Astronomy

In Astronomy, teams answer questions on math and physics relating to the year's topic. For 2014, the topic of Astronomy will be Stellar Evolution and Variable Stars. Some questions pertain to specific DSOs on the year's DSO list.

As with any Science Olympiad event, there is never too much studying to be done for Astronomy. Test writers are free to interpret the rules however they want, resulting in a variety of possible test formats and information that may show up. As always, it is best to study everything, even collecting information for topics outside of the rules- it's always possible for the test writer to twist them in, some way or another.

''This page is for the general Astronomy information. For specific topics, see the following pages:

Deep Space Objects
In terms of this event, the Deep Space Objects (DSOs) are objects selected before the year that relate in some way to the topic of the year. There are generally about 16 of them, and participants are expected to research the characteristics that make them unique and relevant. Other information is also necessary, including, but not limited to, constellation, alternate names, magnitude, type of star, stellar classification, right ascension/declination, color index, and images.

It is important to know as much as possible for DSOs, as they will almost always show up on a test. Some tests end up being almost completely on DSOs and their characteristics.

For lists of this year's and past years' DSOs, please see the DSO list.

Kepler's Laws
Kepler's Laws govern the orbits of satellites. They were originally formed with respect to planetary motion around the sun, but they apply to other elliptical orbits as well.

Kepler's First Law
The first law says that all of the orbits of the planets are elliptical with the Sun at one focus. In terms of ellipses, the foci are two points along the semi-major axis (a in the diagram) of the ellipse around which the planet orbits. At any given point in time, the sum of the planet's distances to both foci is constant, giving it is slightly flattened shape. In the case of a circle, both foci are at the same point. The diagram below illustrates this point.



Kepler's Second Law
The second law is slightly more complex. This law says that a planet traces out equal areas in equal time. Since the satellite does not trace out as much area when it is closer to the Sun, it has to move faster in order for this law to be true, so this law basically proves that objects move faster the closer they are to the central object. This law is more easily explained with a diagram.



Now, you may be wondering how can this law be exactly true? This requires a little bit of physics and calculus to do. This YouTube video has a very clear and direct explanation of this, even if you have not taken a calculus class before. A quick summary of the video is that an elliptical orbit can be regarded as a circular orbit when the angle that the object is tracing out is infinitely small, so by manipulating the formulas for angular momentum ($$L=mv_{\perp}r$$) and partial area of a circle ($$A=\frac{\theta r^2}{2}$$), a value for the change in area with respect to the change in time ($${\operatorname{d}\!A\over\operatorname{d}\!t}$$ for all of you familiar with derivatives) can be found. This expression only depends on the angular momentum (which is always conserved) and the mass of the satellite, neither of which changes over time. Therefore, Kepler's Second Law must be true.

Kepler's Third Law
All of these laws are important for a basic knowledge of astrophysics, but Kepler's Third Law is the one of most relevance to the Astronomy event. According to this law, the square of the satellite's period is directly proportional to the cube of the length of its semi-major axis. This law can be presented symbolically as $$p^2\propto a^3$$. If we want an actual equation, we have to use a constant.

$$p^2=(\frac{4\pi^2}{GM})a^3$$ Where G is the gravitational constant and M is the mass of the central object.

In the case of the Earth, when p is expressed in solar years, M is expressed in solar masses, and a is expressed in AU, G cancels out. Then, the formula is simply

$$p^2=\frac{a^3}{M}$$

Where M is the total mass of the system in solar masses. Thus, when talking about our solar system, the solar mass is 1 and we get the most common form of Kepler's Third Law:

$$p^2=a^3$$

IMPORTANT: This formula only works if the correct units are used such that everything cancels. If you do not use years for period or AU for semi-major axis length, then you will get strange answers that are incorrect.

See here for a proof of this law.

Binary Systems
Orbital calculations involving planets often assume that the location of the massive body (eg the sun) is fixed and that the less massive object orbits the center of mass of the massive body. This approximation works for most practical purposes when the ratio of the bodies' masses is very large. However, more technically, both bodies in a binary system orbit their shared center of mass, or barycenter. For example, in a system that contained only Jupiter and the Sun, the barycenter would be located just outside the sun (it actually shifts around constantly with multiple significantly massive planets). The difference is far more pronounced when the bodies are similar in mass, such as Pluto and Charon or two binary stars.

For the remainder of this section, we will assume two massive bodies in isolation. The physics becomes far more complicated when one considers more than two bodies. One of the most important things to note is that the two bodies orbit in direct opposition to each other with the same period. The more massive body is always closer to the center of mass, while the less massive object orbits further from the barycenter. These are related such that for an object with a mass ma and a distance from the barycenter ra and a second object with a mass mb and a distnance rb:

ma/mb=rb/ra

As the period is constant, the object must travel the full circumference in one period. Therefore as circumference is proportion to radius, so also the orbital velocity is directly proportional to the distance from the barycenter.

va/ra=vb/rb

(Work in Progress)

Supernovae
For more information about supernovae, please see Astronomy/Type Ia Supernovae and Astronomy/Type II Supernovae.

A supernova is where a star explodes, and, depending on the star's mass, leaves a neutron star or a black hole.

Type Ia supernovae
Type Ia supernovae are caused not by high-mass stars reaching the end of their lives, but by white dwarves that gain too much mass. They generally occur in binary systems in which a white dwarf pulls enough mass off of its companion to go supernova. This limit is 1.4 solar masses. When the white dwarf exceeds this limit, it blows itself up in a supernova that is significantly brighter than a Type II supernova. All Type Ia supernovae are of the same brightness, and this fact can be used to determine intergalactic distances.

Type II supernovae
A Type II supernova is where a star of at least eight solar masses cannot fuse any more elements together to create energy. This happens when iron is created; no nuclear energy can be made from iron with fusion or fission. When this happens, the star blows itself apart. Heavy elements - elements with atomic numbers greater than 26 - are created in these supernovae. If the star's core has a mass of 1.4 to 3.2 solar masses, a neutron star is formed. Neutron stars are incredibly dense - a neutron star with a diameter of about 12 km has the same mass as the Sun. Some neutron stars rotate quickly enough to emit beams of radiation at the magnetic poles; these are called pulsars, as the beams appear to "pulse" at a constant rate. However, if the core has a mass greater than 3.2 solar masses, a black hole is formed. These are made of degenerate elementary particles and have infinite density. Their gravity is so great that at a certain distance, called the event horizon, not even light can escape. This is where they get the name "black" holes.

H-R Diagram


The Hertzsprung-Russell diagram relates the absolute magnitudes and luminosities of stars with their spectral types and temperatures. They are especially important in understanding stellar evolution. Although some diagrams may have more characteristics labeled on them than others, including characteristics not listed above like Color Index, they all have basically the same shape. Here, a basic introduction to the diagram and its usefulness will be given.

First, the H-R Diagram reveals key relationships in characteristics of stars. The first and most apparent of these is in the main sequence, which contains all of the stars that form a band in the middle of the diagram. The vast majority of stars fall within this band, including the Sun. Also, giants are found in a group above the main sequence, and white dwarves have their own conglomerate on the lower-left part of the diagram. The fact that these stars occupy distinct sections shows how a star's age can change its physical properties.

Another use of the H-R Diagram is that it can predict the location of a new, previously unknown star based on certain observations. For example, say a new star was discovered that had a temperature of 10,000 K and was known to be part of the main sequence. By looking at the diagram, you can predict that the star will have a luminosity of between 100 to 1000 solar luminosities.

The axes of H-R diagrams relate the luminosity of the star (often in relation to the Sun), to the temperature of the star. Temperatures can be represented in degrees (Kelvin), through Spectral Class (Letters O, B, A, F, G, K and M, with O being the hottest and M being the coolest), or both. A common mnemonic for spectral classification is "Oh Be A Fine Girl, Kiss Me".

Determining Distances
A large part of the Astronomy event is being able to determine distances to objects in space from Earth. Often a question will give certain information and the participant will have to interpret and use the information to find the distance, luminosity, or some other characteristics of the object in question.

Cepheids and RR Lyrae
''This section deals with the uses of Cepheids and RR Lyrae in determining distances. For information about their physical properties, please see Astronomy/Variable Stars''

Cepheids and RR Lyrae are two types of variable stars that are especially good for finding distances to galaxies or other groups of stars because they have direct correlations between luminosity and period. In both Cepheids and RR Lyrae, the longer the period, the higher the luminosity. Cepheids typically have periods of about 1 to 50 days. Type I Cepheids, or Classical Cepheids, are brighter, newer Population I stars (see section about stellar populations below for an explanation). Type II Cepheids are similar to Type I in terms of the relationship, but they are smaller, dimmer Population II stars. These are also called W Virginis stars.

RR Lyrae are different from Cepheids in that they are older and fainter than Cepheids. RR Lyrae stars typically have shorter periods than Cepheids - usually less than one day. They have masses about half that of our Sun, and are Population II stars. Also, the luminosity does not increase as much to a change in period, as most RR Lyrae have absolute magnitudes close to 0.75. Therefore, they are only useful in our galaxy and the one closest to us, Andromeda. However, this makes them very useful in determining distance, because once an RR Lyrae star has been found, one only needs to know the apparent magnitude in order to put it into the distance modulus equation and find distance. RR Lyrae have been linked to globular clusters, since most variable stars in globular clusters are RR Lyrae. They are named after the original RR Lyrae in the constellation Lyra.

These variable stars are useful in calculations because once the period is found, the luminosity can be calculated or determined through the use of a period-luminosity graph. Then, through other formulas, the distance can also be determined. This gives them the use as "standard candles" in galaxies relatively close to ours in our universe. NGC 4603, one of the listed DSO's, is the furthest galaxy that a Cepheid has been used to calculate distance at 108 million light years away.

Distance Equations


There are many equations that are used to find distances to objects in space. Several of these equations can be found in the [[Media:Formula Sheet.pdf|Astronomy formula sheet]].

Triangulation/Parallax
Triangulation is often used to determine distances. This method is based on parallax shifts, apparent changes in a star's location when viewed from different locations. The parallax of a star is one-half of the angular shift seen of an object produced over six months, which corresponds to a distance of 2 AU. In other words, it is the angle subtended by a star as the Earth moves by 1 AU. The parallax decreases as distance increases. A star's distance in parsecs is equal to 1/parallax, so a parsec is defined as the distance to a star that has a parallax of one arcsecond. Parallax is only useful to measure stars up to 1000 parsecs away, since past that the parallax is so small that it is not accurate.

Hubble's Law
Hubble's Law uses the fact that objects in space are receding from us to determine distance. Edwin Hubble found that the recessional velocity is proportional to the distance away an object is and created an equation, $$v=H_oD$$, where v is the recessional velocity, $$H_o $$ is Hubble's constant, and D is the distance. The exact value of Hubble's constant is disputed, but most values are about 70.

The value of v is found by looking at an object's spectrum. The recessional velocity is the redshift multiplied by the speed of light, and in order to find redshift, a spectrum must be used. Redshift is how much a spectrum shifts toward the red side of the spectrum due to recession. Redshift, or Z, is found by dividing the change in wavelength of the spectrum by the wavelength the object was expected to have.

Distance Modulus
The distance modulus equation is also very important. It relates an object's distance with the difference between the apparent magnitude (m) with the absolute magnitude (M). This difference is known as the distance modulus.
 * $$5(log(d)-1)=m-M$$ where d is in parsecs

This equation can be written in many different ways so that different values can be found, but the essential purpose of the formula remains the same. A good way to practice using this equation before the competition is to take the apparent magnitude and approximate distance to a DSO and use them to find the absolute magnitude. This experience will be a time-saver if you have to use it during the test.

Stellar Populations
Populations of stars are classified by their metallicity, or by how much heavy metals a star has. Population I has the greatest concentration of metals, and most of them are relatively new stars that have taken metals expelled from other stars. The Sun is included within this group, as are many stars in the outer reaches of our galaxy. These make up the majority of stars in spiral and irregular galaxies. Population II has some heavy metals, but not as much as Population I, as they are older and did not benefit from as much metal dust as newer stars did. Stars in globular clusters and near the core of our galaxy belong to this population. Smaller galaxies also have more stars in this population. Population II stars also make up the majority of stars in elliptical galaxies. There is also a hypothetical Population III consisting of the very first stars with little to no metal content, as they did not exist near the beginning of the universe. They did not last very long, but helped the metals to form for the later populations.

Stellar Life Cycle
For information regarding stellar evolution, please see the Stellar Evolution main page.

Variable Stars
For information regarding variable stars, please see the Variable Stars main page.

The Competition
The competition usually consists of a test, which is normally a pencil-and-paper test, but also may be PowerPoint or station-based. Each team member may bring a laptop or a binder. It is advisable to bring as much information as you can, as a wide breadth of material may be covered. Organize your information so that it is easily referenced during the exam. Most Astronomy tests include mathematical computations, so it is important to have a calculator and a formula sheet ready.

Laptop or Binder?
The question of using laptops or binders as resources has plagued Science Olympians for years. In the end, it comes down to personal preference, and you may have to toy with combinations of two laptops or binders or one of each to see what works best for you and your partner. Here is a list of advantages and disadvantages to help you get a feel for each resource type.


 * Binder
 * Advantages
 * You can take things in and out of the rings
 * The process of organizing your binder helps you retain information
 * You have a hard-copy of all of your information
 * You can write notes on your papers
 * Disadvantages
 * More limited in terms of data storage
 * If you're not very familiar with your binder, it can be hard to find certain information
 * Large binders use up LOTS of paper and ink
 * Laptop
 * Advantages
 * Much higher capacity for data storage
 * Easier to carry
 * Availability of Find/Search functions
 * Process of opening your files before competition makes you look pro
 * Disadvantages
 * Harder to look at multiple pages at once
 * No hard-copy of the information (unless you use one binder and one laptop)
 * More difficult to write personal notes

Useful Resources

 * [[Media:Formula Sheet.pdf|Formula Sheet for Math Portion of Astronomy]] for the mathematical section
 * List of Deep Space Objects
 * Good overall site for the basics of Astronomy
 * American Association of Variable Star Observers
 * Images from the Chandra X-Ray Observatory
 * NASA Astronomy Picture of the Day
 * Reach for the Stars for some sample pictures
 * SIMBAD Astronomy Database for DSOs
 * NASA Space Math provides work sheets for a wide variety of Astronomy math problems
 * List of Messier objects Helpful for identification
 * Khan Academy- Cosmology and Astronomy Easy to digest videos on the basics of Astronomy
 * Onward to the Edge An astronomy blog run by scioly.org's own AlphaTauri, syo_astro, and foreverphysics.
 * asdfqwerzzz2's Astronomy Notes PDF
 * Stellar Evolution Notes PDF
 * HR Diagrams, Light Curves, and Radiation PPT
 * Kepler's Laws, Spectra, and the EM Spectrum PPT
 * Stellar Evolution PPT