Celestial Mechanics
3
2019-2020
01001398
Mathematics
Portuguese
Face-to-face
SEMESTRIAL
6.0
Elective
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.
Work Placement(s)
NoSyllabus
- 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