Trade Study Of Earth To Pluto Trajectories Utilizing A Jovian Gravitational Assist

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Trade Study Of Earth To Pluto Trajectories Utilizing A Jovian Gravitational Assist"

Transcription

1 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 5-8 January 2009, Orlando, Florida AIAA Trade Study Of Earth To Pluto Trajectories Utilizing A Jovian Gravitational Assist Alan R. Campbell, Charles M. Cimet, and Nathan T. Depenbusch Pennsylvania State University, University Park, PA, 16802, U.S.A. V T F T h R Due to Pluto s extreme distance from our region of the solar system, very few scientific studies have been conducted on this solar body. Because of this distance, it is advantageous to employ a gravitational assist so as to reduce the necessary transfer time and propellant consumption. It is the objective of this paper to analyze the launch window from January 1, 2009 to December 31, 2019 for feasible trajectories to Pluto using a gravitational fly-by of Jupiter. Although this general problem has been studied and solved previously, the specific considerations in this paper appear to be unique. Trajectories were calculated beginning in a Low-Earth parking orbit with a single maneuver into a Lambert s transfer targeting Jupiter. At Jupiter, the geometry of a dark side swing-by was determined to enter a second Lambert s transfer targeting Pluto. A second burn was then calculated for an orbit capture at Pluto. All calculations were performed in MATLAB by varying the launch dates and both transfer times over small intervals. Orbital position assumptions were made using a linearly varying ephemerides model corresponding to the years C.E C.E Gravitational effects for other solar bodies, particularly the moons of Jupiter, were assumed to be inconsequential. Finally, since the Lambert s transfers were calculated independently, the approach and departure velocities at Jupiter were not set to be equal, however, only those that closely matched were considered. As expected, the results indicate a yearly cyclical pattern of viable launch dates with perturbations resulting from the orbital procession of Jupiter and Pluto. An inverse relationship between the necessary propellant usage and the total time of flight is also evident. Specifically, the geometry appears to be most favorable as soon as possible, particularly the window from June 18, 2009 to October 11, Although there are many viable options for an Earth to Pluto mission in the next dozen years, the most beneficial launch windows require mission planning to begin in the very near future. Impulsive change in velocity, km/s Time of flight, years Date, years after J2000 altitude, km radius, km Subscript E Earth J Jupiter P Pluto t Turning T OT Total Nomenclature Undergraduate Student, Department of Aerospace Engineering, 229 Hammond Building, Univeristy Park, PA 16802, Student Member, AIAA. 1 of 8 Copyright 2009 by the American Institute of Aeronautics and American Astronautics, Institute Inc. All of rights Aeronautics reserved. and Astronautics

2 I. Introduction Despite its recent demotion from planethood, Pluto is the most familiar solar object not yet visited. This is soon to change with the 2006 launch of the New Horizons mission scheduled to perform a fly-by of Pluto in July of More can be learned about the body, however, by putting a scientific satellite into its orbit. This paper focuses on finding feasible trajectories and launch dates to accomplish this mission. Due to Pluto s distance and eccentricity about the Sun, it is nearing a phase characterized by the freezing of its atmosphere, therefore making the effectiveness of an observationary probe drop significantly. 1 In order to reach Pluto before the atmosphere freezes, we must consider launches within the upcoming decade, focusing on faster trajectories. One way of doing this is to enlist the help of another celestial body in a gravitational assist. Studies have shown that a Jovian swing-by is an ideal candidate for a direct route to Pluto. 2 It is a result of the similarity of this mission to the current New Horizons mission that much of the numerical analysis is roughly filtered by the capabilities of New Horizons. A. Background The en route New Horizons mission, designed and built by the Johns Hopkins Applied Physics Laboratory (APL) for the National Aeronautics and Space Administration (NASA) was launched January 19, 2006 and flew by Jupiter on February 28, It is scheduled to reach Pluto in July The scientific goals of the New Horizons mission are primarily observatory in regards to Pluto and its moon, Charon. The mission is based on several scientific studies to be performed on Pluto and Charon as the probe flys by. 3 Pluto s atmosphere is also currently escaping out to space. There are no other celestial bodies presently acting in such a way, and it is thought that Earth s early atmosphere of hydrogen and helium was lost in this manner. By studying this phenomenon, we may be able to gain insight into the early atmospheric formation of our planet. In addition, Pluto s composition is known to be similar to that of an asteroid in that it contains large amounts of water and carbon compounds. It is these ingredients that may have sparked life on Earth, transported to our planet by an asteroid impact. These studies, along with the others, are limited by the extreme relative speed of the probe with respect to the Pluto-Charon system. As a result, New Horizons has only a seven month study window. B. Overview In an attempt to lengthen the available window, an orbital capture maneuver will be performed at Pluto to allow prolonged study of its environment. Some simplifying assumptions are made. The probe is taken to already be in parked orbit around Earth, and will undergo a pair of transfer ellipses obtained from the solution of Lambert s problem to the vicinity of Pluto. An initial burn will set us onto the first transfer ellipse heading toward the Jovian swing-by. The swing-by will then send the probe on course to Pluto, where it shall manuever into orbit around the body. Minor correctional manuevers may be required to keep the spacecraft on its interplanetary paths. These will not be considered as significant in this paper. The gravitational effects of all other solar objects (such as other planets and moons) will also be ignored. This is a reasonable assumption throughout most of the journey, with the possible exception of the Jupiter swing-by where any of the numerous moons of Jupiter could have an effect. II. Model The solution of trajectories to fit the mission involved a two-part process: calculating possible trajectories and determining which of these solutions are feasible. Calculation was done by iterating launch date (T E ), total time of flight (T F EP ), and time of flight from Earth to Jupiter (T F EJ ). Trajectories were analyzed by limiting particular characteristics to those allowed by physics, mission requirements, and/or human capability. A. Calculative Procedure Determining the most efficient trajectories to Pluto required solving several separate smaller problems. In order to do so, a MATLAB program was compiled to take all of these scenarios into effect. An entirely temporal constraint of the iteration was used. 2 of 8

3 The first part of the problem was solved by writing an ephemerides function to compute the approximate time-varying positions of the three important solar bodies in this mission. Linear approximation functions valid for the time period C.E were obtained from a Caltech Solar System Dynamics Group paper. 5 These functions were evaluated over a relevant time period for this mission. Planetary position and velocity vectors were calculated in the solar inertial reference frame. Another major part of the solution was the creation of a functional solution to Lambert s Problem. This was done based on an algorithm developed by R.L. Anderson (Univ. of Colorado). 6 Requiring an initial and final position vector, as well as desired time of flight, this algorithm implements a change of variables to solve the problem, then iterates over a differential value to achieve time of flight convergence. At that point, the Stumpff functions are calculated. From here, the initial and final velocity vectors are obtained and used in the main function. Trajectory calculation was performed by decoupling the Earth to Jupiter Lambert transfer from the Jupiter to Pluto transfer. Since the trajectories are decoupled at this point, the velocities with respect to Jupiter do not necessarily match. For this to be physically viable, the velocity magnitude change with respect to the planet in the Jovian sphere of influence had to be limited to small values able to be carried on board. Values were set at a V of 0.5 km/s for calculation. One further constraint was placed inside Jupiter s sphere of influence. The minimum turning radius, (R t ) was set at one Jupiter radius (R J ) to prevent a collision with the planet. The turning radius was calculated geometrically with a dark-side swing-by assumption. 7 These results were implemented together with other less complex functions to allow for the complete calculation of trajectory characteristics. Since the main focus of this study was to find trajectories from Earth to Pluto, the analysis was not concerned with the details of ground to Earth orbit launch; it was therefore assumed that the spacecraft would start in an Earth parking orbit (h 350 km). A parking orbit at Pluto was also assumed (h 50 km). B. Analytic Procedure Upon review of the data calculated by the code, analysis of the prescribed trajectories commenced by discarding what was considered unfeasible. For a trajectory to be considered feasible it had to meet several constraints. These constraints were set with regards to a number of factors, including human technological capability, physical representation, and radiative effects. First, all trajectories with a total V greater than 32 km/s were rejected. This value was chosen as roughly double the V of the New Horizons mission and used as a conservative upper limit. The next constraint was to limit the necessary V t to a value less than km/s, a number based on the amount of corrective propellant carried by New Horizons. Another limitation imposed was a higher limit on the minimum turning radius at Jupiter. Research has shown that fly-bys of a radius less than 5R J can induce potentially catastrophic radiative effects on the spacecraft. Radiation is a concern up to a distance of 14R J, but depending on the hardiness of the craft, such trajectories are possible. III. Results After applying constraints, the remaining data points fall into three distinct launch windows. Each window is identified by the group of data points falling in a small range of launch dates. The first window of launch dates fall between June 18, 2009 and October 11, 2009 (132 days), the second between March 18, 2018 and June 9, 2018 (112 days), and the third between March 16, 2019 and July 6, 2019 (149 days). The first window contains 127 feasible trajectories, the second contains 87, and the third 86 (see figure 1). There are also several notable patterns within the data. As expected, the V T OT vs. T E has a sinusoidal pattern (see figure 2), based upon revolution of Earth around the Sun, skewed by the slower revolutions of Jupiter and Pluto about the Sun. The data curve is incomplete due to aforementioned calculation constraints applied to the trajectory determination. The V T OT vs. T F EP exhibits an inverse relationship (see figure 3), which was expected under the assumption that it takes more propellant to achieve a higher speed. In this plot, each launch window is grouped in a different region of the plot. Windows one, two, and three all have groupings in the upper middle and upper right regions; the upper middle region corresponds to high total V s and moderate times of flight while the upper right region corresponds to high total V s and high times of flight, respectively. Window one also has values starting at approximately a V of 29km/s and time of flight of 8 years, following 3 of 8

4 an inverse trend to V s of approximately 14 km/s with a time of flight of 17.5 years. This range of values also contains trajectories with low V s and moderate times of flight; specific results include a V of 18.00km/s and a time of flight of years. Overall, the data indicates a larger range of possible trajectories earlier in the time period studied. This can be noted in the R t vs. T E plot (see figure 4). This graph also indicates a much higher average R t early in the time period. Together, these observations indicate a much more favorable geometry in earlier dates. A large gap in resulting trajectories was observed between T s of 12 and 15 (correlating to the years of 2012, 2013, and 2014). This gap, when read in conjunction with the above R t graph can be explained by poor planetary alignment. For example, in this range, the trajectory would require the probe to travel through Jupiter in order for the spacecraft to reach the correct Lambert s transfer ellipse. Based on the R t vs. T F EP graph (see figure 5), there is a Gaussian-like trend in the turning radius for viable trajectories in window 1, which peaks for a 10.5 year time of flight and subsequently decreases for all greater times of flight. This trend does not appear in launch windows two and three, which show a slightly inverse correlation between turning radius and total time of flight. Given that a larger turning radius results in less energy being transfered from Jupiter to the spacecraft, this graph also shows that the spacecraft requires a lower energy transfer for low time of flight trajectories in launch window one. IV. Conclusion It is evident that planetary geometry is most favorable in the first launch window. Trajectories calculated in this period had both lower V s and times of flight than those in windows two and three. Given that window one is in 2009, and the less favorable windows two and three occur in 2018 and 2019, respectively, it can be deduced that planetary geometry will become less favorable as the next decade progresses. Since Pluto s atomosphere should completely freeze by 2020, the second and third launch windows will yield arrival dates after this process has ended. This loss of atmosphere is unique, and in order to sufficiently study this phenomena the initial launch window must be used. In order to reach Pluto in time to be of any scientific benefit, shorter flight times from the first launch window need to be utilized. This naturally brings about an increase in necessary V. For missions constrained by fuel, the first launch window also appears advantageous because trajectories with lower V s can be attained. An additional benefit of the planetary geometry in the first launch window is a result of the higher necessary turning radii. This would allow the hardiness of the spacecraft to be of less concern. A specific trajectory can be chosen in the initial launch window to meet specific mission needs. Trade-offs involving total V, on-board propellant, arrival date, and turning radius should be considered in depth in choosing a definite trajectory. 4 of 8

5 Appendix Figure 1. Total time of flight as a function of launch date. 5 of 8

6 Figure 2. Total V as a function of launch date. Figure 3. Total V as a function of total time of flight. 6 of 8

7 Figure 4. Turning radius as a function of launch date. Figure 5. Turning radius as a function of total time of flight. 7 of 8

8 Acknowledgments The authors would like to collectively thank Dr. David B. Spencer, Associate Professor of Aerospace Engineering, Pennsylvania State University, for both the inspiration and for divulging a good deal of the theory behind our study. References 1 Guo, Y. and Farquhar, R.W., Baseline design of newhorizons mission to Pluto and the Kuiper belt, Acta Astronautica, Vol. 58, April 2006, pp Minovitch, M.A., Fast Missions to Pluto Using Jupiter Gravity-Assist and Small Launch Vehicles Journal of Spacecraft and Rockets, Vol. 31, No. 6, November-December 1994 pp Kusnierkiewicz, D.Y., et al., A description of the Pluto-bound New Horizons spacecraft Acta Astronautica, Vol. 57, May 2005, pp Beisser, K., Why Go to Pluto?, New Horizons: NASAs Pluto-Kuiper Belt Mission, [cited 8 December 2007]. 5 Standish, E.M., Keplerian Elements for Approximate Positions of the Major Planets Solar System Dynamics Group, Jet Propulsion Laboratory, California Institute of Technology. 6 Anderson, R.L., Solution to the Lambert Problem using Universal Variables University of Colorado; rla/lambert.pdf, [cited 23 November 2007]. 7 Wiesel, W.E. Interplanetary Trajectories Spaceflight Dynamics 2nd Ed., Chapter 11, McGraw-Hill, of 8

Lecture L17 - Orbit Transfers and Interplanetary Trajectories

Lecture L17 - Orbit Transfers and Interplanetary Trajectories S. Widnall, J. Peraire 16.07 Dynamics Fall 008 Version.0 Lecture L17 - Orbit Transfers and Interplanetary Trajectories In this lecture, we will consider how to transfer from one orbit, to another or to

More information

Astrodynamics (AERO0024)

Astrodynamics (AERO0024) Astrodynamics (AERO0024) 6. Interplanetary Trajectories Gaëtan Kerschen Space Structures & Systems Lab (S3L) Course Outline THEMATIC UNIT 1: ORBITAL DYNAMICS Lecture 02: The Two-Body Problem Lecture 03:

More information

Understanding the motion of the Universe. Motion, Force, and Gravity

Understanding the motion of the Universe. Motion, Force, and Gravity Understanding the motion of the Universe Motion, Force, and Gravity Laws of Motion Stationary objects do not begin moving on their own. In the same way, moving objects don t change their movement spontaneously.

More information

UCM-Gravity. 2. The diagram shows two bowling balls, A and B, each having a mass of 7 kilograms, placed 2 meters apart.

UCM-Gravity. 2. The diagram shows two bowling balls, A and B, each having a mass of 7 kilograms, placed 2 meters apart. 1. A space probe is launched into space from Earth s surface. Which graph represents the relationship between the magnitude of the gravitational force exerted on Earth by the space probe and the distance

More information

Strategies for Continuous Mars Habitation with a Limited Number of Cycler Vehicles

Strategies for Continuous Mars Habitation with a Limited Number of Cycler Vehicles Strategies for Continuous Mars Habitation with a Limited Number of Cycler Vehicles Damon Landau James M. Longuski October 2005 Prepared for Dr. Buzz Aldrin Starcraft Enterprises By Purdue University School

More information

Names of Group Members:

Names of Group Members: Names of Group Members: Using telescopes and spacecraft, astronomers can collect information from objects too big or too far away to test and study in a lab. This is fortunate, because it turns out that

More information

Chapter 7 Reading Quiz Clickers. The Cosmic Perspective Seventh Edition. Our Planetary System Pearson Education, Inc.

Chapter 7 Reading Quiz Clickers. The Cosmic Perspective Seventh Edition. Our Planetary System Pearson Education, Inc. Reading Quiz Clickers The Cosmic Perspective Seventh Edition Our Planetary System 7.1 Studying the Solar System What does the solar system look like? What can we learn by comparing the planets to one another?

More information

astronomy 2008 1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times.

astronomy 2008 1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times. 1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times. 5. If the distance between the Earth and the Sun were increased,

More information

Chapter 13 - Gravity. David J. Starling Penn State Hazleton Fall Chapter 13 - Gravity. Objectives (Ch 13) Newton s Law of Gravitation

Chapter 13 - Gravity. David J. Starling Penn State Hazleton Fall Chapter 13 - Gravity. Objectives (Ch 13) Newton s Law of Gravitation The moon is essentially gray, no color. It looks like plaster of Paris, like dirty beach sand with lots of footprints in it. -James A. Lovell (from the Apollo 13 mission) David J. Starling Penn State Hazleton

More information

4.1.6. Interplanetary Travel. Outline. In This Section You ll Learn to...

4.1.6. Interplanetary Travel. Outline. In This Section You ll Learn to... Interplanetary Travel 4.1.6 In This Section You ll Learn to... Describe the basic steps involved in getting from one planet in the solar system to another Explain how we can use the gravitational pull

More information

CORE STANDARDS, OBJECTIVES, AND INDICATORS

CORE STANDARDS, OBJECTIVES, AND INDICATORS Aerospace Engineering - PLtW Levels: 11-12 Units of Credit: 1.0 CIP Code: 14.0201 Core Code: 38-01-00-00-150 Prerequisite: Principles of Engineering, Introduction to Engineering Design Test: #967 Course

More information

Trajectory Design with STK/Astrogator. New Horizons Mission Tutorial

Trajectory Design with STK/Astrogator. New Horizons Mission Tutorial Trajectory Design with STK/Astrogator New Horizons Mission Tutorial STK/Astrogator New Horizons Mission Tutorial Page 2 Mission Overview In this tutorial, we will model a Mission to Pluto. Starting from

More information

Does currently available technology have the capacity to facilitate a manned mission to Mars?

Does currently available technology have the capacity to facilitate a manned mission to Mars? Furze Platt Senior School Does currently available technology have the capacity to facilitate a manned mission to Mars? Daniel Messias Date: 8/03/2015 Candidate Number: 7158 Centre Number: 51519 Contents

More information

Use the following information to deduce that the gravitational field strength at the surface of the Earth is approximately 10 N kg 1.

Use the following information to deduce that the gravitational field strength at the surface of the Earth is approximately 10 N kg 1. IB PHYSICS: Gravitational Forces Review 1. This question is about gravitation and ocean tides. (b) State Newton s law of universal gravitation. Use the following information to deduce that the gravitational

More information

Lecture 13. Gravity in the Solar System

Lecture 13. Gravity in the Solar System Lecture 13 Gravity in the Solar System Guiding Questions 1. How was the heliocentric model established? What are monumental steps in the history of the heliocentric model? 2. How do Kepler s three laws

More information

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law

More information

Orbital Mechanics. Angular Momentum

Orbital Mechanics. Angular Momentum Orbital Mechanics The objects that orbit earth have only a few forces acting on them, the largest being the gravitational pull from the earth. The trajectories that satellites or rockets follow are largely

More information

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION 1 DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION Daniel S. Orton email: dsorton1@gmail.com Abstract: There are many longstanding

More information

Using Spectral Data to Explore Saturn and Titan

Using Spectral Data to Explore Saturn and Titan Using Spectral Data to Explore Saturn and Titan Middle grades Lesson Summary Students compare known elemental spectra with spectra of Titan and Saturn s rings from a spectrometer aboard the NASA Cassini

More information

Overview. Hubble Pluto Satellite Search Team reporting the discovery to the New Horizons Science Team on November 2, 2005 at the Kennedy Space Center

Overview. Hubble Pluto Satellite Search Team reporting the discovery to the New Horizons Science Team on November 2, 2005 at the Kennedy Space Center The discovery of two new moons of Pluto Hubble Pluto Satellite Search Team reporting the discovery to the New Horizons Science Team on November 2, 2005 at the Kennedy Space Center Andrew Steffl Marc Buie

More information

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law

More information

DWARF PLANETS A S T R O N O M Y. The Academic Support Daytona State College (Science 109, Page 1 of 33)

DWARF PLANETS A S T R O N O M Y. The Academic Support Daytona State College (Science 109, Page 1 of 33) DWARF PLANETS A S T R O N O M Y The Academic Support Center @ Daytona State College (Science 109, Page 1 of 33) DWARF PLANETS The Academic Support Center @ Daytona State College (Science 109, Page 2 of

More information

AP1 Gravity. at an altitude equal to twice the radius (R) of the planet. What is the satellite s speed assuming a perfectly circular orbit?

AP1 Gravity. at an altitude equal to twice the radius (R) of the planet. What is the satellite s speed assuming a perfectly circular orbit? 1. A satellite of mass m S orbits a planet of mass m P at an altitude equal to twice the radius (R) of the planet. What is the satellite s speed assuming a perfectly circular orbit? (A) v = Gm P R (C)

More information

AAS/AIAA Astrodynamics Specialists Conference

AAS/AIAA Astrodynamics Specialists Conference Paper AAS 03-548 RELATING POSITION UNCERTAINTY TO MAXIMUM CONJUNCTION PROBABILITY Salvatore Alfano Copyright 2003 by The Aerospace Corporation. Published by the American Astronautical Society, with permission

More information

Exemplar Problems Physics

Exemplar Problems Physics Chapter Eight GRAVITATION MCQ I 8.1 The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration

More information

Homework #3 Solutions

Homework #3 Solutions Chap. 7, #40 Homework #3 Solutions ASTR100: Introduction to Astronomy Fall 2009: Dr. Stacy McGaugh Which of the following is a strong greenhouse gas? A) Nitrogen. B) Water Vapor. C) Oxygen) The correct

More information

Penn State University Physics 211 ORBITAL MECHANICS 1

Penn State University Physics 211 ORBITAL MECHANICS 1 ORBITAL MECHANICS 1 PURPOSE The purpose of this laboratory project is to calculate, verify and then simulate various satellite orbit scenarios for an artificial satellite orbiting the earth. First, there

More information

Chapter 6: Our Solar System and Its Origin

Chapter 6: Our Solar System and Its Origin Chapter 6: Our Solar System and Its Origin What does our solar system look like? The planets are tiny compared to the distances between them (a million times smaller than shown here), but they exhibit

More information

Motion and Gravity in Space

Motion and Gravity in Space Motion and Gravity in Space Each planet spins on its axis. The spinning of a body, such a planet, on its axis is called rotation. The orbit is the path that a body follows as it travels around another

More information

Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X?

Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? Solar System 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? A) Earth B) Sun C) Moon D) Polaris 2. Which object orbits Earth in both the Earth-centered

More information

Kepler, Newton and Gravitation

Kepler, Newton and Gravitation Kepler, Newton and Gravitation Kepler, Newton and Gravity 1 Using the unit of distance 1 AU = Earth-Sun distance PLANETS COPERNICUS MODERN Mercury 0.38 0.387 Venus 0.72 0.723 Earth 1.00 1.00 Mars 1.52

More information

Astromechanics Two-Body Problem (Cont)

Astromechanics Two-Body Problem (Cont) 5. Orbit Characteristics Astromechanics Two-Body Problem (Cont) We have shown that the in the two-body problem, the orbit of the satellite about the primary (or vice-versa) is a conic section, with the

More information

Version A Page 1. 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart.

Version A Page 1. 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart. Physics Unit Exam, Kinematics 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart. What is the magnitude of the gravitational force exerted by

More information

The Main Point. Lecture #34: Solar System Origin II. Chemical Condensation ( Lewis ) Model. How did the solar system form? Reading: Chapter 8.

The Main Point. Lecture #34: Solar System Origin II. Chemical Condensation ( Lewis ) Model. How did the solar system form? Reading: Chapter 8. Lecture #34: Solar System Origin II How did the solar system form? Chemical Condensation ("Lewis") Model. Formation of the Terrestrial Planets. Formation of the Giant Planets. Planetary Evolution. Reading:

More information

Lecture Outlines. Chapter 15. Astronomy Today 7th Edition Chaisson/McMillan. 2011 Pearson Education, Inc.

Lecture Outlines. Chapter 15. Astronomy Today 7th Edition Chaisson/McMillan. 2011 Pearson Education, Inc. Lecture Outlines Chapter 15 Astronomy Today 7th Edition Chaisson/McMillan Chapter 15 The Formation of Planetary Systems Units of Chapter 15 15.1 Modeling Planet Formation 15.2 Terrestrial and Jovian Planets

More information

Is Pluto a planet? Historical overview. Personal anecdotes. Launch of the Hubble Space Telescope April 24, 1990

Is Pluto a planet? Historical overview. Personal anecdotes. Launch of the Hubble Space Telescope April 24, 1990 Is Pluto a planet? Max Mutchler Space Telescope Science Institute Johns Hopkins University Odyssey Lecture Series Hubble s Expanding Universe March 13, 2008 Historical overview Discovery of Pluto and it

More information

Section 4: The Basics of Satellite Orbits

Section 4: The Basics of Satellite Orbits Section 4: The Basics of Satellite Orbits MOTION IN SPACE VS. MOTION IN THE ATMOSPHERE The motion of objects in the atmosphere differs in three important ways from the motion of objects in space. First,

More information

Newton s Law of Gravity

Newton s Law of Gravity Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has

More information

Correct Modeling of the Indirect Term for Third-Body Perturbations

Correct Modeling of the Indirect Term for Third-Body Perturbations AAS 07-47 Correct Modeling of the Indirect Term for Third-Body Perturbations Matthew M. Berry * Vincent T. Coppola The indirect term in the formula for third body perturbations models the acceleration

More information

WEIGHTLESS WONDER Reduced Gravity Flight

WEIGHTLESS WONDER Reduced Gravity Flight WEIGHTLESS WONDER Reduced Gravity Flight Instructional Objectives Students will use trigonometric ratios to find vertical and horizontal components of a velocity vector; derive a formula describing height

More information

DEVELOPMENT OF AN ARCHITECTURE OF SUN-SYNCHRONOUS ORBITAL SLOTS TO MINIMIZE CONJUNCTIONS. Brian Weeden Secure World Foundation

DEVELOPMENT OF AN ARCHITECTURE OF SUN-SYNCHRONOUS ORBITAL SLOTS TO MINIMIZE CONJUNCTIONS. Brian Weeden Secure World Foundation DEVELOPMENT OF AN ARCHITECTURE OF SUN-SYNCHRONOUS ORBITAL SLOTS TO MINIMIZE CONJUNCTIONS Brian Weeden Secure World Foundation Sun-synchronous orbit (SSO) satellites serve many important functions, primarily

More information

Chapter 2. Mission Analysis. 2.1 Mission Geometry

Chapter 2. Mission Analysis. 2.1 Mission Geometry Chapter 2 Mission Analysis As noted in Chapter 1, orbital and attitude dynamics must be considered as coupled. That is to say, the orbital motion of a spacecraft affects the attitude motion, and the attitude

More information

Astro 110-01 Lecture 10 Newton s laws

Astro 110-01 Lecture 10 Newton s laws Astro 110-01 Lecture 10 Newton s laws Twin Sungrazing comets 9/02/09 Habbal Astro110-01 Lecture 10 1 http://umbra.nascom.nasa.gov/comets/movies/soho_lasco_c2.mpg What have we learned? How do we describe

More information

Background Information Students will learn about the Solar System while practicing communication skills.

Background Information Students will learn about the Solar System while practicing communication skills. Teacher Information Background Information Students will learn about the Solar System while practicing communication skills. Materials clipboard for each student pencils copies of map and Available Destinations

More information

Chapter 25.1: Models of our Solar System

Chapter 25.1: Models of our Solar System Chapter 25.1: Models of our Solar System Objectives: Compare & Contrast geocentric and heliocentric models of the solar sytem. Describe the orbits of planets explain how gravity and inertia keep the planets

More information

USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION

USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION Ian Cooper School of Physics The University of Sydney i.cooper@physics.usyd.edu.au Introduction The numerical calculations performed by scientists and engineers

More information

Solar Power for Outer Planets Study

Solar Power for Outer Planets Study Solar Power for Outer Planets Study Presentation to Outer Planets Assessment Group November 8, 2007 Scott W. Benson/NASA Glenn Research Center 1 Background & Outline Alan Stern request: a quick look study

More information

ASTR 1010 Astronomy of the Solar System Professor Caillault Fall 2009 Semester Exam 2 Answers

ASTR 1010 Astronomy of the Solar System Professor Caillault Fall 2009 Semester Exam 2 Answers ASTR 1010 Astronomy of the Solar System Professor Caillault Fall 2009 Semester Exam 2 Answers 1. Radio waves travel through space at what speed? (d) at the speed of light, 3 10 8 m/s 2. In 1675, Rømer

More information

Newton s Law of Universal Gravitation

Newton s Law of Universal Gravitation Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just two different versions of the same thing.

More information

Rocketry for Kids. Science Level 4. Newton s Laws

Rocketry for Kids. Science Level 4. Newton s Laws Rocketry for Kids Science Level 4 Newton s Laws Victorian Space Science Education Centre 400 Pascoe Vale Road Strathmore, Vic 3041 www.vssec.vic.edu.au Some material for this program has been derived from

More information

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD

More information

Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015

Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Why are celestial motions and forces important? They explain the world around

More information

Understanding the motion of the Universe. Motion, Force, and Gravity

Understanding the motion of the Universe. Motion, Force, and Gravity Understanding the motion of the Universe Motion, Force, and Gravity Laws of Motion Stationary objects do not begin moving on their own. In the same way, moving objects don t change their movement spontaneously.

More information

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13.

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. Chapter 5. Gravitation Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. 5.1 Newton s Law of Gravitation We have already studied the effects of gravity through the

More information

Solar System Fundamentals. What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System

Solar System Fundamentals. What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System Solar System Fundamentals What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System Properties of Planets What is a planet? Defined finally in August 2006!

More information

Spacecraft Dynamics and Control. An Introduction

Spacecraft Dynamics and Control. An Introduction Brochure More information from http://www.researchandmarkets.com/reports/2328050/ Spacecraft Dynamics and Control. An Introduction Description: Provides the basics of spacecraft orbital dynamics plus attitude

More information

THE SOLAR SYSTEM - EXERCISES 1

THE SOLAR SYSTEM - EXERCISES 1 THE SOLAR SYSTEM - EXERCISES 1 THE SUN AND THE SOLAR SYSTEM Name the planets in their order from the sun. 1 2 3 4 5 6 7 8 The asteroid belt is between and Which planet has the most moons? About how many?

More information

Our Planetary System. Earth, as viewed by the Voyager spacecraft. 2014 Pearson Education, Inc.

Our Planetary System. Earth, as viewed by the Voyager spacecraft. 2014 Pearson Education, Inc. Our Planetary System Earth, as viewed by the Voyager spacecraft 7.1 Studying the Solar System Our goals for learning: What does the solar system look like? What can we learn by comparing the planets to

More information

ACTIVITY. What use is Solar Power? What use is Solar Power? Learning objectives. Resources (per group of 4 children) Introduction

ACTIVITY. What use is Solar Power? What use is Solar Power? Learning objectives. Resources (per group of 4 children) Introduction ACTIVITY Learning objectives To: describe how we can use the Sun to generate electricity give examples of where solar power is used design and build a solar powered vehicle explore how gears can convert

More information

Lecture 5: Newton s Laws. Astronomy 111

Lecture 5: Newton s Laws. Astronomy 111 Lecture 5: Newton s Laws Astronomy 111 Isaac Newton (1643-1727): English Discovered: three laws of motion, one law of universal gravitation. Newton s great book: Newton s laws are universal in scope,

More information

The Hidden Lives of Galaxies. Jim Lochner, USRA & NASA/GSFC

The Hidden Lives of Galaxies. Jim Lochner, USRA & NASA/GSFC The Hidden Lives of Galaxies Jim Lochner, USRA & NASA/GSFC What is a Galaxy? Solar System Distance from Earth to Sun = 93,000,000 miles = 8 light-minutes Size of Solar System = 5.5 light-hours What is

More information

The Formation of Planetary Systems. Astronomy 1-1 Lecture 20-1

The Formation of Planetary Systems. Astronomy 1-1 Lecture 20-1 The Formation of Planetary Systems Astronomy 1-1 Lecture 20-1 Modeling Planet Formation Any model for solar system and planet formation must explain 1. Planets are relatively isolated in space 2. Planetary

More information

The Lunar L 1 Gateway: Portal to the Planets

The Lunar L 1 Gateway: Portal to the Planets The Lunar L 1 Gateway: Portal to the Planets Halo Orbit at Lunar L 1 LL 1 Lunar Orbit Surrey Astrodynamics Workshop Lunar Gateway Module Shane Ross Control & Dynamical Systems California Institute of Technology

More information

Spacecraft Power for Cassini

Spacecraft Power for Cassini NASA Fact Sheet Spacecraft Power for Cassini Cassini s electrical power source Radioisotope Thermoelectric Generators (RTGs) have provided electrical power for some of the U.S. space program s greatest

More information

CHAPTER 11. The total energy of the body in its orbit is a constant and is given by the sum of the kinetic and potential energies

CHAPTER 11. The total energy of the body in its orbit is a constant and is given by the sum of the kinetic and potential energies CHAPTER 11 SATELLITE ORBITS 11.1 Orbital Mechanics Newton's laws of motion provide the basis for the orbital mechanics. Newton's three laws are briefly (a) the law of inertia which states that a body at

More information

Name: Date: Period: Gravity Study Guide

Name: Date: Period: Gravity Study Guide Vocabulary: Define the following terms. Law of Universal Gravitation Gravity Study Guide Weight Weightlessness Gravitational Field Black hole Escape velocity Math: Be able to use the equation for the law

More information

Copyright 2006, Astronomical Society of the Pacific

Copyright 2006, Astronomical Society of the Pacific 2 1 3 4 Diameter: 590 miles (950 km) Distance to Sun: 257 million miles (414 million km) Orbits: # 18 Composition: Outer layer probably ice and frozen ammonia, no Diameter: 750 miles (1200 km) Distance

More information

LESSON 3 THE SOLAR SYSTEM. Chapter 8, Astronomy

LESSON 3 THE SOLAR SYSTEM. Chapter 8, Astronomy LESSON 3 THE SOLAR SYSTEM Chapter 8, Astronomy OBJECTIVES Identify planets by observing their movement against background stars. Explain that the solar system consists of many bodies held together by gravity.

More information

THE SOLAR SYSTEM NAME. I. Physical characteristics of the solar system

THE SOLAR SYSTEM NAME. I. Physical characteristics of the solar system NAME I. Physical characteristics of the solar system THE SOLAR SYSTEM The solar system consists of the sun and 9 planets. Table 2 lists a number of the properties and characteristics of the sun and the

More information

The Origin of the Solar System and Other Planetary Systems

The Origin of the Solar System and Other Planetary Systems The Origin of the Solar System and Other Planetary Systems Modeling Planet Formation Boundary Conditions Nebular Hypothesis Fixing Problems Role of Catastrophes Planets of Other Stars Modeling Planet Formation

More information

Explain the Big Bang Theory and give two pieces of evidence which support it.

Explain the Big Bang Theory and give two pieces of evidence which support it. Name: Key OBJECTIVES Correctly define: asteroid, celestial object, comet, constellation, Doppler effect, eccentricity, eclipse, ellipse, focus, Foucault Pendulum, galaxy, geocentric model, heliocentric

More information

Interaction of Energy and Matter Gravity Measurement: Using Doppler Shifts to Measure Mass Concentration TEACHER GUIDE

Interaction of Energy and Matter Gravity Measurement: Using Doppler Shifts to Measure Mass Concentration TEACHER GUIDE Interaction of Energy and Matter Gravity Measurement: Using Doppler Shifts to Measure Mass Concentration TEACHER GUIDE EMR and the Dawn Mission Electromagnetic radiation (EMR) will play a major role in

More information

Aphelion The point in the orbit of a planet or other celestial body where it is furthest from the Sun.

Aphelion The point in the orbit of a planet or other celestial body where it is furthest from the Sun. SKYTRACK Glossary of Terms Angular distance The angular separation between two objects in the sky as perceived by an observer, measured in angles. The angular separation between two celestial objects in

More information

A Taxonomy for Space Curricula

A Taxonomy for Space Curricula A Taxonomy for Space Curricula Arthur W. Draut, Ph.D. College of Aviation Embry-Riddle Aeronautical University Abstract Many universities have added courses and curricula related to satellites and space.

More information

Gravitation and Newton s Synthesis

Gravitation and Newton s Synthesis Gravitation and Newton s Synthesis Vocabulary law of unviversal Kepler s laws of planetary perturbations casual laws gravitation motion casuality field graviational field inertial mass gravitational mass

More information

Planning strategy and supporting tools for the science operations of ESA s Planetary Science Missions

Planning strategy and supporting tools for the science operations of ESA s Planetary Science Missions Planning strategy and supporting tools for the science operations of ESA s Planetary Science Missions Raymond Hoofs 1,.Detlef Koschny 1, Peter van der Plas 2, 1 Planetary Missions Division, ESA/ESTEC,

More information

Group Leader: Group Members:

Group Leader: Group Members: THE SOLAR SYSTEM PROJECT: TOPIC: THE SUN Required Project Content for an Oral/Poster Presentation on THE SUN - What it s made of - Age and how it formed (provide pictures or diagrams) - What is an AU?

More information

Chapter 7 Our Planetary System. What does the solar system look like? Thought Question How does the Earth-Sun distance compare with the Sun s radius

Chapter 7 Our Planetary System. What does the solar system look like? Thought Question How does the Earth-Sun distance compare with the Sun s radius Chapter 7 Our Planetary System 7.1 Studying the Solar System Our goals for learning:! What does the solar system look like?! What can we learn by comparing the planets to one another?! What are the major

More information

TOPO Trajectory Operations Officer

TOPO Trajectory Operations Officer ISS Live! was developed at NASA s Johnson Space Center (JSC) under NASA Contracts NNJ14RA02C and NNJ11HA14C wherein the U.S. Government retains certain rights. Console Handbook TOPO Trajectory Operations

More information

Orbital Mechanics and Space Geometry

Orbital Mechanics and Space Geometry Orbital Mechanics and Space Geometry AERO4701 Space Engineering 3 Week 2 Overview First Hour Co-ordinate Systems and Frames of Reference (Review) Kepler s equations, Orbital Elements Second Hour Orbit

More information

The Origin of the Solar System

The Origin of the Solar System The Origin of the Solar System Questions: How did the various constituents of Solar System form? What were the physical processes involved? When did they form? Did they all form more-or less simultaneously?

More information

ASTR 115: Introduction to Astronomy. Stephen Kane

ASTR 115: Introduction to Astronomy. Stephen Kane ASTR 115: Introduction to Astronomy Stephen Kane ASTR 115: The Second Mid-Term Exam What will be covered? - Everything from chapters 6-10 of the textbook. What will be the format of the exam? - It will

More information

The Space Shuttle: Teacher s Guide

The Space Shuttle: Teacher s Guide The Space Shuttle: Teacher s Guide Grade Level: 6-8 Curriculum Focus: Astronomy/Space Lesson Duration: Two class periods Program Description This video, divided into four segments, explores scientists'

More information

Can Hubble be Moved to the International Space Station? 1

Can Hubble be Moved to the International Space Station? 1 Can Hubble be Moved to the International Space Station? 1 On January 16, NASA Administrator Sean O Keefe informed scientists and engineers at the Goddard Space Flight Center (GSFC) that plans to service

More information

ASTR 380 Possibilities for Life on the Moons of Giant Planets

ASTR 380 Possibilities for Life on the Moons of Giant Planets Let s first consider the large gas planets: Jupiter, Saturn, Uranus and Neptune Planets to scale with Sun in background 67 62 14 The many moons of the outer planets.. Most of the moons are very small 1

More information

Science Focus 9 Space Exploration Review Booklet

Science Focus 9 Space Exploration Review Booklet Science Focus 9 Unit E Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 Topic 8 Space Exploration Space Link: NASA http://www.nasa.gov/home/index.html For Our Eyes Only Frames of Reference What

More information

REMARKS FOR ADMINISTRATOR BOLDEN NATIONAL CONTRACT MANAGEMENT ASSOCIATION GOVERNMENT CONTRACT MANAGEMENT SYMPOSIUM. Nov. 19, 2013

REMARKS FOR ADMINISTRATOR BOLDEN NATIONAL CONTRACT MANAGEMENT ASSOCIATION GOVERNMENT CONTRACT MANAGEMENT SYMPOSIUM. Nov. 19, 2013 REMARKS FOR ADMINISTRATOR BOLDEN NATIONAL CONTRACT MANAGEMENT ASSOCIATION GOVERNMENT CONTRACT MANAGEMENT SYMPOSIUM Nov. 19, 2013 Thank you for inviting me to your gathering and for giving me this opportunity

More information

Solar System Observations contains two components: Planetary Astronomy and Near Earth Object Observations.

Solar System Observations contains two components: Planetary Astronomy and Near Earth Object Observations. C.6 SOLAR SYSTEM OBSERVATIONS 1. Scope of Program Solar System Observations supports both ground-based astronomical observations and suborbital investigations of our Solar System involving sounding rockets

More information

Artificial Satellites Earth & Sky

Artificial Satellites Earth & Sky Artificial Satellites Earth & Sky Name: Introduction In this lab, you will have the opportunity to find out when satellites may be visible from the RPI campus, and if any are visible during the activity,

More information

The Planets An HD Odyssey

The Planets An HD Odyssey Cassini Unlocking Saturn s Secrets The Cassini mission is an international cooperative effort involving NASA, the European Space Agency, and the Italian space agency Agenzia Spazia Italiano, as well as

More information

Lesson 6: Earth and the Moon

Lesson 6: Earth and the Moon Lesson 6: Earth and the Moon Reading Assignment Chapter 7.1: Overall Structure of Planet Earth Chapter 7.3: Earth s Interior More Precisely 7-2: Radioactive Dating Chapter 7.5: Earth s Magnetosphere Chapter

More information

7. Our Solar System. Planetary Orbits to Scale. The Eight Planetary Orbits

7. Our Solar System. Planetary Orbits to Scale. The Eight Planetary Orbits 7. Our Solar System Terrestrial & Jovian planets Seven large satellites [moons] Chemical composition of the planets Asteroids & comets The Terrestrial & Jovian Planets Four small terrestrial planets Like

More information

Analysis on the Long-term Orbital Evolution and Maintenance of KOMPSAT-2

Analysis on the Long-term Orbital Evolution and Maintenance of KOMPSAT-2 Analysis on the Long-term Orbital Evolution and Maintenance of KOMPSAT-2 Ok-Chul Jung 1 Korea Aerospace Research Institute (KARI), 45 Eoeun-dong, Daejeon, South Korea, 305-333 Jung-Hoon Shin 2 Korea Advanced

More information

The University of Texas at Austin. Gravity and Orbits

The University of Texas at Austin. Gravity and Orbits UTeach Outreach The University of Texas at Austin Gravity and Orbits Time of Lesson: 60-75 minutes Content Standards Addressed in Lesson: TEKS6.11B understand that gravity is the force that governs the

More information

SPEED, VELOCITY, AND ACCELERATION

SPEED, VELOCITY, AND ACCELERATION reflect Look at the picture of people running across a field. What words come to mind? Maybe you think about the word speed to describe how fast the people are running. You might think of the word acceleration

More information

Quasi-Synchronous Orbits

Quasi-Synchronous Orbits Quasi-Synchronous Orbits and Preliminary Mission Analysis for Phobos Observation and Access Orbits Paulo J. S. Gil Instituto Superior Técnico Simpósio Espaço 50 anos do 1º Voo Espacial Tripulado 12 de

More information

Space Travel B OT H MANNED A ND U NMANNED

Space Travel B OT H MANNED A ND U NMANNED Space Travel B OT H MANNED A ND U NMANNED What Caused the Start of Space Travel? Cold War- After WWII, the United Stated and Russia severed all ties to each and became enemies. The two countries lost trust

More information

2. Orbits. FER-Zagreb, Satellite communication systems 2011/12

2. Orbits. FER-Zagreb, Satellite communication systems 2011/12 2. Orbits Topics Orbit types Kepler and Newton laws Coverage area Influence of Earth 1 Orbit types According to inclination angle Equatorial Polar Inclinational orbit According to shape Circular orbit

More information

Chapter 7 Our Planetary System. Agenda. Intro Astronomy. Intro Astronomy. What does the solar system look like? A. General Basics

Chapter 7 Our Planetary System. Agenda. Intro Astronomy. Intro Astronomy. What does the solar system look like? A. General Basics Chapter 7 Our Planetary System Agenda Pass back & discuss Test 2 Where we are (at) Ch. 7 Our Planetary System Finish Einstein s Big Idea Earth, as viewed by the Voyager spacecraft A. General Basics Intro

More information

Chapter 13 Newton s Theory of Gravity

Chapter 13 Newton s Theory of Gravity Chapter 13 Newton s Theory of Gravity Chapter Goal: To use Newton s theory of gravity to understand the motion of satellites and planets. Slide 13-2 Chapter 13 Preview Slide 13-3 Chapter 13 Preview Slide

More information