Becoming An Astronomer

We were recently, or not so recently—I'm very good at procrastinating—assigned a multi-part blogging to find out what it truly means to be an astronomer.  I realise as a sophomore astrophysics major that I still don't understand the specifics of what being an astronomer entails or means to me.  To quote my friend Alexa,

I just want to be one. So much. “Space” is, if you think about it, everything but Earth. When we study it, we’re pausing our narcissistic tendencies for just a moment. We’re not everything; we’re part of everything. Ignoring that is shameful.

She stated in the best way possible what attracts me to astronomy, but that still doesn't mean I know what astronomy is.  Right now I just think of astronomy as some nebulous loosely defined field of Things I Would Like To Do Because They Are Amazing, but that's not an acceptable answer to the question.  So without further delay I shall attempt to synthesise my thoughts on the topic.

Is There Life On Maaaars?

I've been having an uncharacteristic moment of curiosity lately, and that curiosity is about life outside Earth.  Usually I don't care.  I'm much more of a "let's explore and discover the physical laws of the universe" kind of guy.  But today, it's all about life out there, and why not?  Some pretty interesting things have happened in the last week.

1. ESA's Mars500 Simulation Ended
So I have to admit, I knew nothing about this project until I read the article today.  Doesn't prevent me from thinking it's amazing.  In short, a crew of 6 was stuck together in an in-lab "spacecraft" for 17 months, performing the tasks necessary for a real mission to Mars including "entering" orbit and "landing" on Mars.  Conditions were controlled exactly as if they were actually travelling and they completed experiments on the problems brought about by long space missions.  Maybe this will open up opportunities for an actual space mission to Mars after studying the physiological and psychological effects of longterm isolation.  Very cool.  Here is a compiled video diary of their time during the simulation:

2. A New Way to Look for Aliens

Avi Loeb and Edwin Turner of the Harvard-Smithsonian Center for Astrophysics and Princeton University, respectively have suggested a new way to look for extraterrestrial intelligence: doing it the same way we find civilisation on earth.  They intend to look for the lights from their cities.  These two operate on the assumption that life evolves in the light of the nearest star and that any intelligent life forms would have learned to make light and extend their days.  They would have to find a way to filter out the light from the star.  They suggest that one method of doing this is to look for bright areas in a dark phase of the planet's orbit (think of the dark side of the moon).  Unfortunately, this method would require far more powerful telescopes than we now have, but it's definitely a start.

3. Organic Molecule "Sweet Spots"

This isn't technically, astrophysics, however I think it still has a place in a post about life outside Earth.  Astrobiologists at Rensselaer (one of the reasons I didn't apply there was I couldn't spell it on the first try) have discovered areas of higher methanol concentration surrounding some, but not all, newly formed stars.  Methanol is apparently one of the precursors to more complex organic molecules which may give rise to life.  They call this a "sweet spot" of physical conditions that allow these organic molecules to form.  Even more interestingly, from studying concentrations in comets, they have determined that our solar system is painfully average in the methanol department.  In other words, we're not all that special and life still managed to appear on earth.  The implication here is there may be other solar systems out there with greater methanol concentrations that lend themselves more easily to the appearance of life than our own!

Sources

http://www.sciencedaily.com/releases/2011/11/111106142036.htm

http://www.esa.int/SPECIALS/Mars500/

http://www.sciencedaily.com/releases/2011/11/111103190356.htm

http://www.sciencedaily.com/releases/2011/11/111102190028.htm

Hydrostatic Equilibrium and the Sun

Abstract
We would like to know how the sun is being "supported".  We assume that this mechanism is hydrostatic equilibrium, but to be sure we work through the derivation.

Introduction
We know that the sun is somehow being prevented from gravitational contraction.  Our theory is that it is supported by hydrostatic equilibrium, which means that the internal pressure provides an opposing support force.  We calculate the gravitational force on a mass shell, the pressure required to balance it, and then derive the force equation for hydrostatic equilibrium.

Methods and Results
We first assume the Sun to be a spherical gas cloud with density ρ(r).  We consider a differential mass shell of this sphere with radius r.  We recall that the volume of a sphere is ⁴/₃πr³ and that the differential volume is its derivative. Then we get a differential mass dM:

We know the equation for universal gravitation:

Here we let M be the total mass enclosed by the mass shell and m be the differential mass element.  As a result, we get the differential gravitational force to be:

We know that pressure is equal to force divided by area.  So we can say:

Now dividing by dr on both sides of the equation we arrive at the equation of hydrostatic equilibrium:

Conclusions

We have derived from simple physical laws that the equation for hydrostatic equilibrium is a plausible explanation for the way the sun is supported.  A quick search shows that we are indeed correct.  Hooray!

Stellar Properties From Afar (Problem 1)

Abstract
Considering the angular diameter of the sun and the astronomical unit, we can estimate the radius of the sun, the AU in solar diameters, and the mass of the sun using Kepler's 3rd law.

Methods
Applying basic trigonometric identities and taking the astronomical unit a to be the distances from us to the closest point of the sun to us (i.e., the centre of the circle we see from earth), we can see that:

Multiplying through by a we get a value for the radius of the sun.  It is clear from here that if we divide a by twice the solar radius we can easily determine the answer to the second part of our question.  Finally, we have Kepler's 3rd law:

Where P is the period of the earth and G = 6.7 x 10^-8 dyne-cm²/g².  From here we can solve for the mass of the sun.

Results
Solving the first equation using a = 1.5 x 10¹³ cm we get the radius of the sun equal to 6.545 x 10¹⁰ cm which is very close to the actual value of 6.955 x 10¹⁰7 s.  Dividing, we get 1 AU = 114.6 solar diameters.  Then, solving for the mass of the sun in Kepler's 3rd law with P = 3.154 x 10⁷ s, we have the mass of the sun equal to 2.007 x 10³³ g which is a surprisingly accurate number.

Surface Temperature of Planets

by Eric S. Mukherjee, Nathan Baskin, and I forget who else (sorry).


Abstract
In this problem we consider the how the temperature of the sun affects the temperature of the earth.  This is possible to estimate by assuming both the sun and the earth to behave like perfect blackbodies.

Introduction
Assuming the Earth has constant surface temperature and that it behaves like a blackbody, we can estimate the surface temperature using the energy emitted by the sun.  We also assume the sun to be a perfect blackbody.  Under these assumptions we can find the surface temperature of the Earth by knowing the temperature of the sun, the radius of the sun, the mass of the sun, the mass of the earth^*, and the radius of the earth.

Methods
We start with the equation for flux at the surface of a blackbody (σ is the Stefan-Boltzmann constant):

From this we derive the luminosity of the sun by multiplying through by the surface area:

Then the flux of the sun at the surface of the earth is (where a is the astronomical unit):

If we consider the area of the earth through which the flux passes, it is the circle of area π R_⊕².  Multiplying through by this quantity we get the power input to the earth from the sun.  We then realise that this is necessarily equal to the power output of the earth due to energy conservation which, at the surface of the earth, is equal to σT⁴π R_⊕².   Thus we have an equation of the form:

Using this equation with R_☉= 695,500 km and T_☉= 5778 K, we get T_⊕ = 279 K.

Conclusions
This temperature that we calculate is around 5.5°C which sounds reasonable for an earth without accounting for atmospheric greenhouse effects and allowing for the temperature at the poles.  The true average temperature of the earth is around 16°C but that is measured with the warming effect of the atmosphere.  The sun is not a perfect blackbody which also contributes to the difference between our calculation and the true value.

Acknowledgements
I'd like to thank the entire Ay 20 class and teachers for collective brainpower due to the fact that I can't remember who exactly worked on this problem and I'm sure we drew from the knowledge of many people in the room.  I'd also like to thank the superior computational power of Wolfram Alpha for bringing to my attention that there exponents matter when calculating ratios and that the temperature of the earth is most definitely not 1270 K.



*Note: It has been brought to my attention by Professor Johnson that the masses of the earth and sun do not actually factor into this calculation at all unless we need them to derive some of our other known constants.

A slight belated correction on AGN

As my readers may remember, a few weeks back I posted about the properties of AGN and how they affect their host galaxies.  One of these ways I listed was star formation rate.  Actually, a bit less than two weeks ago an article was reprinted from UCSD by ScienceDaily that AGN do not stop star formation as previously thought.

Prior research showed a correlation between the presence of AGN and the lack of star formation in galaxies.  This new study claims that this was a function of observational bias.  Older, more massive galaxies are easier to detect, and are also the ones with decreased star formation rate.  This study finds AGN in all types of galaxies including those in which stars are still being formed.

Read the full article here.

Eric Answers

Hey all, as you may know I've been collecting astronomy questions from people.  Now I'm going to answer a few of them.

Jessica and choirqueer asked: "Astronomy vs. astrology vs. astrophysics.  What is the difference?"

I've combined the two questions for ease of answering.  Technically, astronomy has more to do with the qualitative or observational study of all objects not contained in the Earth's atmosphere.  Astrophysics is part of astronomy, but is focused on the applications of physics to astronomy and understanding why things are the way they are through physics.  The title of this blog comes from something an old friend of mine used to say despite the fact that he was, in fact, an astrophysicist.

Astrology is completely different in today's world although in antiquity astrology was astronomy.  Astrology is a belief that astronomical phenomena affect our lives as humans on earth and is widely regarded as unscientific.  I personally don't believe constellations and planetary motion have any effect on our lives as constellations are patterns that humans have assigned to stars which aren't even necessarily close together and planets are predictably governed by physics, but belief is very personal and I am not one to tell people they are wrong.

 LilyForest asked: "How noisy is the sun, assuming we could actually here it?"

I actually attended a colloquium at the CfA that dealt with this over the summer.  It was a fascinating topic.  Here's a video from ESA talking about the vibrational modes of the sun way more eloquently than I possibly could.

Basically, the sun produces "noise" due to its surface vibration.  However, this noise is generally not in the human audible range and also cannot reach us on earth.  Here is a clip from Stanford of the audio from 3 modes: Solar Sounds

 NastyNate (Nathaniel) asked: "How many total planets have been discovered and recorded in the universe?"

This is actually a question for my professor, who studies planets outside of our solar system.  However, since this is my blog and not his, according to this website which seems like a credible source run by a Paris Observatory scientist gives the current number a 694 planet candidates found outside of our solar system as of today.

Greg asked: "Given the universe is expanding at an accelerating rate, will the rate of expansion eventually pass the speed of light?

The expansion of the universe is a very tricky subject.  Currently, the recession velocity of galaxies due to the expansion, which is proportion to the speed of light multiplied by the redshift, can be greater than the speed of light for redshifts greater than 1.  However, this is greatly dependant on the coordinate system and reference frame.  Since we can argue that galaxies are moving apart due to expansion of the universe, the short answer is yes: the expansion for distant objects is even currently greater than the speed of light.  The coordinates in which these are moving faster than c, are not the same coordinates used in relativity so this doesn't really contradict relativity.  Presumably this is a result of the odd behaviour of comoving coordinates which are explained best in Ned Wright's tutorial.

Jogirl asked: "Why is Pluto not considered a planet anymore?  How can it be a planet one day and not the next?"

Pluto no longer fits the criteria for a planet.  According to the International Astronomical Union, the current criteria for a planet are the following:

1. It is in orbit around the sun
2. It has sufficient mass to have taken on a spherical shape due to self gravity
3.  It has cleared the neighbourhood of its orbit.

Looking at 1 and 2, Pluto may be a planet.  However, it does not fill the third requirement.  Pluto has very little mass in comparison to the combined mass of numerous objects in its orbit.  In comparison, the Earth is by far the most massive object in its orbit.  Basically, Pluto failed to gravitationally bind or expel the other similarly small objects in its immediate neighbourhood and is therefore one of many similar objects in the area rather than The One Large Thing in its orbit, if that makes any sense.

One answer I can give you for your second question is that science progresses by falsification.  This means that the rules in science are constantly changing and things are being redefined in order to comply with new rules.  As we learn more about the universe we realise that some things we thought before are not the case.  For instance, we now know that the earth orbits the sun.  It's not that one day the sun orbited the earth and then it changed, but that science changed and our theory was then modified to better fit the new model.