The Solar System Flashcards
What are the key objectives of the course
Basic structure; dynamical structure; inverse square law leads to Keplers laws; 3 body problem, derivation of the 5 Lagrangian points, derive their stability properties, applications of these results to the motion of coorbital objects in the solar system.; the effects of orbiting satellites: 2 tides, resulting in prograde orbits; apply knowledge to planetary rings of systems; solar nebula and planetary formation; how the gravitational, radiative and radiogenic processes affect the thermal state of the planet; resonances in the solar system; origin and evolution of asteroids and comets.
What do the resonance 1:2 mean?
For every 1 orbit of the inner satellite and every 2 orbits in the outer satellite the two satellites coincide and are in resonance.
What is the preference of commensurability?
A comparison between resonant values of orbits as integers and the ratio of mean motions of satellites to determine whether there is a resonance between satellites.
What are Kepler’s laws?
A planet moves in an ellipse with the sun at one of the foci.
A planet sweeps out equal areas in equal times.
The square of the orbital period is proportional to the cube of the average distance from the sun.
What is Newton’s law of universal gravitation?
F = (Gmm)/r^2
What is the Titus-Bode law?
That the bodies in some orbital systems orbit at semi-major axis in a function of planetary sequence.
One formulation with Earth’s semi major axis = 10
a = 4 + n. Where n = 0,3,6,12,24,48. Where after step 1 each value is twice the previous value.
Or a = 1.5 x 2^(n-1) + 4: Where n= -infinity, 2,3,4,5…….
Or if divide by 10 to get in AU’s. So that a = 0.4 + 0.3 x 2^m. Where m=-infinity,0,1,2,3,4…….
Where does the Titus-Bode law come from?
They used to think that as the order from the solar system increased the distance between each subsequent planet increased by a factor of 2. Starting with the Earth is a distance of 10 away from the sun. Mercury must be 4 of the same units away from the Sun. So that a- the semi major axis — a = 4+n. Where n=0,3,6,12,24…- but it makes sense to have n going up in line with the planets position from the sun.
So another form is conveniently used a = 4 + 1.5 x 2^(n-1). Where n= -infinity, 2,3,4- Even more convenient to change this to AU’s.
What was Kepler’s first model of the Solar system based on?
The 5 Platonic solids.
What are Platonic solids?
They are solids that consist of regular polygons joined together to make a closed solid shape- there can be only five that can be enclosed by a circle.
Why did Kepler use the Platonic shapes in his theory?
He saw a regular pattern in the distances between the planets.
What is the basis of Kepler’s model of Platonic shapes
That the central objects the Earth was enclosed by a dodecahedron-(as quintessence is the fifth and most special element), the sphere of the Earth touches the sides of the Dodecahedron the next orbit is in a shell where the inside of the shell touches the vertices of the dodecahedron. The width of the shell was based on the eccentricity of the planets orbit. The outside shell again would touch the faces of the Platonic shape surrounding this shell.
What were the problems with Kepler’s Platonic model?
There are more then five planets, (which they were not aware of until Neptune was discovered).
What is resonance?
When the orbital period of the planets/moons coincide by an integer factor.
What does an orbital resonance of 1:1. Mean.
They moons/ planets are co-orbital this means that they have the same semi-major axis- ie in the same orbit.
What does is the resonance between two bodies that have a ratio of 3:4?
The first body completes 3 orbits to the other bodies orbits 4 times.
