Astronomy 1X
Dynamical Astronomy
Dr G. Woan
Room 312, Kelvin Building. 
9 lectures, starting Friday 29 September 2006

This course introduces the student to Newtonian Gravitation, and its application to simple two body problems. We will cover ideas of force, energy, momentum, and angular momentum as applied to the motion of a body in a gravitational field, and explore how the parameters of the orbit cam be deduced from observations of the motion.

 

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  • Course details and lecture notes
  • Handouts
  • Question sheets
  • Recommended books
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    Course details

    Copies of lecture notes will appear here as the course proceeds. They are for reference only, and should not be used to replace your own lecture notes. You will find the course much harder if you don't create your own written version, so please do not print these notes out in quantity.

    Introduction Motion under gravity; gravity as a long range force; Newton's Law of Universal Gravitation; gravitational attraction of spherical bodies; 1, 2 and n-body interactions; Kepler's Laws of planetary motion
    lecture notes:  1 2 3 4 5 6 7
    Pictures: [ galaxy M83 |  globular cluster 47 Tuc ]
    Handouts:[ quick facts #1: orbital motion | force from a spherical body (not examinable) | Newton's Principia ]
    Animations[ Newton's cannon | Eros | Eros flyover ]


    Planetary motion  Newton's laws of motion;  linear momentum; circular motion; angular velocity; certripetal acceleration; orbital period; Kepler's laws derived for circular orbits; natural units for the solar system; geostationary orbits; angular momentum

    lecture notes:  1 2 3 4 5 6 7
    Applets: [satellite positions in 3D ]

    Elliptical orbits  Conic sections (ellipse, circle, hyperbola); properties of the ellipse; aphelion and perihelion; response of orbits to an impulse; semi-latus rectum
    lecture notes:  1 2 3 4 5 6 7
    Pictures: [ conic sections  |  comet Encke ]
    Applets: [ comet Encke ]

    Conservation laws Idea of conserved quantities; energy; momentum; angular momentum;  gravitational potential energy (general and at small heights); virial theorem; escape velocity; orbital velocity law derived
    Applications Relationship between semi-major axis and energy; equation of the ellipse; proof of K1; relation between angular momentum and semi-latus rectum
    lecture notes:  1 2 3 4 5 6 7 8 9 10 11 12 13 14
    Handouts: [ Kepler's 1st law from Newtonian dynamics (not examinable)]

    Hohmann transfer orbits As the 'most efficient' transfer orbit; example of LEO-->GEO; transfer times and delta-vees; example of Earth-->Mars transfer
    lecture notes:  1 2 3 4 5 6 7
    sites: [ Mars Global Surveyor (transfer orbit example)]
    Picture: [ MGS transfer orbit | Venus Express transfer orbit ]

    Rockets  Gravity assist; examples of Voyager and Cassini; the rocket equation
    lecture notes:  1 2 3 4 5 6 7 8
    Pictures: [ Cassini | Cassini flightpath ]

    The two-body problem  Form of two-body orbits; relative motion;  reduced mass and radius vector
    lecture notes:  1 2 3 4 5 6 7 8

    Handouts:[ quick facts #2: The two-body problem ]

    Learning Objectives: On completion of this course, the student should be able to apply the basic concepts of Newtonian gravitation and motion and  use these concepts quantitatively. In particular the student will be able to carry out dynamical calculations for planetary, stellar and spacecraft orbits corresponding to the planar 1 and 2 body problems.

    Handouts
    Extra copies of the handouts are available from the astronomy secretary's office (room 608) as they appear in the course.  All are reproduced above in pdf format.

    Question Sheets
    Problems for this course can be found in the A1 problems handbook. See the A1 Astronomy Home Page.

    Books
    There is no single textbook which is an essential purchase for this  module. However An Introduction to Modern Astrophysics, B W Carroll and D A Ostlie, Addison Wesley is strongly recommended, and is essential for the Astronomy 2 course It has its own website here. Its approach is in places more advanced than required for A1X and Y, however there is much useful material in it.

    Astronomy - Principles and Practice, 4th Edition, A E Roy & D Clarke, IoP Publishing will also be of great help. This is abrand new version of an excellent book - also useful for positional astronomy and instrumental courses.

    For wider background reading, students may find the following list useful: