RBE 595 Space and Planetary Robotics Lecture 1
RBE 595: Space and Planetary Robotics Lecture 1 Professor Marko B Popovic A term 2019
Robotics in space and planetary environments so far… In the context of spaceflight, a satellite is an object that has been intentionally placed into orbit… Satellites are usually semi-independent computer-controlled systems. (Robots? ) Satellite subsystems attend many tasks, such as power generation, thermal control, telemetry, attitude… A space probe is a robotic spacecraft that does not orbit Earth, but instead, explores further into outer space. A space probe may approach the Moon; travel through interplanetary space; flyby, orbit, or land on other planetary bodies; or enter interstellar space. Robotic manipulator arms attached to spacecraft or space station to deploy, maneuver and capture payloads and assist with docking procedures. They include: Canadarm 1 (on now decommissioned Space Shuttle orbiters), Canadarm 2 (on ISS), Dextre (2 arm robot on ISS), JEMRMS (on ISS) A rover (or sometimes planetary rover) is a space exploration vehicle designed to move across the surface of a planet or other celestial body. Some rovers have been designed to transport members of a human spaceflight crew; others have been partially or fully autonomous robots. Includes Moon rovers (Lunokhod 1 and 2, Apollo Lunar Roving Vehicle, Yutu and Yutu 2) and Mars rovers (Sojourner, Opportunity, Spirit and Curiosity). Class of various robot assistants on ISS including: Robonaut 1 and 2, Sphere, Astrobee, Fedor….
Robonaut, a joint DARPA–NASA project designed to create a humanoid robot which can function as an equivalent to humans during the 1970 s and exploration. The large goal of the Robonaut project is to build a robot with dexterity that exceeds that of a suited astronaut. Robonaut A few robot images Dextre is a two armed robot, or telemanipulator, which is part of the Mobile Servicing System on the International Space Station (ISS). It replaces some activities otherwise requiring spacewalks. It was launched March 11, 2008 on mission STS-123. Dextre on ISS The Curiosity landed on Mars surface August 6, 2012. This was the largest rover NASA has put on Mars, being twice as long and five times as heavy as its processors. The Curiosity took many design elements from the previous generation of Mars rovers such as six wheel drive, rocker-bogie suspension, and cameras mounted to the mast of the rover to help the mission's team direct the rover. However unlike the previous generation the Curiosity contains an entire inboard laboratory for analyzing the soil and rocks on Mars. NASA engineered the Curiosity to be capable of rolling over obstacles up to 65 centimeters high and traverse up to about 200 meters per day on Martian terrain. Curiosity got its electrical power from a Radioisotope thermoelectric generator. Curiosity rover
Robotics in space and planetary environments in the near future… It appears, a lot of focus will be on the Moon… https: //www. nasa. gov/specials/moon 2 mars/ So, one may anticipate new lunar based robots: -Robots that can operate individually or in groups (maybe more intelligently than in traditional swarms). -Robots that are fast and that are capable to efficiently, robustly transverse lunar terrain, excavate (work with regolith, rocks, polar ice, …), analyze and process local resources. -Robots that will provide full telepresence for us on the Moon, and perhaps build a Lunar base, build and repair themselves, and work along humans when we finally arrive to the Moon. One should also anticipate a new generation of robots that can work with space debris, those specialized for asteroids, meteors, and comets, as well as new space stations (Moon and Earth orbits) builders. One should also expect more space military robots…
Cosmic Journeys by National Geographic Magazine (c. 2012) http: //visualoop. com/infographics/cosmic-journeys
Some quick facts about the Solar system Our solar system consists of the sun, eight planets, moons, many dwarf planets (or plutoids), an asteroid belt, comets, meteors, and others. The sun is the center of our solar system; the planets, their moons, a belt of asteroids, comets, and other rocks and gas orbit the sun. The eight planets that orbit the sun are (in order from the sun): Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. Another large body is Pluto, now classified as a dwarf planet or plutoid. A belt of asteroids (minor planets made of rock and metal) lies between Mars and Jupiter. These objects all orbit the sun in roughly circular orbits that lie in the same plane, the ecliptic (Pluto is an exception; it has an elliptical orbit tilted over 17° from the ecliptic).
Size matters The largest planet is Jupiter. It is followed by Saturn, Uranus, Neptune, Earth, Venus, Mars, Mercury, and finally, tiny Pluto (the largest of the dwarf planets). Jupiter is so big that all the other planets could fit inside it.
Inner vs. Outer The inner planets (those planets that orbit close to the sun) are quite different from the outer planets (those planets that orbit far from the sun). The inner planets are: Mercury, Venus, Earth, and Mars. They are relatively small, composed mostly of rock, and have few or no moons. The outer planets include: Jupiter, Saturn, Uranus, Neptune, and Pluto (a dwarf planet). They are mostly huge, mostly gaseous, ringed, and have many moons (again, the exception is Pluto, the dwarf planet, which is small, rocky, and has four moons).
Temperature matters too… Generally, the farther from the Sun, the cooler the planet. Differences occur when the greenhouse effect warms a planet (like Venus) surrounded by a thick atmosphere.
Magnetic fields
Density and Mass The outer, gaseous planets are much less dense than the inner, rocky planets. The Earth is the densest planet. Saturn is the least dense planet; it would float on water. Jupiter is by far the most massive planet; Saturn trails it. Uranus, Neptune, Earth, Venus, Mars, and Pluto are orders of magnitude less massive.
Surface gravitational acceleration The planet with the strongest gravitational attraction at its surface is Jupiter. Although Saturn, Uranus, and Neptune are also very massive planets, their gravitational forces are about the same as Earth. This is because the gravitational force a planet exerts upon an object at the planet's surface is proportional to its mass and to the inverse of the planet's radius squared.
Surface gravitational acceleration
Daily rotations A day is the length of time that it takes a planet to rotate on its axis (360°). A day on Earth takes almost 24 hours. The planet with the longest day is Venus; a day on Venus takes 243 Earth days. (A day on Venus is longer than its year; a year on Venus takes only 224. 7 Earth days). The planet with the shortest day is Jupiter; a day on Jupiter only takes 9. 8 Earth hours! When you observe Jupiter from Earth, you can see some of its features change.
And period of revolution
Orbital speed As the planets orbit the Sun, they travel at different speeds. Each planet speeds up when it is nearer the Sun and travels more slowly when it is far from the Sun (this is Kepler's Second Law of Planetary Motion).
Revolution vs distance
Planet (or Dwarf Planet) Distance from the Sun (Astronomical Units miles km) Period of Revolution Period of Rotation Around the Sun (1 planetary day) (1 planetary year) 0. 39 AU, 36 million miles 87. 96 Earth days 58. 7 Earth days 57. 9 million km 0. 723 AU 224. 68 Earth 67. 2 million miles 243 Earth days 108. 2 million km Mercury Venus Mass (kg) Diameter (miles km) 3. 3 x 1023 3, 031 4, 878 km miles 4. 87 x 10 24 7, 521 12, 104 km miles 5. 98 x 10 24 7, 926 12, 756 km miles Earth 1 93 million 149. 6 million km AU miles 365. 26 days Mars 1. 524 141. 6 million 227. 9 million km AU 686. 98 miles days Earth 24. 6 Earth hours 4, 222 6. 42 x 10 23 =1. 026 Earth days 6, 787 km miles Jupiter 5. 203 483. 6 million 778. 3 million km AU 11. 862 miles years Earth Saturn 9. 539 886. 7 million 1, 427. 0 million km AU 29. 456 miles years Earth 24 hours Apparent size from Earth Temperature (K Range or Average) 5 -13 arc seconds 100 -700 mean=452 K 10 -64 arc seconds 726 K 0 Not Applicable 260 -310 K 1 4 -25 arc seconds 150 -310 K 2 31 -48 arc seconds 120 (cloud tops) 9. 84 Earth hours 1. 90 x 10 27 88, 729 142, 796 km miles 10. 2 Earth hours 5. 69 x 10 26 74, 600 120, 660 km miles 15 -21 arc seconds 88 K excluding rings Uranus 19. 18 1, 784. 0 million 2, 871. 0 million km AU miles 84. 07 Earth years 17. 9 Earth hours 8. 68 x 10 25 32, 600 51, 118 km miles Neptune 30. 06 2, 794. 4 million 4, 497. 1 million km AU 164. 81 miles years 19. 1 Earth hours 1. 02 x 10 26 30, 200 48, 600 km miles 39. 53 3, 674. 5 million 5, 913 million km AU miles 247. 7 years 6. 39 Earth days 1. 29 x 10 22 1, 413 2, 274 km miles Pluto (a planet) dwarf Earth Number of Moons K K 0 67 (18 named plus many smaller ones) 62 (30 unnamed) 3 -4 arc seconds 59 K 27 (6 unnamed) 2. 5 arc seconds 48 K 13 0. 04 arc seconds 37 K 4
Escape velocity
Location with respect to Ve (km/s)[9] Location on the Sun's gravity 617. 5 on Mercury's gravity 4. 3[10]: 230 on Venus's gravity on Earth's gravity on the Moon's gravity on Mars' gravity on Ceres's gravity on Jupiter's gravity on Io Io's gravity 2. 558 on Europa's gravity 2. 025 on Ganymede's gravity 2. 741 on Callisto's gravity 2. 440 on Saturn's gravity on Titan's gravity on Uranus' gravity on Neptune's gravity on Triton's gravity 1. 455 on Pluto's gravity 1. 2 at Solar the Milky Way's gravity System galactic radius on the event horizon a black hole's gravity with respect to Ve (km/s)[9] at Mercury the Sun's gravity 67. 7 at Venus the Sun's gravity 49. 5 at the Earth/Moon the Sun's gravity 42. 1 at the Moon the Earth's gravity at Mars the Sun's gravity 34. 1 at Jupiter the Sun's gravity 18. 5 at Saturn the Sun's gravity 13. 6 21. 3[10]: 240 at Uranus the Sun's gravity 9. 6 23. 8[10]: 240 at Neptune the Sun's gravity 7. 7 10. 3 11. 2[10]: 200 2. 4 5. 0[10]: 234 1. 4 0. 51 59. 6[10]: 236 35. 6[10]: 238 2. 639 492– 594[11][12] 299, 792 (speed of light
Kepler’s Laws In the early 1600 s, Johannes Kepler proposed three laws of planetary motion. Kepler was able to summarize the carefully collected data of his mentor - Tycho Brahe - with three statements that described the motion of planets in a sun-centered solar system. Kepler's efforts to explain the underlying reasons for such motions are no longer accepted; nonetheless, the actual laws themselves are still considered an accurate description of the motion of any planet and any satellite. Kepler's three laws of planetary motion can be described as follows: The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses) An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas) The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)
The Law of Ellipses Kepler's first law - sometimes referred to as the law of ellipses - explains that planets are orbiting the sun in a path described as an ellipse. An ellipse can easily be constructed using a pencil, two tacks, a string, a sheet of paper and a piece of cardboard. Tack the sheet of paper to the cardboard using the two tacks. Then tie the string into a loop and wrap the loop around the two tacks. Take your pencil and pull the string until the pencil and two tacks make a triangle (see diagram at the right). Then begin to trace out a path with the pencil, keeping the string wrapped tightly around the tacks. The resulting shape will be an ellipse. An ellipse is a special curve in which the sum of the distances from every point on the curve to two other points is a constant. The two other points (represented here by the tack locations) are known as the foci of the ellipse. The closer together that these points are, the more closely that the ellipse resembles the shape of a circle. In fact, a circle is the special case of an ellipse in which the two foci are at the same location. Kepler's first law is rather simple - all planets orbit the sun in a path that resembles an ellipse, with the sun being located at one of the foci of that ellipse.
The Law of Equal Areas Kepler's second law - sometimes referred to as the law of equal areas describes the speed at which any given planet will move while orbiting the sun. The speed at which any planet moves through space is constantly changing. A planet moves fastest when it is closest to the sun and slowest when it is furthest from the sun. Yet, if an imaginary line were drawn from the center of the planet to the center of the sun, that line would sweep out the same area in equal periods of time. For instance, if an imaginary line were drawn from the earth to the sun, then the area swept out by the line in every 31 -day month would be the same. This is depicted in the diagram below. As can be observed in the diagram, the areas formed when the earth is closest to the sun can be approximated as a wide but short triangle; whereas the areas formed when the earth is farthest from the sun can be approximated as a narrow but long triangle. These areas are the same size. Since the base of these triangles are shortest when the earth is farthest from the sun, the earth would have to be moving more slowly in order for this imaginary area to be the same size as when the earth is closest to the sun.
The Law of Harmonies Kepler's third law - sometimes referred to as the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets. Unlike Kepler's first and second laws that describe the motion characteristics of a single planet, the third law makes a comparison between the motion characteristics of different planets. The comparison being made is that the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets. Additionally, the same law that describes the T 2/R 3 ratio for the planets' orbits about the sun also accurately describes the T 2/R 3 ratio for any satellite (whether a moon or a man-made satellite) about any planet.
The Law of Harmonies Planet Period (yr) Average Distance (au) T 2/R 3 (yr 2/au 3) Mercury 0. 241 0. 39 0. 98 Venus . 615 0. 72 1. 01 Earth 1. 00 Mars 1. 88 1. 52 1. 01 Jupiter 11. 8 5. 20 0. 99 Saturn 29. 54 1. 00 Uranus 84. 0 19. 18 1. 00 Neptune 165 30. 06 1. 00 Pluto 248 39. 44 1. 00
The asteroid and Kuiper belts The asteroid belt is the circumstellar disc in the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets. Kuiper belt= a circumstellar disc in the Solar System beyond the planets, extending from the orbit of Neptune (at 30 AU) to approximately 50 AU from the Sun. It is similar to the asteroid belt, but it is far larger— 20 times as wide and 20 to 200 times as massive. Like the asteroid belt, it consists mainly of small bodies, or remnants from the Solar System's formation. Although many asteroids are composed primarily of rock and metal, most Kuiper belt objects are composed largely of frozen volatiles (termed "ices"), such as methane, ammonia and water. The Kuiper belt is home to three officially recognized dwarf planets: Pluto, Haumea, and Makemake. Some of the Solar System's moons, such as Neptune's Triton and Saturn's Phoebe, are also thought to have originated in the region.
Appendix: Proof of Kepler’s laws, p 1
Appendix: Proof of Kepler’s laws, p 2
Appendix: Proof of Kepler’s laws, p 3 L is Lagrange function T is kinetic energy V is potential energy
Appendix: Proof of Kepler’s laws, p 4
Appendix: Proof of Kepler’s laws, p 5
Appendix: Proof of Kepler’s laws, p 6
Appendix: Proof of Kepler’s laws, p 7
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