Astronomy 1
Dynamical Astronomy
Prof. Graham Woan
10 lectures, online

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.

Live and recorded lectures on Stream
(see Moodle for the alternative Zoom link)
Moodle link for this course
Padlet for lecture questions

  • Course details and lecture notes
  • Recommended books
  • Course details

    Copies of lecture notes appear here for reference.  You will find the course harder if you don't create your own written version of these notes, so try to do that rather than simply read the material.

    All the slides can be found in a single pdf here.

    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 M83globular cluster 47 Tuc ]
    Handouts:[ quick facts #1: orbital motion | force from a spherical body (not examinable) | Newton's Principia | Newton's "A Treatise of the System of the World" ]
    Animations[Stars at the centre of the Galaxy, more |  Newton's cannon | Cassini's orbits |   orbit simulations ]

    Planetary motion  Newton's laws of motion;  linear momentum; circular motion; angular velocity; centripetal 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
    Animation: [geostationary orbit | Kepler 2 simulation ]

    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 ]
    Animation: [ comet Encke  comet 67P | kick simulation ]

    Conservation laws Idea of conserved quantities; energy; momentum; angular momentum;  gravitational potential energy (general and at small heights); virial theorem; escape speed; 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 laws from Newtonian dynamics (not examinable)]
    Links: [Emmy NoetherGW150914 (orbit decays because of gravitational waves) ]
    Animation: [ escape speed simulation ]

    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: [ Perseverance’s Route to Mars (transfer orbit example)]
    Picture: [Exomars transfer orbitMaven 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 ]
    Links: [JPL Horizons  and coding examples (in Python)]

    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

    Example exam questions and answers with hints and tips

    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.

    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 A1, 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 also useful for positional astronomy and instrumental courses.

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