# MAE 180A: Spacecraft Guidance I, Summer 2009 Final Exam Saturday, August 1st.

Save this PDF as:

Size: px
Start display at page:

Download "MAE 180A: Spacecraft Guidance I, Summer 2009 Final Exam Saturday, August 1st."

## Transcription

1 MAE 180A: Spacecraft Guidance I, Summer 2009 Final Exam Saturday, August 1st. Part I: Questions. (40pt) 8:00AM-8:35AM. Guidelines: Please turn in a neat and clean exam solution. Answers should be written in the blank spaces provided in these exam sheets. Vector quantities are denoted in bold letters in what follows. This part of the exam is closed book, closed notes, no use of calculator allowed. Student s Name:... Student s ID:... Question 1 (10 pts). State in words the three Kepler s laws.

2 Question 2 (30 pts) Select the true answer (only one) out of the choices from the list provided for each question. A complementary and brief mathematical proof of your answer on the available space would be welcome, but it is not needed in order to get full credit. 2.1 A polar orbit has an inclination i of a) 45 b) 90 c) 0 d) The geocentric-equatorial system of coordinates a) is centered at the Earth and the x-axis points towards the Saggitarius constellation. b) is centered at the Earth and the x-axis points towards the Aries constellation. c) is perpendicular to the celestial equator. d) is centered at the Sun. 2.3 A mean solar day is a) longer than a sidereal day since the Earth is not a perfect sphere. b) longer than a sidereal day because of the orbital path of the Earth around the Sun and the rotation of the Earth about its polar axis. c) equal to a sidereal day. d) shorter than a sidereal day. 2.4 The argument of latitude at epoch of a circular equatorial orbit is a) always 0. b) 90. c) undefined. d) The ground trace of a geosynchronous satellite in a 45 -inclination elliptic orbit is a) a stationary spot on the same place of the surface of the Earth since the orbit is synchronous. b) a distorted 8 shape trace that goes from the northern hemisphere to the southern hemisphere. c) a square of side equal to the periapsis radius. d) a 5 shaped trace.

3 2.6 If the launch site is very close to the equator then a) the spacecraft can be generally inserted into an equatorial orbit very easily. b) it is impossible to insert a spacecraft into an equatorial orbit. c) the orbit is always polar. d) the orbit is always retrograde. 2.7 The specific mechanical energy of a satellite orbiting around the Earth a) is not constant and varies sinusoidally with time. b) is constant but only for US-manufactured satellites. c) is constant if the satellite is not subject to any dissipative forces or external forces other than gravitational interactions. d) is always constant. 2.8 The orbital period of a satellite in a circular orbit of radius r 1 around the Earth is P 1. The orbital period of another satellite in a circular orbit of the same radius r 1 around a planet of twice the mass of the Earth is a) 2 1/2 P 1. b) undefined. c) the same. d) 2 3/2 P The angular momentum in an orbital motion is a) constant and parallel to the orbit plane. b) constant and normal to the orbit plane. c) not constant, and it is parallel to the orbit plane. d) not constant, and it is normal to the orbit plane An elliptic orbit of perigee radius r p = 4 DU and apogee radius r a = 10 DU is used to transfer a spacecraft from a circular orbit of radius r 1 = 10 DU to a smaller coplanar orbit of radius r 2 = 3 DU. Then a) the spacecraft will arrive safely at the inner circular orbit. b) it would take too much fuel to perform this maneuver. c) this transfer orbit cannot be used since the spacecraft will not arrive at the inner circular orbit. d) the transfer orbit is parallel to the equatorial plane.

4 2.11 A satellite is launched from the Baikonur Cosmodrome to a inclination low-earth orbit (LEO), and it is about to be transferred to a Geostationary orbit (GSO). Then a) it is more economical to perform the plane change to the equatorial plane when the satellite is still in the LEO before executing any other maneuver. b) it is more economical to perform the plane change to the equatorial orbit at the intersection of the equatorial plane and the transfer ellipse (i.e. at the descending node of the transfer ellipse). c) the launch azimuth was 0. d) the perigee radius is equal to the radius of the Earth The Molniya orbit is a) a nearly-equatorial orbit intended for the International Space Station (ISS). b) is a geosynchronous orbit. c) has a period of 1 week. d) a high-inclination, eccentric orbit of nearly 12 h period intended to give communication capabilities to high-latitude areas such as Russia For a given impulse and initial mass of the spacecraft, the smaller the specific impulse of the propulsion system, a) the larger the propellant consumption. b) the larger the eccentricity of the orbit attained. c) the smaller the propellant consumption. d) the smaller the eccentricity of the orbit attained In a Hohmann transfer from an outer circular orbit to an inner circular orbit, the spacecraft first undergoes to become injected in the transfer ellipse, and then for insertion into the inner circular orbit. a) an acceleration / a deceleration b) a deceleration / a deceleration c) an acceleration / an acceleration d) a deceleration / an acceleration 2.15 The regression of the line of nodes and the rotation of the line of apsides are produced by a) the eccentricity of the Earth and are more important in nearly-equatorial orbits. b) the eccentricity of the Earth and are more important in nearly-polar orbits. c) the precession of the Earth s rotation axis and are more important in nearly-polar orbits. d) the solar radiation.

5 2.16 The regression of the line of nodes causes the ground trace of a satellite in a direct orbit to be displaced more towards the than it should be by only the Earth rotation. a) East b) North c) South d) West 2.17 An interplanetary mission is designed to take a space probe from Earth to Saturn by a Hohmann-type transfer trajectory. Once that the probe arrives at Saturn a) it can come back to Earth by simply following the other half of the Hohmann transfer ellipse used to arrive at Saturn. b) it has to be transferred to an elliptic orbit. c) it cannot come back to Earth by simply following the other half of the Hohmann transfer ellipse used to arrive at Saturn since the phase angle between the two planets has changed. d) it will run out of propellant The synodic period a) is the time that the Earth takes to rotate 360 degrees about its axis. b) is the time that the Earth takes to rotate 1 solar day about its axis. c) is the time that Mars takes to rotate 1 solar year about the Sun. d) is the period of time after which the relative position of two planets is exactly repeated For missions to inner planets in the Solar System like Venus and Mercury, a) the spacecraft has to be launched with a negative hyperbolic excess speed (in the opposite direction to the Earth s orbital motion). b) the spacecraft has to be launched with a positive hyperbolic excess speed (in the same direction as the Earth s orbital motion). c) the spacecraft has to be launched at the escape speed. d) the launch azimuth angle must be In an acceleration gravity-assist maneuver around Venus, a) the relative velocity of the spacecraft with respect to Venus increases. b) the relative velocity of the spacecraft with respect to Venus decreases. c) the velocity of the spacecraft with respect to the Sun increases. d) the velocity of the spacecraft with respect to the Sun decreases.

6 MAE 180A: Spacecraft Guidance I, Summer 2009 Final Exam Saturday, August 1. Part II: Problems. (60pt) 8:40AM-11:00AM. Guidelines: Please turn in a neat and clean exam solution. Answers should be written in the blank spaces provided in these exam sheets. Show all work. Vector quantities are denoted in bold letters in what follows. This part of the exam is open book, open notes, use of calculator allowed. Student s Name:... Student s ID:... Problem 1: The Geostationary-Orbit (GSO) Mission (30 pts) A Geostationary satellite is launched by an Atlas rocket at the Cape Canaveral launch site (latitude 28 N) with an azimuth angle β = 90, and it is injected into a circular low-earth orbit (LEO) of 300 nautical miles altitude above the Earth s surface. The local sidereal time at the projection of the ascending node onto the Earth s surface is θ LST = 30. The satellite is transferred to a Geotransfer orbit (GTO) at the ascending node of the LEO, and finally injected into a Geostationary orbit (GSO) at the intersection of the GTO with the equatorial plane. In this analysis, the GTO is assumed to be a Hohmann tranfer ellipse. Note: a GSO orbit is a circular equatorial orbit of period equal to the period of rotation of the Earth about its axis, P = 1 sidereal day = h. K Satellite L GTO (Hohmann) LEO J θlst n I GSO Figure 1: The GSO Mission. Answer to the following questions:

7 a) Calculate the semi-major axis, eccentricity, inclination angle, longitude of the ascending node and the argument of the periapsis of the initial LEO. Additionally, calculate the true longitude at epoch of the satellite at the transfer point to the GTO. b) Calculate the orbital velocity of the satellite along the LEO, and the impulse V 1 needed to transfer from the LEO to the GTO. c) Calculate the time of flight from i) the transfer point to GTO to ii) the intersection of the GTO with the GSO. d) Calculate the impulse V 2 needed to change from the GTO plane to the GSO plane at the intersection of the GSO with the GTO.

8 e) Calculate the tangential impulse V 3 needed to inject the satellite into the GSO once the plane-change maneuver has been performed f) Obtain the total impulse V T = V 1 + V 2 + V 3. g) The company responsible for the satellite engines decides to install a new propulsion system in the satellite that has thrust-vectoring capabilities, such that the last two maneuvers d) and e) (plane change and tangential circularization) can be combined into a simultaneous single one. Calculate the V 23 necessary to perform this two maneuvers simultaneously and obtain the total impulse V T = V 1 + V 23. How much is the total impulse reduced by using the new propulsion system?

9 Problem 2: The Mars-Lander Mission (30 pts) A NASA Mars-Lander spacecraft is sent to Mars with the objective of human exploration of the the Martian surface. The spacecraft is composed of an Orbiter and a Lander, and its mass-distribution specifications are Structure Propellant (MMH / N 2 O 4 ) Orbiter 2717 kg 1875 kg Lander 500 kg 100 kg The specific impulse of the Orbiter propulsion system is I s = 320 s. Detailed design calculations have shown that an impulse V CM = 1 km/s must be reserved for control maneuvers such as trajectorycontrol and attitude-control maneuvers during the interplanetary flight. The space probe is placed into the payload fairing of an Ares-V rocket before launch at the Cape Canaveral base (latitude 28 N) on the East Coast of USA, and it is to be launched from this place with an azimuth angle of β = 90 in a direct orbit. After launch, the space probe remains attached to a powerful Upper Stage orbiting in a circular LEO of 350 nautical miles altitude above the Earth s surface. Simplifying assumption: The Earth and Mars orbits are assumed to be circular and are both contained in the ecliptic plane, which is inclined 23.4 with respect to the Earth s equator. Additionally 1 AU/TU =3.768 DU /TU, 1 DU /TU =0.12 AU/TU. Answer to the following questions pertaining each of the mission stages. Phase 1) Launch from Cape Canaveral. The spacecraft is launched with the azimuth angle specified above. Question a) Calculate the inclination and radius of the initial LEO attained. Question b) Calculate the circular velocity of the probe + Upper Stage in the initial circular parking LEO. Phase 2) Departure. Permission for departure is given from the NASA mission center, and the Upper Stage performs a change of plane to the ecliptic and a subsequent impulse maneuver at the perigee of the departure hyperbola, to launch the spacecraft into the interplanetary trajectory, which is Hohmann ellipse tangent to the Earth at perihelion. After performing these two maneuvers, the Upper Stage is jettisoned and the spacecraft continues alone along the interplanetary path (see figure 2)

10 MARS AT ARRIVAL PERIGEE EARTH AT ARRIVAL 01 INITIAL LEO EARTH AT DEPARTURE MARS AT DEPARTURE coplanar SPACECRAFT (a) (b) To Hohmann Transfer (in the ecliptic) VES Figure 2: (a) Interplanetary trajectory. (b) Departure phase at the Earth. Question c) Calculate the V 1 needed to change planes from the initial circular parking LEO to an identical circular orbit on the ecliptic plane. Question d) Determine the velocity of the spacecraft at the perihelion of the transfer ellipse. Question e) Obtain the burnout velocity, the C 3 of the Upper Stage, and the V 2 necessary to attain the injection velocity calculated in part d) for the interplanetary trajectory.

11 Phase 3) Interplanetary Flight. The interplanetary trajectory consists on a Hohmann transfer to Mars as depicted in figure 2(a). During this phase, the spacecraft performs the Control Maneuvers to attain the correct arrival trajectory. Question f) Determine the velocity of the probe at the aphelion of the Hohmann transfer ellipse. Phase 4) Arrival at Mars. The arrival trajectory is a hyperbola of minimum approach distance 1.5b, where b is the effective colision section (see figure 3). The retro-rockets of the spacecraft are activated at the periapsis to transfer from the hyperbolic trajectory to a tangent circular parking orbit. PERIAPSIS SPACECRAFT From Hohmann Transfer (in the ecliptic) 1.5b Figure 3: Arrival phase at Mars. Question g) Calculate the hyperbolic excess velocity of the spacecraft at arrival. Question h) Calculate the effective collision section b.

12 Question i) Calculate the impulse V 3 necessary to transfer to the specified circular parking orbit. Question j) Obtain the total amount of propellant spent by the spacecraft. Is there enough propellant on board the spacecraft to perform this mission?. Phase 4) Lander Reentry in the Martian Atmosphere. At some point along its circular orbit, the Lander is ejected from the spacecraft tangentially to the orbit, leaving the Orbiter alone. This ejection maneuver causes the Lander to be tangentially injected into an elliptic ballistic trajectory towards the Martian surface (see figure 4). φ Vr LANDER ORBITER MARS Figure 4: Lander Reentry maneuver.

13 Question k) Calculate the Lander ejection velocity with respect to the Orbiter, if the allowable reentry angle (i.e. the flight path angle) is φ = 11 for avoiding the Lander disintegration during the reentry. For this part, assume that the radius of the Martian atmosphere is approximately equal to the radius of the planet Mars. Question l) Determine the Mach number at reentry, M = V r /a, where V r is the reentry velocity of the Lander and a = 244 m/s is a characteristic speed of sound in Mars.

### 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

### 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

### 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

### 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:

### 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

### 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

### 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

### 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,

### EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1

Instructor: L. M. Khandro EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 1. An arc second is a measure of a. time interval between oscillations of a standard clock b. time

### 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

### 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

### 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

### A. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great.

Q12.1 The mass of the Moon is 1/81 of the mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth is A. 81 2

### Orbital Dynamics: Formulary

Orbital Dynamics: Formulary 1 Introduction Prof. Dr. D. Stoffer Department of Mathematics, ETH Zurich Newton s law of motion: The net force on an object is equal to the mass of the object multiplied by

### 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

### Trajectory design for the Solar Orbiter mission

Monografías de la Real Academia de Ciencias de Zaragoza. 25: 177 218, (2004). Trajectory design for the Solar Orbiter mission G. Janin European Space Operations Centre. European Space Agency. 64293 Darmstadt,

### 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

### Spacecraft orbits and missions

General Astrophysics and Space Research Course 210142, Space Physics Module Spring 2009, Joachim Vogt Spacecraft orbits and missions Topics of this lecture Basics of celestial mechanics Geocentric orbits

### Celestial Sphere. Celestial Coordinates. Lecture 3: Motions of the Sun and Moon. ecliptic (path of Sun) ecliptic (path of Sun)

Lecture 3: Motions of the and Moon ecliptic (path of ) ecliptic (path of ) The 23.5 degree tilt of Earth s spin axis relative to its orbital axis around the causes the seasons Celestial Sphere Celestial

### 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

### 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

### Understanding Orbital Mechanics Through a Step-by-Step Examination of the Space-Based Infrared System (SBIRS)

Understanding Orbital Mechanics Through a Step-by-Step Examination of the Space-Based Infrared System (SBIRS) Denny Sissom Elmco, Inc. May 2003 Pg 1 of 27 SSMD-1102-366 [1] The Ground-Based Midcourse Defense

### 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

### 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

### 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

### Section 2. Satellite Orbits

Section 2. Satellite Orbits References Kidder and Vonder Haar: chapter 2 Stephens: chapter 1, pp. 25-30 Rees: chapter 9, pp. 174-192 In order to understand satellites and the remote sounding data obtained

### 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

### 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,

### 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

### Chapter 6. Orbital Mechanics. Maj Edward P. Chatters IV, USAF; Maj Bryan Eberhardt, USAF; and Maj Michael S. Warner, USAF

Chapter 6 Orbital Mechanics Maj Edward P. Chatters IV, USAF; Maj Bryan Eberhardt, USAF; and Maj Michael S. Warner, USAF Knowledge of orbital motion is essential for a full understanding of space operations.

### 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

### 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.

### 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

### Satellite Orbits From Planet Earth

Satellite Orbits From Planet Earth Grade Level: 7 Time Required: Several class periods, depending on research Countdown: 1 copy of table for each student 1 copy of Elliptical Orbits worksheet for each

### Problem Set #13 Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.0L: Physics I January 3, 06 Prof. Alan Guth Problem Set #3 Solutions Due by :00 am on Friday, January in the bins at the intersection of Buildings

### 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

### Astronomy 1140 Quiz 1 Review

Astronomy 1140 Quiz 1 Review Prof. Pradhan September 15, 2015 What is Science? 1. Explain the difference between astronomy and astrology. (a) Astrology: nonscience using zodiac sign to predict the future/personality

### Exam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti

Exam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti INSTRUCTIONS: Please, use the `bubble sheet and a pencil # 2 to answer the exam questions, by marking

### The Gravitational Field

The Gravitational Field The use of multimedia in teaching physics Texts to multimedia presentation Jan Hrnčíř jan.hrncir@gfxs.cz Martin Klejch martin.klejch@gfxs.cz F. X. Šalda Grammar School, Liberec

### 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.

### OBJECT: To become familiar with some of the motions of the stars, Sun, Moon and planets as seen from the surface of the Earth.

INSIDE LAB 2: Celestial Motions OBJECT: To become familiar with some of the motions of the stars, Sun, Moon and planets as seen from the surface of the Earth. DISCUSSION: As seen from a point of view centered

### Chapter 13. Gravitation

Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G = 6.67

### 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

### Flight and Orbital Mechanics

Flight and Orbital Mechanics Lecture slides Challenge the future 1 Material for exam: this presentation (i.e., no material from text book). Sun-synchronous orbit: used for a variety of earth-observing

### 9210-228 Level 7 Post Graduate Diploma in Mechanical Engineering Aerospace engineering

9210-228 Level 7 Post Graduate Diploma in Mechanical Engineering Aerospace engineering You should have the following for this examination one answer book non-programmable calculator pen, pencil, drawing

### The Four Seasons. A Warm Up Exercise. A Warm Up Exercise. A Warm Up Exercise. The Moon s Phases

The Four Seasons A Warm Up Exercise What fraction of the Moon s surface is illuminated by the Sun (except during a lunar eclipse)? a) Between zero and one-half b) The whole surface c) Always half d) Depends

### Coordinate Systems. Orbits and Rotation

Coordinate Systems Orbits and Rotation Earth orbit. The earth s orbit around the sun is nearly circular but not quite. It s actually an ellipse whose average distance from the sun is one AU (150 million

### 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

### Planetary Orbit Simulator Student Guide

Name: Planetary Orbit Simulator Student Guide Background Material Answer the following questions after reviewing the Kepler's Laws and Planetary Motion and Newton and Planetary Motion background pages.

### Sun Earth Relationships

1 ESCI-61 Introduction to Photovoltaic Technology Sun Earth Relationships Ridha Hamidi, Ph.D. Spring (sun aims directly at equator) Winter (northern hemisphere tilts away from sun) 23.5 2 Solar radiation

### Chapter 5: Circular Motion, the Planets, and Gravity

Chapter 5: Circular Motion, the Planets, and Gravity 1. Earth s gravity attracts a person with a force of 120 lbs. The force with which the Earth is attracted towards the person is A. Zero. B. Small but

### 1 Newton s Laws of Motion

Exam 1 Ast 4 - Chapter 2 - Newton s Laws Exam 1 is scheduled for the week of Feb 19th Bring Pencil Scantron 882-E (available in the Bookstore) A scientific calculator (you will not be allowed to use you

### 1. The orbit of each planet is an ellipse with the Sun at one focus. 2. The line joining the planet to the Sun sweeps out equal areas in equal times.

Appendix A Orbits As discussed in the Introduction, a good first approximation for satellite motion is obtained by assuming the spacecraft is a point mass or spherical body moving in the gravitational

### 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

### CELESTIAL CLOCK - THE SUN, THE MOON, AND THE STARS

INTRODUCTION CELESTIAL CLOCK - THE SUN, THE MOON, AND THE STARS This is a scientific presentation to provide you with knowledge you can use to understand the sky above in relation to the earth. Before

### 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

### The ecliptic - Earth s orbital plane

The ecliptic - Earth s orbital plane The line of nodes descending node The Moon s orbital plane Moon s orbit inclination 5.45º ascending node celestial declination Zero longitude in the ecliptic The orbit

### 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.

### Physics Competitions Vol 13 No 2 2011 & Vol.14 No 1 2012. A few good orbits. 400 088. # Corresponding author: anikets@hbcse.tifr.res.

A few good orbits Chiraag Juvekar 1, Mehul Jain 1 and Aniket Sule 2,# 1 Indian Institute of Technology (Bombay), Mumbai, Maharashtra, India - 400 076. 2 Homi Bhabha Centre for Science Education (HBCSE).

### EN4 Dynamics and Vibrations. Design Project. Orbital Design for a Lunar Impact Mission. Synopsis

EN4 Dynamics and Vibrations Design Project Orbital Design for a Lunar Impact Mission Synopsis NASA has identified a need for a low-cost mission to launch a satellite that will impact the moon. You will

### RS platforms. Fabio Dell Acqua - Gruppo di Telerilevamento

RS platforms Platform vs. instrument Sensor Platform Instrument The remote sensor can be ideally represented as an instrument carried by a platform Platforms Remote Sensing: Ground-based air-borne space-borne

### Niraj Sir GRAVITATION CONCEPTS. Kepler's law of planetry motion

GRAVITATION CONCEPTS Kepler's law of planetry motion (a) Kepler's first law (law of orbit): Every planet revolves around the sun in an elliptical orbit with the sun is situated at one focus of the ellipse.

### 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

### 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,

### 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

### 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

### The Two-Body Problem

The Two-Body Problem Abstract In my short essay on Kepler s laws of planetary motion and Newton s law of universal gravitation, the trajectory of one massive object near another was shown to be a conic

### Hatch a Plot to Track Some Satellites!

Hatch a Plot to Track Some Satellites! Overview There are literally hundreds of satellites that are currently orbiting Earth, including the International Space Station. Clearly, satellites are important

### Note S1: Eclipses & Predictions

The Moon's Orbit The first part of this note gives reference information and definitions about eclipses [14], much of which would have been familiar to ancient Greek astronomers, though not necessarily

### Dynamics of Iain M. Banks Orbitals. Richard Kennaway. 12 October 2005

Dynamics of Iain M. Banks Orbitals Richard Kennaway 12 October 2005 Note This is a draft in progress, and as such may contain errors. Please do not cite this without permission. 1 The problem An Orbital

### Development of an automated satellite network management system

Development of an automated satellite network management system Iasonas Kytros Christos Porios Nikitas Terzoudis Varvara Chatzipavlou Coach: Sitsanlis Ilias February 2013 Abstract In this paper we present

### A satellite of mass 5.00x10² kg is in a circular orbit of radius 2r around Earth. Then it is moved to a circular orbit radius of 3r.

Supplemental Questions A satellite of mass 5.00x10² kg is in a circular orbit of radius 2r around Earth. Then it is moved to a circular orbit radius of 3r. (a) Determine the satellite s GPE in orbit. (b)

### 1-2. What is the name given to the path of the Sun as seen from Earth? a.) Equinox b.) Celestial equator c.) Solstice d.

Chapter 1 1-1. How long does it take the Earth to orbit the Sun? a.) one sidereal day b.) one month c.) one year X d.) one hour 1-2. What is the name given to the path of the Sun as seen from Earth? a.)

### CELESTIAL MOTIONS. In Charlottesville we see Polaris 38 0 above the Northern horizon. Earth. Starry Vault

CELESTIAL MOTIONS Stars appear to move counterclockwise on the surface of a huge sphere the Starry Vault, in their daily motions about Earth Polaris remains stationary. In Charlottesville we see Polaris

### Chapter 13. Newton s Theory of Gravity

Chapter 13. Newton s Theory of Gravity The beautiful rings of Saturn consist of countless centimeter-sized ice crystals, all orbiting the planet under the influence of gravity. Chapter Goal: To use Newton

### Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

### Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007. Name:

Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007 Name: Directions: Listed below are twenty (20) multiple-choice questions based on the material covered by the lectures this past week. Choose

### 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

### Earth-Sun Relationships. The Reasons for the Seasons

Earth-Sun Relationships The Reasons for the Seasons Solar Radiation The earth intercepts less than one two-billionth of the energy given off by the sun. However, the radiation is sufficient to provide

### 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!

### 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,

### Geography I Pre Test #1

Geography I Pre Test #1 1. The sun is a star in the galaxy. a) Orion b) Milky Way c) Proxima Centauri d) Alpha Centauri e) Betelgeuse 2. The response to earth's rotation is a) an equatorial bulge b) polar

### F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26

Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,

### circular motion & gravitation physics 111N

circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would

### 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

### Latitude and Longitudes in Geodesy James R. Clynch February 2006

Latitude and Longitudes in Geodesy James R. Clynch February 2006 I. Latitude and Longitude on Spherical Earth Latitude and longitude are the grid lines you see on globes. For a spherical earth these are

### ADVANCED TOPICS IN ASTRODYNAMICS GRAVITATIONAL ASSISTED TRAJECTORIES

ADVANCED TOPICS IN ASTRODYNAMICS SUMMER COURSE BARCELONA, JULY 2004 NOTES FOR THE GRAVITATIONAL ASSISTED TRAJECTORIES LECTURES E. Barrabés, G. Gómez and J. Rodríguez-Canabal Contents 1 Introduction 3 1.1

### SPATIAL REFERENCE SYSTEMS

SPATIAL REFERENCE SYSTEMS We will begin today with the first of two classes on aspects of cartography. Cartography is both an art and a science, but we will focus on the scientific aspects. Geographical

### From Aristotle to Newton

From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. The Geocentric Model Ancient Greek astronomers

### The Sun. Solar radiation (Sun Earth-Relationships) The Sun. The Sun. Our Sun

The Sun Solar Factoids (I) The sun, a medium-size star in the milky way galaxy, consisting of about 300 billion stars. (Sun Earth-Relationships) A gaseous sphere of radius about 695 500 km (about 109 times

### Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.

Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.

### 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

### 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

### Principles of Satellite Remote Sensing

Chapter 5 Principles of Satellite Remote Sensing Goal: Give a overview on the characteristics of satellite remote sensing. Satellites have several unique characteristics which make them particularly useful

### 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

### 226 Chapter 15: OSCILLATIONS

Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion

### Newton s Law of Gravity

Newton s Law of Gravity Example 4: What is this persons weight on Earth? Earth s mass = 5.98 10 24 kg Mar s mass = 6.4191 10 23 kg Mar s radius = 3400 km Earth s radius = 6378 km Newton s Form of Kepler