
Astronomy 1
Dynamical
Astronomy
Prof. G. Woan
Room 312, Kelvin
Building.
9 lectures, starting
Monday 26 September 2016
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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password for offsite access to the notes.
See the Moodle link to this site.
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, 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 nbody interactions; Kepler's
Laws of planetary motion
Pictures: [ galaxy
M83  globular
cluster 47 Tuc ]
Handouts:[ quick facts #1: orbital
motion  force from a
spherical body (not examinable)  Newton's
Principia ]
Animations[Stars
ar the centre of the Galaxy more,
and more
 Newton's
cannon and web
version  Rosetta
orbit  orbit
simulations (2 and 3 body) ]
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
Animation: [geostationary
orbit ]
Elliptical orbits Conic sections (ellipse,
circle, hyperbola);
properties of the ellipse; aphelion and perihelion; response of orbits
to an impulse; semilatus rectum
Pictures: [ conic sections
 comet Encke ]
Applets: [ comet
Encke 67P]
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 semimajor axis
and energy; equation of the ellipse; proof of K1; relation between
angular momentum and semilatus rectum
Handouts: [ Kepler's laws
from Newtonian dynamics
(not examinable)]
Links: [Emmy
Noether  GW150914
(orbit decays because of gravitational waves) ]
Hohmann transfer orbits As the 'most efficient'
transfer orbit;
example of LEO>GEO; transfer times and deltavees; example of
Earth>Mars
transfer
sites: [ Mars
Maven Mission (transfer orbit example)]
Picture: [Exomars
transfer orbit  Maven
transfer orbit  Venus
Express transfer orbit ]
Rockets Gravity assist; examples of
Voyager and Cassini;
the rocket equation
Pictures: [ Cassini  Cassini
flightpath ]
Links: [JPL Horizons and coding examples (in Python)]
The twobody problem Form of twobody
orbits; relative
motion; reduced mass and radius vector
Handouts:[ quick facts #2:
The twobody 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.
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 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: