# Celestial Mechanics

Year
3
2018-2019
Code
01001398
Subject Area
Mathematics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Elective
Level
1st Cycle Studies

## Recommended Prerequisites

Astronomy Elements, Linear Algebra and Analytic Geometry I and II, Infinitesimal Analysis I and II, Differential Equations and Modelling.

## Teaching Methods

A significant part of practical classes is expositive in nature, complemented by the presentation of specific examples and problem solving for applying the acquired knowledge. Personal and group work and discussion in the classroom are encouraged by the teacher. Students are also accompanied individually to discuss their work and to identify any difficulties.

## Learning Outcomes

This course aims at letting the students understand the movements of celestial bodies, including the discussion of the recent discoveries of extrasolar planets. It is also expected that students will master the use of star catalogues, for understanding and building systems of reference.

The main competencies are: capacity analysis and synthesis; ability to formulate and solve problems; ability to work in groups; critical thinking; autonomous learning ability; initiative and entrepreneurshipt; ability to apply theoretical knowledge in practice.

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.

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