Celestial Mechanics

Recommended Prerequisites

Elements of Astronomy, Linear Algebra and Analytic Geometry I and II, Calculus I and II, Differential Equations and Modelling.

Teaching Methods

A significant part of the theoretical-practical classes is expository, complemented by the presentation of illustrative examples and the resolution of proposed exercises to help gaining practical experience about the acquired knowledge. Individual, team work and group discussion in class are encouraged by the instructor. Students also have  individual attendance, where they should discuss their work and clarify possible understanding difficulties.

Learning Outcomes

The aim of this course is to provide the students an understanding of the celestial bodies’ motions, including the discussion of recent discoveries on extra-solar planets. It is also expected that students will master the use of star catalogs, to understand and build reference systems.

The main competencies to develop are: analysis and synthesis; ability to formulate and solve problems; capacity for working in group; competence in critical thinking; ability to learn independently; initiative and  entrepreneurship; competence in applying  theoretical knowledge in practice.

Work Placement(s)

No

Syllabus

 - Brief introduction to Newtonian Mechanics: a brief historical review (Ptolemy, Copernicus, Tycho Brahe, Kepler and Newton) and fundamental concepts (Kepler's three laws for the motion of planets around the sun, Newton’s three laws for the motion of a particle, inertial reference systems, Newton’s law of attraction and the gravitational constant).

- Proper motion of the stars and correction of the coordinates.

- The one-body problem in a Newtonian field.

- The two-body problem.

- Some applications:

- The annual movement of the Earth and the Sun's apparent annual movement.

- Effects on the observations: annual parallax and aberration.

- Study of the motion of artificial satellites.

- The n-body problem. Introduction to perturbation theory.

- Some applications:

- Study of precession and nutation of the Earth and effects on the observations.

- Extra-solar planets.

- Conversion between apparent coordinates and mean coordinates. Star catalogs.

Head Lecturer(s)

Margarida Maria Lopes da Silva Camarinha

Assessment Methods

Continuous assessment
Mini Tests: 30.0%
Frequency: 70.0%

Final assessment
Exam: 100.0%

Bibliography

F. R. Moulton, An Introduction to Celestial Mechanics, Dover Publications, 1970.

P. M. Fitzpatrick, Principles of Celestial Mechanics, Academic Press, 1970.

R. Green, Spherical Astronomy, Cambridge University Press, 1993.