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Last Astro Final
| Question | Answer |
|---|---|
| Tycho Brahe | Made accurate instruments to observe the sky |
| Johannes Kepler | Worked as Tycho Brahe's assistant. Wanted to develop a refined system of planetary motion with the SUN at the center of the universe. Started with mars. Determined that Mar's orbit was an ellipse. Harmonice Mundi (Harmony of the Worlds) |
| Kepler's 1 law of planetary motion | Law of the ellipse: orbits are ellipses with the sun at one focus |
| Semi-major axis | radius if the ellipse is a circle |
| Kepler's 2 law of planetary motion | Law of Areas: A line drawn between the Sun and the planet sweeps out equal areas in equal time. Implies that the planet moves faster at perihelion |
| Kepler's 3 law of planetary motion | The law of harmonics: the square of the period of revolution of a planet about the sun is proportional to the cube of its mean orbital distance from the sun (a) IF AND ONLY IF T is in years and a is in AU |
| centripetal force | force that acts towards the center of a circle |
| Law of Shells | For large distances we can approximate objects as particles. So for orbits of most planets around a star we treat the star and planet as point particles and we ignore their radii |
| Law of Shells and Newton | A uniform shell of matter attracts a particle outside the shell as if all the matter were concentrated at the center. A uniform shell of matter exerts NO NET gravitational force on a particle located inside it |
| Law of shells and planets | The Earth/Sun/Planets/Stars/Galaxies can be approximated as a series of concentric shells (with all the mass concentrated in a point at the center). When we look at objects in orbit at a certain A above the surface of a planet we add the A to R |
| Orbital Motion | An object is in "orbit" when the combination of its tangential velocity and its ac allow it to move and fall at the same rate that the surface below it curves. So it is constantly falling but never hits the surface |
| Center of mass | The COM is just a mathematical point but behaves like a particle whose mass equals the total mass of the system. The point acts as if all of the mass were concentrated there and all external forces act at that point |
| Barycenter | Center of mass for 2 point like objects bound together by gravity |
| Center of mass part two | Barycenter. Lies on a line connecting the two objects. Suppose we had 2 particles with mass m1 and m2 separated by a distance d. We define the center of mass of the system by a weighted position |
| In astronomy, we more commonly put the COM (barycenter) | at the origin |
| Two objects will orbit | about the barycenter |
| Center of mass is more | convenient to work in a radial coordinate system. The ratio of the two objects orbital distances equal to the inverse ratio of their masses. So the more massive object orbits closer to the COM |
| Visual Binary | The best way to determine stellar masses is to find stars in binary (double star) systems and observe the gravitational interactions (mutual orbits) This is how we know the masses of the different spectral type stars |
| Types of visual binaries | eclipsing binary and spectroscopic binary |
| Range of Stellar Masses | So we use binary stars systems to determine the correlation between the spectral type and mass and then we assume that this correlation holds true for non-binary stars as well. |
| From comparing the masses of the stars to their luminosities | we get a crude empirical formula relating the two qualities: Luminosity is directly proportional to Mass^3.5, So, the more massive the star, the more luminous it is. So more massive stars produce more energy by fusing H to He at faster rate than low mass |
| In the case of eclipsing and/or spectroscopic binaries we | cannot measure the separation between the stars (a1+a2). We can measure their orbital velocities which gives us equivalent information |
| If orbit is face on | we cannot get radial velocity |
| If orbit is perfectly edge on | the derived equations are exactly correct (i=90 degrees) |
| So, changing the inclination from edge on (90 degrees) to some angle (i.e 45 degrees) | increases the total mass of the system needed to explain the observed orbital velocities |
| Star and Exoplanet | Sometimes, if you have high enough resolution and the planets are far enough from the star you can see the planets using a coronagraph which blocks out the light of the star, otherwise the light overwhelms the light from the planet |
| The Goldilocks Zone | It is the distance from a star at which the planetary temperature can support liquid water. So Goldilocks zones are further from hot/high luminosity stars but closer to cool/low luminosity stars |
| Albedo | is the measure of the reflectivity of a surface ranging from 0 (no reflection) to 1 (perfect reflection). It determines how much solar energy a surface absorbs or reflects, with light -colored surfaces like snow having a high albedo |
| The temperature of a planet depends on | how much flus the planet receives from the star. The flux the planet receives depends on the Luminosity of the star and the distance to the star. The amount of energy the planet absorbs depends on its radius/surface area and albedo |
| Viral Theorum | It is trivial to solve for the orbits of a 2 particle system. But for more than 2 we cannot do it analytically. Fortunately, for gravitationally bound systems in equilibrium it can be shown that total E is always 1/2 the time averaged PE |
| Viral Theorum applies to a wide variety of systems | gas clouds, solar systems, stellar clusters, galaxy clusters |
| Viral theorum applies to a wide variety of systems as long as they are in | gravitational equilibrium. Outward pressure (KE of particles) is balanced by the force of gravity inwards. So that the system is gravitationally stable and will remain so for a long time |
| Viral Theorum can be used to | determine the initial conditions of protostellar collapse |
| The condition for gravitational stability is | called the theoretical Jeans mass of the cloud AKA the viral mass. If a system of particles has an actual mass equal to this theoretical jeans mass then the system is stable, it will neither collapse under G or expand due to P |
| If the object has a mass < the Jeans Mass then | pressure>gravity and the object will expand |
| If the object has a mass> the jeans mass then | gravity>pressure and the cloud will collapse |
| Viral Theorum and Jean's mass | If the particles in the cloud/stars in the cluster do not have enough KE to balance the force of gravity the cloud will collapse. If the actual mass of the object exceeds the jeans mass then the object will collapse |
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