaction
Newton’s Laws: Newton Continued. . . • 1687, Principia Published • Law of Universal Gravitation (Attraction)
Newton’s Laws: Newton Continued. . . • 1687, Principia Published • Law of Universal Gravitation (Attraction)
Universal Gravitation, Applied: • When in space why do you float? i. e. Weightlessness
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
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= ):
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
Earth, the Moon, Mars, and the Stars Beyond A Brief Discussion on Mission Design
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)
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
Orbit Definition: Keplerian Elements - Semi major axis (a) - Size - Eccentricity (e) - Shape
Orbit Definition: Keplerian Elements - Inclination (i) - Angle to the Equator
Orbit Definition: Keplerian Elements - Right Ascension of Ascending Node (RAAN, Ω) - Rotation about the Earth’s Spin Axis
Orbit Definition: Keplerian Elements - 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
Orbital Elements: • Used to determine a satellite’s location in orbit:
Types of Orbits:
Types of Orbits:
Types of Orbits (cont. ) • Geosynchronous/ Geostationary
Types of Orbits (cont. ) • Critical Inclination
Types of Orbits (cont. ) • Repeating Ground Trace
Types of Orbits (cont. ) • Polar/ Sun Synchronous
Types of Orbits (cont. ) • Molniya
Circular Orbit: For a 250 km circular Earth Orbital Velocity Orbital Period
Circular Orbit: For a 500 km circular Earth Orbital Velocity Orbital Period 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 where
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
Changing Orbits: Therefore: DV 1 is to start transfer DV 2 is to circularize orbit Time to do transfer is
How well do you understand Hohmann Transfers? • 1 to 2? • 2 to 3? • 3 to 1? • 1 to 3? 3 2 1
Circular Orbit:
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