Unit 3 AE Review
3.1 Space Travel
What is Space?
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
What is the universe?
– Everything. All that we see and cannot see.
How big is the universe?
– Hubble Space Telescope sees 10 billion light years
– Light-year is the distance that light travels in one year, about 6 trillion miles
– Radio waves sense few billion light years beyond
What is a galaxy?
– An assembly of stars and related matter and gas, all held together by mutual gravity
What is a star?
– A great ball of fire
What is a planet?
– An orbiting body large enough to become round due to its own gravity
– Large enough to dominate the vicinity of its orbit
Order of the planets
– Terrestrial or Earth-like planets: Mercury, Venus, Earth, and Mars
– Gas giants: Jupiter, Saturn, Uranus, and Neptune
– Dwarf planet: Pluto
What is a moon?
– Natural satellite of a planet
How old is the universe?
– Started with the Big Bang 14 billion years ago
What is Space Law
Military uses of space
– UN Conference of Disarmament (CD) established in 1979 with roots back to 1960
– CD goal to reduce all weapons, including arms race in space
Non-military uses of space coordination
– United Nations (UN) established a committee in 1958
– Named United Nations Office of Outer Space Affairs
– Grew from 24 to 69 current member countries
UN Office of Outer Space Affairs
– Promote peaceful use of outer space for all mankind
– Contact with governments and Non-Government Organizations (NGOs)
– Exchange scientific information
– Promote international cooperation
– Maintain registry of objects launched into space
Why do we need space law?
– To responsibly develop space for the good of humankind
What is space law?
– Five international treaties and sets of principles agreed to by many nations
Space law applies to military and non-military applications
Law prevents any claims of possession made for outer space or bodies
Objects launched into space remain the responsibility and possession of original owners
State (i.e., country) from which object is launched is responsible for subsequent damage
International agreements to promote space for all humankind
United Nations used as mechanism for communication and coordination
Space law protects space for humankind
Unit 3 AE Review
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Commercial Space Flight
Original manned spaceflight started in early 1960s
Government was the only organization going into space
Recent government budget changes and technological innovations provided an environment for private industry
to enter space
Within last few years this has become a reality
Trend is advancing and evolving as a legitimate industry and method of transportation
Call to action was initiated by Dr. Peter Diamondis through the formation of the X-Prize Foundation in 1999
X-Prize sparked development with $10M prize & Over 20 teams competed
Scaled Composites in Mojave, CA demonstrated successful flight test on June 21, 2004
Official record set and Ansari X-Prize awarded on October 4, 2004
Suborbital spaceflight achieves flights to altitudes qualifying as space but do not achieve or maintain orbit
• Typically short-duration flight
• Cannot reach ISS
• Typically take-off and land at same location
Spaceship One• First spacecraft to successfully achieve suborbital manned spaceflight as a private company (no
government funding or support)
• Mothership “White Knight” lifts spacecraft to 50,000 feet – above 80%+ of atmosphere
Virgin Galatic
• Initial test flights in 2011-2012
• First commercial flight planned for 2013
• Operates from New Mexico
Retirement of shuttle program in 2011 created need for new spacecraft to support ISS
Commercial Human Orbital Flight Providers
• Russians currently selling seats onboard
• $20M per person
Soyuz
• 10 days on ISS
SpaceX developing Dragon spacecraft
Boeing repurposing Orion capsule development for commercial variant
Bigelow Aerospace developing Orbital Hotel facility
Next 20 years will bring major changes as commercial organizations work to access space
Major goal is to reduce cost for access to space while improving safety and reliability
Similar situation to what commercial airline industry faced in 1930s
Significant number of jobs in aerospace will be provided by these companies
Moon Race
Space age began October 4, 1957
• Russian orbited Sputnik I
• First artificial satellite
First living being November 3, 1957
• Russian orbited Sputnik II
• Dog named “Laika” onboard
National Aeronautics and Space Administration (NASA) created 1958
• Civilian-controlled
• Military maintained own programs
President Kennedy committed in 1961 to land man on Moon before decade’s end
Pioneer IV space probe March 3,1959
• Juno II rocket
• Russian Mechta rocket two months earlier
Able-Baker Mission
• Two monkeys survived space orbit
Russian Yuri Gagarin circled Earth once on April 12, 1961
Mercury Project
• Humans in space
• Allan Shephard's suborbital flight May 1961
Unit 3 AE Review
•
John Glenn became the first American to orbit the Earth
• Gemini Program
• Learning experience to prepare for trips to the Moon
• Ranger and Lunar Orbiter programs (1961-67)
• Provided detailed photographs
• Scouted a landing site
• Surveyor Program (1966-68)
• Gathered moon samples
• Excellent safety record despite risks
• Fire developed in Apollo command module
• Three astronauts died by asphyxiation January 27, 1967
• Virgil I. Grissom
• Roger B. Chaffee
• Edward H. White II
• Apollo program
• Astronauts to Moon
• 3 scenarios
• Direct
• Lunar orbit rendezvous (this
• Earth orbit rendezvous
was chosen)
• Used Saturn rockets
• Neil Armstrong 1st man on Moon July 20, 1969
• America only nation on Moon
• 12 astronauts stepped on Moon
• Five more flights to the Moon
• Last Moon landing in 1972
• Technology from Program
• Gemini and Apollo made electrical power from hydrogen-oxygen fuel cells
• Astronauts used scanning telescope and sextant to take star sights and plot position of spacecraft
• Guidance and navigation information transmitted to Earth-based computers to calculate course or
velocity changes
• Experiments in space
• Skylab
• Hubble space telescope
• Apollo-Soyuz (US and Russia)
• International Space Station (ISS)
• Space Shuttle
• Many countries contributing
• Explore planets
• Mars rover
Space Junk
• What is space junk?
• Natural
• Artificial
• Comets, asteroids
• Satellite break up
• Paint flakes, tools, and thermal blankets
• Human refuse
• Statistics
• 28,000 objects created since 1957
• 75 launches per year
• 9,000 still in orbit (550 are useful)
• Danger?
• Low Earth Orbit (LEO) debris
• 7 km/s = 18,000 mph
• Energy
• Car @ 55 mph
• bowling ball @ 300 mph
• 60 lb safe @ 60 mph
Unit 3 AE Review
•
•
•
•
•
•
•
•
•
•
•
•
How long will it orbit?
• <200 km = days (LEO for space shuttle)
• >800 km = centuries
• 200-600 km = years
• >36,000 km = forever
• 600-800 km = decades
Spacecraft measure objects sized < 0.1 cm @ Millions of objects
Telescopes and radar tracking (> 0.5 cm) @ >100,000 objects
Optical tracking (> 10 cm)@ 11,000 objects
Multi-national effort
• NASA Orbital Debris Program Office
• European Space Operations Centre
Advise orbit changes
Incidents
• CERISE, 1996: Briefcase size 31,500 mph
• South Africa, 2000
• South African land strike
• Satellite and shuttle windshield strikes
• Texas, 1997
Donald Kessler journal publication in 1978
• Example: Iridium 33 and Comos 2251 collision in 2009
Satellite collision generates fragments
• Limit creation
Fragments cause exponential increase in collisions
• Limit explosions with better equipment
Growth of debris belt
• Graveyard orbit above popular geosynchronous orbit
Potentially blocks other craft from that altitude
• Clean up mess
or above
3.2 Orbital Mechanics
Historical Figures
•
•
•
•
•
•
Nicolaus Copernicus (1473-1543)
• First to theorize that the Earth and other planets actually revolved about the Sun
• Assumed the motion to be circular
• Took accurate measurements and found that his assumption was not strictly accurate
• Theory was considered heretical at the time
Tycho Brahe (1546-1601)
• Lectured at University of Copenhagen
• Responsible for gathering a wealth of accurate planetary motion measurements
Johannes Kepler (1571-1630)
• Assistant to Brahe
• Proposed that planetary orbits were elliptical
• Proposed laws of orbital motion that are still used today
Robert Hooke (1635-1703)
• Member of the Royal Society
• Debated Newton on facts about orbital mechanics
Isaac Newton (1643-1727)
• Grew interested in mathematics from reading about astronomy
• From Kepler’s work, deduced the existence of an inverse square law attractive force
• Proposed Theory of Universal Gravitation
• Wrote Principia, considered the greatest scientific book ever written
• Posits his three laws
Orbital Patterns
Low Earth Orbit (LEO)
• LEOs orbit relatively close to the Earth (e.g., several hundred kilometers, km) with no minimum altitude.
• LEO orbits are characterized by short orbital periods.
Unit 3 AE Review
•
•
•
•
•
•
•
• Roughly 90 minutes
• Many revolutions per day and limited swath areas (area that a satellite can see)
•
All staffed space missions except lunar missions have been LEO.
• Many Earth-observing satellites are LEO orbits.
Geostationary (GEO)
• A geostationary satellite stays in one spot with respect to the Earth.
• Achieved by placing satellite at altitude where orbital period exactly equals one day.
• Orbit is about 22,300 miles above Earth and inclination is exactly zero degrees.
• There is only one altitude above Earth with an orbital period of 24 hours
• All geostationary orbits are in a ring around Earth
• Ring is called the geostationary belt
• Geostationary belt is a limited resource
Molniya (“Moly”)
• Geostationary satellites for Russian communications pose severe challenges since a majority of its land
mass is too far north for geostationary belt satellites to see.
• Molniya ground trace differs from most conventional ground traces.
• The image below clearly illustrates the satellite hang time over Russia.
Polar
• Polar orbit has a 90 degree inclination
• Satellite will eventually pass over all of Earth
• Polar orbit satellites can gather information about the entire Earth
• E.g., weather satellites
Constellations
• Single satellites are often insufficient to perform a mission
• Groups of satellites in various orbits work together to accomplish the mission
• This grouping of satellites is called a constellation
• E.g., GPS system
Orbital Mechanic Modeling
Orbits are described by a set of parameters called orbital elements (i.e., Keplerian elements).
The Keplerian element set consists of 6 parameters (plus a time stamp):
o A time stamp, referred to as an “epoch,” must also be included when providing a Keplerian element set.
This is so that it is known WHEN this set of values was accurate for the satellite or when the “snapshot”
of the orbit was taken.
o Two of these describe the size and shape of an orbit:
 Eccentricity (e)
 Semi-major axis (a)
o Three of these describe the orientation of the orbit in space:
 Inclination (i)
 Right ascension of the ascending node
(W)
Apogee
Semi-minor axis, b
 Argument of perigee (w)
Semi-major axis, a
o One of these describes the location of the satellite
Apogee
Perigee
within the orbit:
altitude
Altitude Perigee
 True anomaly (u)
Eccentricity describes the roundness of an orbit.
o It describes the shape of the ellipse in terms of how wide it is.
o Calculate the eccentricity of a circle.
o
Eccentricity can vary from 0  e  1
Unit 3 AE Review
𝑏2
o
𝑒 = √1 − 𝑎2
o
o
Eccentricity of 0 means the orbit is circular.
An eccentricity of 1 or greater means the orbit is not closed. Such would be used for interplanetary
missions. Satellites in these types of orbits do not come back to their starting point.
3
•
𝑇 = 2𝜋 ×
o
o
o
𝑎2
√𝜇
3
= 2𝜋 ×
𝑎2
√𝐺𝑀
𝑇 = 𝑂𝑟𝑏𝑖𝑡𝑎𝑙 𝑃𝑒𝑟𝑖𝑜𝑑
𝑎 = 𝑆𝑒𝑚𝑖𝑀𝑎𝑗𝑜𝑟 𝐴𝑥𝑖𝑠
𝜇 = 𝐺𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟
-11
•
•
•
•
•
•
3
2
o G = Universal Gravitation Constant (6.67x10 m /kg*s )
o 𝑀 = 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑏𝑜𝑑𝑦
Inclination is the angle between the Earth’s equatorial plane and the plane of the orbit.
o It describes the tilt of the orbit.
o Inclination determines the northern and southern latitude limits over which the satellite orbits. For
example, a satellite with a 45o inclination will have a ground trace ranging from 45o north to 45o south.
o An orbit with an inclination of 0 degrees is called an equatorial orbit.
o An orbit with an inclination of 90 degrees is called a polar orbit.
Determining a Satellite’s Orbital Period from its Ground Trace
o Recall that the orbit of a satellite remains fixed in space, and the Earth rotates underneath it.
o The westward regression of the ground trace is due to the rotation of the Earth.
o Determine how many minutes it takes for the Earth to rotate one degree:
o
1440 minutes/360 degrees = 4min/degree
o Determine how many degrees per pass the satellite’s orbit regresses on consecutive orbits (equatorial
crossing is a common reference point). We’ll use 25 degrees as an example.
o How long did it take the Earth to rotate this many degrees? That’s the period of the satellite.
o
25degrees * 4min/degree = 100 minutes
Right Ascension of the Ascending Node (RAAN, W )
o Satellites may have identical eccentricities, semi-major axes, and inclinations (e, a, and i) yet may still be
oriented differently in space – they can be “rotated” or “twisted” about the Earth in various ways.
o Each satellite here starts out above a different longitude on the Earth. However, longitude can’t be used
as a reference point because the Earth will rotate underneath the orbits, changing the reference
longitude on each satellite pass.
o Right ascension of the ascending node is the angle measured along the equatorial plane between a
vector pointing to a fixed reference point in space (the first point of Aries, also known as the vernal
equinox) and the point on the orbit where the orbital motion is from south to north across the equator
(this point is called the ascending node).
Argument of Perigee (ω)
o Orbits may have the same e, a, I, and W, yet may still have different orientations around the Earth. The
location of their perigee point can vary within the orbital plane.
o Argument of perigee describes the orientation of the orbit within the orbital plane
o It is measured as the angle from the ascending node to the perigee point in the direction of the
satellite’s motion.
True Anomaly (υ)
o After an orbit and its orientation have been thoroughly described, there must be a way to describe the
satellite’s position within an orbit at any instant.
o True anomaly is the angle between the perigee point and the satellite’s location (measured in the
direction of the satellite’s motion). This value is constantly changing as the satellite moves in its orbit.
o True anomaly is 0 degrees at perigee, 180 degrees at apogee.
Kepler’s Laws
Unit 3 AE Review
o
o
o
•
st
Kepler’s 1 Law: Satellites will travel around Earth in elliptical paths with the center of Earth at one of
the foci.
Kepler’s 2nd Law: A line drawn between Earth and a satellite will sweep out equal areas during equal
time periods anywhere along the orbit.
Kepler’s 3rd Law: The period of an orbit (T) is related to its semi-major axis (a) by: 𝑇 2 = 4𝜋 2 𝑎3 ⁄𝜇
Orbital Mechanics Physics
Potential energy is energy that is stored within a system due to the position of the system.
o Potential energy has potential to convert into other energy forms.
−𝐺𝑀𝑚
o 𝑈=
𝑅
o U = Potential Energy
-11
•
•
•
•
•
•
3
2
o G = Universal Gravitation Constant (6.67x10 m /kg*s )
o M= Mass of central body
o m= Mass of orbiting body
o R= Distance from center of central body to center of orbiting body
Kinetic energy is energy of motion.
1
o 𝐾 = 𝑚𝑣 2
2
o K= Kinetic Energy
o m= mass of body
o v= velocity of body
Both forms of energy are important to satellite orbits.
Gravitational pull of Earth provides potential energy.
Satellite movement has kinetic energy.
Total Energy of Orbit
𝐺𝑀𝑚
o 𝐸 = 𝐾 + 𝑈 = − 2𝑅
Review
o Potential energy and kinetic energy are two main orbital energies.
o Combine both to find total energy of orbit.
o With both orbit energies, subtract to determine energy to transfer between orbits.
Systems Tool Kit (STK)
•
•
•
•
Software performs complex analysis of land, sea, air, and space vehicles
Physics-based software geometry engine
Calculates the positions of assets and movement over time
Create scenarios to monitor surface events.