Science Tuesday :: What is light?

In the last Science Tuesday article we talked about the first glimpse into the vastness of the universe – the discovery that stars of variable brightness can serve as a new astronomical ruler and the invention of powerful telescopes proved that there were glaxies beyond our Milky Way. As scientific methods to probe the nature of the universe continued to grow by leaps and bounds, astronomers began to revisit age old questions:

1) What is the chemical composition of stars?

2) How do stars move? Do they move at all? If so, how to measure how much they move?

The answer to the 2nd question turned out to have a profound impact on mankind’s  understanding of the nature of the universe. However, the journey to get to the answer was long – spanning nearly 200 years. It would require understanding of the natrure of light and how it interacts with matter, a science knowns as spectroscopy. In order for the answer to make sense, we will need to take a few side roads and try to understand the basics ourselves. But before we go into that, let’s first start with what was known (and unknown) about the motion of stars before the advent of spectroscopy.

The fact that stars were not stationary but appeared to move relative to the background was first discovered by the famous astronomer, Edmund Halley (after whom the comet is named). Halley was studying stars whose positions were recorded in the 2nd century AD and realized that they were now in slightly different positions. While it was known that stars appeared to move, astronomers could not measure how much or how fast they moved for several centuries.

Why was it so hard to find out how much stars move?

If you remember, if you want to measure how far an astronomical object is from Earth, e.g a planet, the method used to find out these distances was parallax. The parallax method worked very well for planets (which are much closer to Earth). However the closest star (other than the sun of course) is much further away than any of the planets and hence the motion of the star is much less perceptible to us on Earth. Even the best telescopes do not have the resolution to determine the parallax shift of stars because it is so small.

There is also another interesting dimension to consider regarding the motion of stars.  Does the star approach the Earth as it moves, or does it fly away from the Earth? (this is termed radial motion of the star).

The answers to these questions remained elusive for centuries. It was clear that a new method was required to shed light on the motion of stars and this came about in a remarkable way in the early 1900s. Mankind had come a long way since the “simple” geometric methods that had largely been used in the past to study the universe. The first milestone came about in the understanding of light. Let us talk briefly about light.

What is light?

This seemingly simple question is hard to explain in a simple way. We know of some  properties of light – it helps us see things, it has different colors, heat can generate light (as in a flame or a barbecue grill). You might also be familiar with less conventional forms of light (or radiation) – microwaves that heat food, X rays that are used to take pictures of your teeth. But what is light?

1) Light is a form of energy, just like electricity for example. In fact, light has an electric and a magnetic component.

2) Light is characterized by its wavelength. Imagine water waves in the ocean.

Photograph taken by me.

A wave rises and falls as it moves in the ocean. The wavelength of a water wave is the distance between two consecutive peaks as the wave moves in the ocean. So then what do waves mean when it comes to light? The thing that waves in light is the electric and magnetic field of which it is made of. In order to understand this, let us let us play a little game – get three friends and two jumpropes. Now take position such that the four of you make a + with the four of you standing at each tip of the the +. Now two of you at opposite ends of the + will hold each end of one jumprope and the other two will hold the ends of the other rope. Now you are set to make waves – much like light. One pair of you wave the jumprope up and down and the other pair wave it side to side. The two waving jumpropes are the electric and magnetic fields that make up light.

The wavelength of light is related to it’s energy – the larger the wavelength, the lesser the energy, and vice versa. See the image below for an illustration in terms of our jumpropes.

Photo credit: http://missionscience.nasa.gov/ems/02_anatomy.html

The wavelength (or energy) of light is what gives it a color (or lack there of). You have all seen a rainbow – where do all those colors come from?

Photograph taken by me.

Back in the 1600s, the famous physicist Sir Isaac Newton discovered that sunlight is actually a mixture of light of different colors – the colors that make up a rainbow. If you put a piece of glass, called a prism, in the path of sunlight and put a sheet of white paper behind the prism, you will see the colors of the rainbow (see the picture below).

Photo credit: http://users.zoominternet.net/~matto/M.C.A.S/prism_spectroscope.htm

The red light has a wavelength of 700nm whereas blue light has a wavelength of 400nm. These colors make up what is called the visible spectrum of electromagnetic radiation (as most human eyes can perceive these individual colors). Now there are all types of radiation that we cannot see – microwaves, ultraviolet, and X rays to name a few. Microwaves have much lower energy than visible light and hence longer wavelengths, while X rays  have muvh higher energy than visible light and thus much shorter wavelengths.

OK so now we know a bit about light, how does this help us understand of the motion of stars? We need to next learn how light interacts with matter (or stuff) before can get to the next step in our journey to the answer. More about this next week.

Beyond the Milky Way :: Discovery of a new astronomical ruler

Picture of the Small Magellanic Cloud, a satellite galaxy of the Milky Way. Credit: http://apod.nasa.gov/apod/ap071001.html

Picking up from where I left three weeks ago, it is now time to go beyond the Milky Way. Is the Milky Way the universe? Is there more beyond? We know the answer today, but back in the late 19th century, this question was one of the hottest topics of debate among astronomers.

The late 1800s was the era of telescope making. After Galileo invented the instrument, several people spent lifetimes in building bigger and more powerful telescopes. In the last article, I talked about William Herschel’s observations of the Milky Way. In addition to stars, Herschel and others observed what they termed nebulae – hazy light near the perimeter of the Milky Way. As one might deduce, nebulae (the adjective nebulous means hazy) were not pinpricks of light like stars but more like cloudy patches of light. The burning question in those times was – what were these?

There were two diametrically opposed schools of thoughts on this question – one school of thought (of which Herschel was a champion) believed that nebulae were predominantly composed of dust and gas with some “young” stars. The hazy light was attributed to the presence of the gas and dust. This school believed that nebulae were part of the Milky Way.

The other school of thought believed that nebulae were actually galaxies in themselves and were unimaginably distant from the Milky Way. But for several years, there was no compelling proof for either theory.

Now let us take a minute and see how we can try to prove either theory. The absolute proof lies in finding out the actual distance between the nebulae and us on Earth. But this was precisely what was confounding all the astronomers. When you look up at the night sky, you see stars of various brightness – some are brighter than average, some are barely visible, while there are multitudes in between. How bright a star appears to you on Earth is influenced by two things:

a) The intrinsic brightness of the star, i.e., how much fuel it has

b) How far away the star is from you

So now you might appreciate the difficulty astronomers had in figuring out how far stars were – if a star is very bright it could mean it is very close to us, if a star appears dim to us, it could mean it is very far away. How far a star is from us can be estimated only if we know how bright it is. But how can we tell how bright a star is?

Enter Henrietta Levitt’s phenomenal discovery. Before we come to her discovery though, we need to learn about a special type of star.

When astronomers were gazing at stars, they found that the brightness of some stars had an interesting property: they brightness would wax and wane at regular intervals. In other words, some stars pulsated. Imagine you have a light bulb connected to a dimmer switch. Now if you move the switch such that the bulb is brightest and left it that way for an hour and then moved the dimmer so the bulb dims and leave it in this state for an hour and keep doing this all day, you have a pulsating light bulb. Now let us describe the pulsating light bulb in astronomical nomenclature: the interval between two successive bright states of the light bulb (or dim states) is called the period of pulsation; in this case the period is 2 hours. Getting back to pulsating stars, they were named Cepheid variables after a prominent pulsating star called Delta Cephei. See the video below for an illustration of a Cepheid variable.

Now we finally get to Henrietta Levitt’s famous discovery. Back in the late 1800′s and early 1900′s, women in science were very few; the few that did pursue science were relegated to work deemed less intellectual for the males. In the field of astrophysics, the foundation of many profound laws and theories rested on meticulous and tedious observations and cataloguing. This is the type of work that Henrietta devoted her life to – she was one of the “computers” as they were called – a group of women whose job it was to study half a million photographs of stars and catalog each star’s brightness and location.

One of Henrietta’s specialties was variable stars – stars that exhibited variable brightness like the Cepheid variables. Simply cataloguing the brightness did not satisfy Henrietta’s curiosity – instead she attempted to understand this behavior.
As I mentioned before, a Cepheid variable is characterized by it’s brightness and it’s period. While studying photographic plates of Cepheid variables from a cluster of stars known as the Small Magellanic Cloud, Henrietta had a brilliant idea. She had noticed that the brightness of these stars varied and tried to come up with an explanation for why that might be so. She assumed, reasonably, that the Small Magellanic Cloud was very far from Earth. She also assumed, reasonably, that the Cepheid variables within the Cloud were much closer to each other than they were from Earth. Hence, all the Cepheid Variables within the Cloud should be about the same distance from Earth. Imagine a flock of birds flying in the sky. The individual birds in the flock are much closer to each other than they are from you. So on the scale of the distance between you and a bird in the flock, every bird in the flock will be about the same distance from you.
Henrietta plotted the brightness of the Cepheid variables as a function of their period and found something remarkable – there was a clear relationship between them as shown below:
Photo credit: http://www.math.lsa.umich.edu/mmss/coursesONLINE/Astro/Ex1.4/
So a Cepheid (let’s call it A) that has a magnitude of -4.5 has a period of 13 days, a Cepheid that has a magnitude of -5 has a period of 15 days and so on.
OK so now what? If all the Cepheids are about the same distance from Earth and have varying brightness, what does that mean? It means that the brightness varies only because of varying intrinsic brightness, not distance.

If you remember, the raging debate at that time was where were the nebulae, inside or outside the Milky Way? Now that Henrietta had shown the relationship between a Cepheid’s brightness and period, this question could finally begin to be answered. All one had to do was determine the period of the Cepheid of interest – the graph would yield the answer to that Cepheid’s brightness. So if the Cepheid of interest has a brightness of -4.4, you could say it was about the same distance from Earth as Cepheid A in our example above. On the other hand, if the brightness of the Cepheid of interest was -1, then according to the inverse square law, it is twice as far from Earth as Cepheid A. So what Henrietta did was establish a new astronomical ruler for measuring relative distances between stars.

The famous Edwin Hubble made full use of Henrietta’s discovery. He discovered the first variable star in a nebula, the Andromeda nebula. Hubble recorded the period of this Cepheid and used Henrietta’s chart to determine the brightness – this Cepheid was 7000 times brighter than our sun!!! Knowing the apparent and absolute magnitude of the Cepheid and using the inverse square law, Hubble deduced that the Andromeda nebula must be 900,000 light years from Earth!!! In my last post on the size of the Milky Way, we saw that the diameter of our galaxy is 100,000 light years. So Hubble’s discovery of the Cepheid in the Andromeda nebula clearly proved that it was not part of the Milky Way and thus the age-old debate was finally put to rest.

In the next post, we will see the far-reaching implications of Henrietta’s and Hubble’s discovery.

Global Warming – blessing or curse?

Photo credit: http://weakonomics.com/wp-content/uploads/2009/11/Earth-on-Fire.jpg

Global warming has been one of the most emotionally charged issues in recent times, debated almost as fervently and sometimes as irrationally, as religious topics. I did a stint in atmospheric chemistry as a post-doc but my scientific involvement with the subject was “limited” to fundamental research involving chemistry rather than climate change per se. However, recently I embarked upon doing some research on the topic and was struck by the large variety of opinions and uncertainties on virtually everything on the subject. I approached the subject with a view to gain an understanding on the “facts” or the “science”. At the end of it, I have come to the conclusion that the warm times we live in may actually be a blessing. Before you think I am completely crazy, let’s start at the beginning.

1) What is Global Warming?
Global warming refers to the rise in the average temperature of Earth’s atmosphere and oceans and its projected continuation. The warming is mainly attributed to human activities (or fancily called anthropogenic forcing). Concerns on the topic were raised by the Intergovernmental Panel on Climate Change (IPCC) in 1990 wherein it was stated that it is certain that emissions resulting from human activities are substantially increasing the atmospheric concentrations of the greenhouse gases, resulting on average in an additional warming of the Earth’s surface. The amount of warming is about 0.6 degree C on average.

2) What is the significant cause of global warming?
The recent warming observed since the 80′s is attributed to a very significant increase in greenhouse gases such as carbondioxide and methane. According to thermodynamics, the total energy flux from the sun reaching the earth should equal the energy flux radiated out by earth. However, in the presense of GHGs, some of the energy radiated by earth, is absorbed by these molecules and reemitted in all directions. So some of it comes back to the Earth thereby warming it. It logically follows that if the concentration of GHGs increase, warming should occur. However, where the picture gets fuzzy is when you ask the question “How much?”. There are so many parameters that affect Earth’s climate that it is mind boggling to extract the contribution of the Greenhouse effect in isolation.

3) Why is global warming bad?
Well, if you have you seen “An Inconvenient Truth” you might have shivered in horror like I did. The movie makes such an impact that it did not occur to me to doubt or question anything at that point. Coming back to the question, shrinking ice and rising sea levels are the foreseen direct impact of warming. Shrinking polar ice caps could impact polar bear population and rising sea levels could cause some damage. Now no one can actually predict how much the sea level can rise – that is a number that has huge error bars. But these are the basic consequences of warming. You can make it to be as bad as you want depending on your imagination and inaccuracies of computer models humans use to predict things they do not understand well.

4) What is the evidence for global warming?
Things begin to get interesting when you look for answers to this question. There are several things that are shown as evidence for global warming. The direct evidence should be rising temperatures of Earth’s atmosphere and oceans. One of the most well known climate scientists who has done a lot of work with historical temperature records is James Hansen from the NASA Goddard Institute for Space Studies. Hansen has published graphs of temperature recorded at various meteorological centers across the world as a function of time. He used a quantity known as the Global Surface Mean Temperature as an indicator of global warming. See the graph below:

Ref: http://www.columbia.edu/~jeh1/mailings/2007/20071210_GISTEMP.pdf

Hansen has published a few versions of this graph since 1987 and his work is widely accepted as the basis for global warming today. On the surface, the graph does indicate that the globe is warming. But is it? Let’s probe a bit deeper. Before we blindly accept anything we see, it is good scientific practice to question.

What does average global temperature mean and how is it measured?
Here’s my understanding on this (Ref: Hansen et al, http://pubs.giss.nasa.gov/docs/2001/2001_Hansen_etal.pdf). There is a global temperature record since 1850. Temperatures were recorded at several meteorological stations on land; satellite and ship measurements are available for sea temperatures. The daily maximum and minimum temperature recorded at a particular station are averaged to give the daily mean. The daily means are averaged over a month long period. The monthly average is then subtracted from a reference from the same set of stations – the reference is the average temperature from 1961 to 1990. The reference is the 0 on the y axis in the graph above. It is important to note that the temperatures recorded at different stations need to be compared apples to apples: for ex., were the temperatures at each station measured at the same time every day? It turns out that there are several things that bias the recorded temperature – read the paper for the gory details. The point is, such graphs are a far cry from the raw data coming out of the thermometers. Lots of assumptions are made, lengthy code is written and numbers are fed to a computer to generate the graph shown above. Maybe this is good but what does the quantity called Global Mean Temperature actually mean?
Let’s consider this scenario. Imagine that Earth has a well defined climate distribution and can be neatly divided into four climactic zones. These climactic zones are represented by Helsinki ( Finland), Sydney (Australia), Mumbai (India) and Columbus (Ohio, USA). Now assume that mean temperatures at these four cities were as follows in the month of January 2011 (the temperatures below are close to reality):
———————————————————————————–
City                                  Average Temp (deg F)
———————————————————————————–
Helsinki                                    35.5
Sydney                                    72
Mumbai                                   75
Columbus                               30
———————————————————————————–

So the global average temperature in January 2012 was 53.125 deg F.

Now, in January 2012, the mean temperatures at these four stations were:

———————————————————————————–
City                                  Average Temp (deg F)
———————————————————————————–
Helsinki                                  35.5
Sydney                                   72.5
Mumbai                                  75
Columbus                              30
———————————————————————————–

The mean temperature of the Earth is now 53.235 deg F. Does this mean that the Earth was warmer in Jan 2012 than in Jan 2011? I don’t think so. Basically one data point (Sydney) is skewing the picture. These are dangerous statistical play fields that although seem to be accepted, make me uncomfortable.

5) But let’s move on, what about Earth’s climate before 1850?

Now, it gets even more interesting. It turns out that we have a natural thermometer in age old ice cores. Gas molecules get trapped in ice cores and isotopes of common molecules found in the atmosphere can be dated to reconstruct the temperature back to several thousands of years in the past. (Ref: http://www.gps.caltech.edu/classes/ese148a/Petit_etal_1999.pdf). The concentration of these isotope molecules is dependent on the global temperature and thus the temperature can be reconstructed to several hundreds of thousands of years back in time. This temperature reconstruction is based upon the physical properties of these molecules so no adjusting of data is required. (There are a couple of assumptions that are made though – see the paper for details).

How does the concentration of isotope molecules depend on global temperature?
Let’s consider the water molecule. There are two isotopes of water, normal water with O(16) and water with heavier oxygen, O(18). As we all know from school chemistry, the natural abundance of O(16) is much higher than O(18) so it follows that the natural abundance of normal water in the oceans is much higher than water with O(18). Now glaciers and ice sheets are formed when water from the oceans evaporate and condense – the source of the ice is water from the oceans. Since normal water is lighter than water with O(18), it evaporates at a lower temperature. So if global temperatures a “low”, the concentration of O(18) water molecules in ice cores should be lower than if temperatures were higher. To be more precise, a decrease of one part per million of O(18) in ice reflects a 1.5°C drop in air temperature at the time it originally evaporated from the oceans. For more details on the science behind dating ice cores, see http://www.globalchange.umich.edu/globalchange1/current/lectures/kling/paleoclimate/index.html

Below is a graph of the reconstruction of temperature as a function of time at Vostok in Antarctica.

Ref: http://www.gps.caltech.edu/classes/ese148a/Petit_etal_1999.pdf
Now, this is interesting. The blue curve shows the variation of temperature as a function of time. The present is at 0 on the x axis and the graph goes out to 400,000 years into the past. This graph shows that the Earth’s climate is a pendulum swinging between temperate (or interglacials where life thrives) to glacial ice ages (when life comes to end). The reason for this oscillating nature of Earth’s climate is attributed to the peculiarities of Earth’s orbit around the sun. At certain positions, the earth receives a greater amount of solar energy and the periodicity of the ice core temperature data correlate closely with the quasi periodic variations in orbital eccentricity, obliquity and precession of Earth’s orbit. So this phenomenon is termed solar forcing. The ice core data does show correlation between the concentration of greenhouse gases and temperature. But it appears that the CO2 peaks come after the temperature peaks – in other words increased CO2 concentrations are the effect and not the cause of high temperatures

[References:

• Indermühle et al. (GRL, vol. 27, p. 735, 2000), who find that CO₂ lags behind the temperature by 1200±700 years, using Antarctic ice-cores between 60 and 20 kyr before present (see figure).
• Fischer et al. (Science, vol 283, p. 1712, 1999) reported a time lag 600±400 yr during early de-glacial changes in the last 3 glacial–interglacial transitions.
• Siegenthaler et al. (Science, vol. 310, p. 1313, 2005) find a best lag of 1900 years in the Antarctic data.
• Monnin et al. (Science vol 291, 112, 2001) find that the start of the CO₂ increase in the beginning of the last interglacial lagged the start of the temperature increase by 800 years. ]

The paper by Petit et al notes that the current interglacial (or Holocene) is a unique feature of Earth’s climate in the past 420,000 years because of it’s length and stability. The instrumental temperature record that we saw earlier exists for about 100 years – it is a mere blip in the big picture. Is the current warming just a part of the “normal” oscillating nature of Earth’s climate? If it is true that current greenhouse gas emissions are at a record high, will that amplify the warming?

Conclusion

After becoming a little educated on global warming, I have a healthy skepticism on whether it is caused by anthropogenic forcing or not. The high concentration of greenhouse gases might amplify the natural warming of Earth’s atmosphere and oceans but it is difficult to prove unambiguously because of the extreme complexity of Earth’s climate. Well, even if it does amplify the effect, going by the past record, the destruction of an ice age (that going by the past we are heading for in a few thousand years) is far more significant.

My skepticism does not indicate that I am OK with indiscriminate consumption of precious fossil fuels that end up in greenhouse gas emissions. That is a different aspect that should not mix with the science as then the science gets tainted with ideology. Let the debate continue by all means – with more science and less name calling, politics and ideology. Let us not forget that we can afford the luxury of a debate on this topic precisely because we live in warm times. For an excellent description of life as it blossomed and faded between ice ages, I strongly recommend chapter 27, Ice Time, of Bill Bryson’s “A Short History of Nearly Everything“.

Science Tuesday :: Beyond the solar system

Last week, we talked about the solar system. What lies beyond? When you look up at the sky on a clear night, you can see a few thousand stars (if you were patient enough to count). A whole new world opened up with the invention of the telescope by Galileo. When Galileo pointed the telescope up to up to the sky in 1609, he was shocked to find a whole new and enormous population of stars that were previously unknown. These stars are what make up what we now know as the Milky Way. To the naked eye, the Milky Way appears to be a wisp of foggy light (hence the name). The Milky Way was called the Galaxy which is Greek for milk.

The English astronomer, William Herschel, was the first to try and estimate the size of the Milky Way. Herschel actually counted the number of stars in various spots in the Milky Way and concluded that there are about 100 million stars in the galaxy. Herschel also suggested that the stars in the Milky Way were arranged in a certain way – like a disc with a bulge in the middle  (like a frisbee with a bulge in the center).

Photo credit: http://www.astro.keele.ac.uk/workx/milkyway/page.html

Note that in the picture above, the size of the Milky Way is shown in light years. More on that later. Also, the sizes shown are what we know them to be today. It took mankind a very long time to get to these numbers – about two centuries to be specific. Below is an actual photograph of the Milky Way as seen from earth.

Photo credit: http://www.gigagalaxyzoom.org/B.html

Herschel used a well known physical law of brightness to estimate the size of the galaxy. This law is called the inverse square law and says that the brightness of a star is inversely proportional to the square of it’s distance from earth. If that did not make sense, here is the long explanation. Consider two stars, A and B. If A is four times as bright as B, then A is at half the distance of B to earth.

By Herschel’s time, astronomers had used the parallax method to determine the distance of some of the nearest, brightest stars from earth. By measuring the brightness of stars in the Milky Way relative to the bright star Sirius, Herschel proposed that the diameter of the Milky Way is about 850 times the distance between earth and Sirius and that its thickness was 155 times that distance. The distance between earth and Sirius is 8.8 light years, so according to Herschel, the galaxy was 7500 light years in diameter and 1300 light years thick. There’s that term light year again. This is a term we will see again and again as we continue our journey farther and farther away from the earth. As distances become larger and larger, the number of zeroes you need to add if you measure in miles becomes so many that it gets overwhelming. So astronomers introduced a new measuring unit – a light year. One light year is the distance light travels in one year. Light travels at the speed of 186000 miles per second. So one light year is about 5878 billion miles. So 7500 light years is about 44 million billion miles – you see the problem with measuring in miles?

As you can see, Herschel’s estimate was not very accurate mainly because of the crude method of determining the brightness of stars at that time. There were no instruments to measure the amount of light emitted by a star at that time. The estimate of the size of the milky way was refined by an astronomer named Kapteyn. The invention of the camera enabled Kapteyn to measure the brightness of stars with better accuracy. Kapteyn proposed that the size of the galaxy was 4 times wider and 5 times thicker than that proposed by Herschel, i.e. a diameter of 30000 light years and a diameter of 6500 light years. Kapteyn’s estimate again was not very accurate due to inaccuracies in measuring star brightness but was a step in the right direction.

Thus remained the state of affairs until a breakthrough came about via an excellent observation made by one of the earliest woman contributors to science. In 1912, Henrietta Leavitt made an observation from a lot of astonomical photographs that would allow astronomers to accurately measure a star’s brightness. This discovery opened new doors to astronomers to discover the nature of the universe. At this point, things start to get a bit complicated – more next week,

Science Tuesday :: The size of the solar system

Photo Credit: universetoday.com

It’s time to move on from earth and the moon to what lies beyond, our solar system. One of the questions I was asked by my daughter was “How were planets discovered?” As you probably know, many planets are visible to the naked eye – Mercury, Venus, Mars, Jupiter, and Saturn to be specific. Venus and Jupiter in particular, are very bright and easy to spot. Hence, these planets were known to mankind since very early times. So how are planets different from stars to an observer who knows nothing about either? One important feature of a planet is that it moves in the sky relative to other objects (or stars). This is the reason they were called planets which means “wanderer” in Greek. Stars on the other hand, appear to move much less in the sky.

The very early astronomers had studied the motions of the planets and observed that just like the sun and moon, they generally move from west to east relative to the stars. This motion is not to be confused with the rising and setting of bodies – the sun rises in the east and sets in the west. What we are talking about here is if you observe a planet, say Mars night after night, it will appear to be moving from west to east with respect to the background stars (that don’t move so much as they are very much further away). They also observed that Mercury was the fastest, followed by Venus, Mars, Jupiter, and Saturn. Planetary motion was however, a bit different from the motion of the sun and moon in that sometimes, the direction would mysteriously reverse and the planet would move east to west relative to the stars for some time before turning around again and resuming the west to east motion. This was one of the most confounding observations that took several years to explain. This so-called retrograde motion of planets was one important piece of evidence for the now well-known heliocentric model of the solar system – i.e. the planets orbit the sun at different speeds. To see an excellent illustration of retrograde motion, see the video below:

Observe the motion of Mars relative to the stars and what happens when earth overtakes it. What is happening here is that Mars orbits the sun at a speed which is less than that of the earth on average. So at some point, the earth will overtake Mars and from earth’s point of view, Mars will now appear to have reversed direction.

One of the properties of planetary motion is called the orbital period. If you track the motion of a planet based upon its location relative to a star, then the orbital period is the time taken for the planet to move across the sky and come back to the same position as it was when you first started tracking it. We now know  that the orbital period of earth is 365 days (what we know as 1 year). One of the greatest observers of heavenly bodies was a man called Tycho Brahe. Brahe spent years meticulously observing and recording details of planetary motion. In particular, the motion of the planet Mars was studied in great detail. Such detailed observations of planetary motion and their orbital periods were a big stepping stone in discovering the scale of the solar system. A German astronomer named Johannes Kepler studied Brahe’s detailed planetary observations for several years. Kepler’s efforts resulted in one of the biggest breakthroughs in understanding the universe. Kepler proposed three laws that govern planetary motion that cracked open the mystery of the planets:

1) Planetary orbits are not circles but ellipses as was thought at that time. An ellipse is an oval that has some specific mathematical properties. Contrary to what is tempting to believe, the sun is not in the center of the planetary orbits but rather off a bit to the side. This law was based purely on the planetary observations of Brahe. Kepler plotted the orbit of Mars and found to his surprise that it was an oval.

2) A line connecting the sun to the planet sweeps out equal areas in equal times. This means that if the planet is closer to the sun, it moves faster than when it is further away from the sun. Again, this was very surprising – it is easier to imagine planets orbiting the sun at the same speed throughout than at a varying speed. The 2nd law was the consequence of a great number of calculations required to explain Mars’ strange motion. The planet did not seem to move at a constant speed – and as we already saw above, also apparently reverses gear and shoots off in the opposite direction some times. Kepler spent several years figuring this out and is famously known to have referred to this phase in his career as his “war with Mars”.

3) Using the first two laws, Kepler derived the third -

T² = kR³

where T is the orbital period and R is the average distance of the planet from the sun and k is a constant. The orbital periods of the the five then known planes were observed to be as given in the table below:

————————————————–

Planet               Orbital period (Days)

————————————————–

Mercury                    87.97

Venus                     224.7

Earth                     365.25

Mars                      686.97

Jupiter                  4332.82

Saturn                 10755.7

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Now if you could figure out the average distance of  just one planet from the sun, you could find them all:

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Planet               Relative average distance from sun

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Mercury                                0.387 AU

Venus                                  0.723 AU

Earth                                   1.000 AU

Mars                                    1.523 AU

Jupiter                                 5.203 AU

Saturn                                 9.539 AU

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In the table above, 1 AU represents the average earth-sun distance.

Unfortunately, Kepler did not enjoy the satisfaction of cracking the size of the solar system himself. This was not achieved until 1672 by astronomer Giovanni Cassini. By Cassini’s time, another clever method of measuring distances had been discovered, the parallax method.

Parallax is essential the result of an optical illusion: close one eye and align your thumb to a background object, say a door knob, or a mark on the wall. Now, close the other eye and observe the position of your thumb relative to the doorknob – it has now shifted! Your thumb has not moved in reality but appears to have because your point of view has changed. The same principle can be applied to heavenly bodies. Below is an illustration of the experiment to observe the parallax of Mars.

Photo credit: astronomyforbeginners.com

By doing some complicated math, you can figure out the distance between Paris and Mars – the distance PM in the figure above. This Earth-Mars (or Paris-Mars) minimum distance was calculated to be 46,800,000 miles. We can turn to our friend, geometry, to figure out the Earth – Sun distance.

The above experiment was done when Mars was at its closest distance to the earth. This implied a configuration where the sun, earth, and Mars lined up almost in a straight line in that order from left to right. So we can then write the Earth-Mars distance as the Mars – sun distance minus the earth – sun distance. From the orbital period table above, T (Mars) / T (earth) = 1.88. Now, we apply Kepler’s 3rd law and find that (1.88)² = [R_Mars-Sun / R_Earth-Sun ]³ .

You can rewrite the Mars-sun distance in terms of the Earth-sun distance: (1.88)²  = [(R_Earth-Sun + R_Earth-Mars ) / R_Earth-Sun ]³ . This yields the Earth – Sun distance to be 93,000,000 miles, which is 93 million miles. This is huge (in number and in importance) - in an instant (compared to how long it took to figure things up to now), we can calculate the scale of the solar system. Neptune is 2.77 billion miles from the sun. To put that in perspective, if you wanted to fly to Neptune in an airplane, it would take you over 550 years! And the solar system does not even stop there.

Next week, we will talk about what lies beyond our solar system on our quest to finding out the size of the universe. What is a galaxy? How were they discovered? How far are some galaxies from earth? Until then, ponder the fact that our solar system is on the order of a few billion miles in size – it’s BIG!

Science Tuesday :: Baby steps in determining the scale of the universe

Last week we talked about what the universe is made of. Today we take a little detour into the science of measurements in order to get to the larger question : what is the size of the universe? As it turns out, it took several centuries for mankind to figure out the size of the solar system, which is a baby step in figuring out the answer.

Let’s start with relatively simple methods that were devised by creative people to measure astronomical distances. Ever wonder what the size of the earth is? Back in 240BC, a Greek scholar named Eratosthenes, figured out an ingenious and simple way to get the answer. It was known that at exactly the same time of day, the sun was directly overhead in a city called Syene in Egypt, but it was not quite so in the city of Alexandria (where Eratosthenes was from). Because of this, a vertical object had a shadow in Alexandria but did not in Syene. Syene was about 500 miles south of Alexandria. Eratosthenes figured out that this observation implied that the earth was not flat but curved. Then Eratosthenes used simple geometry to figure out the size of the earth. Below is an illustration of his reasoning:

All Eratosthenes had to do was figure out the sun-angle in the diagram to calculate the circumference of the earth (the yellow lines are rays from the sun). This angle can be determined by knowing the height of the vertical object producing the shadow and the length of the shadow itself: tan (sun angle) = length of shadow / height of object. This resulted in a value of 7.5 degrees for the sun angle at Alexandria.

Assuming that the earth is a sphere and knowing the distance between the two cities, we can now calculate the circumference of the earth thus:

If you draw a line from the center of the sphere to any point on the surface (called the radius), and sweep it one full rotation about the center (like rotating the minute needle on a clock from 12 back to 12) , the radius sweeps out 360 degrees. In other words, we can represent the circumference as an angle of 360 degrees. Eratosthenes had found that 7.5 degrees corresponds to 500 miles. So 360 degrees must correspond to 360*500 / 7.5 = 24000 miles. This is astonishingly close to what we know today: 24,901.55 miles.

The next step to measuring astronomical distances was measuring the distance between the earth and it’s closest heavenly neighbor, the moon. This was accomplished by another Greek scholar named Aristarchus who was probably a contemporary of Eratosthenes. Back in the day when there was no TV, computers or other forms of entertainment, people probably found the night sky with its myriad objects a big source of entertainment and curiosity. It is amazing that Aristarchus figured out the distance between the earth and moon just by observing a lunar eclipse.

Aristarchus had figured out a couple of things based on some observations: the fact that there are lunar eclipses implies that the moon orbits the earth. In particular, the earth’s shadow is cast on the moon during the eclipse.  To read how a lunar eclipse occurs, click here. Aristarchus observed that the time taken between the event of the moon just entering the earth’s shadow and just emerging out of it is about 3 hours. From this he concluded that the moon is smaller than the earth. He also observed and must have carefully drawn to scale, the curve of the shadow of the earth during an eclipse (as shown in the photograph above). Now if you simply take the dark curve on the 3rd image of the moon in the photograph above and complete a circle, that gives you the size of the earth’s shadow. Aristarchus assumed (correctly) that the size of the shadow is close enough to the size of the earth because the sun is very far away from the earth. Now he knew from this simple exercise that the earth is about three times the size of the moon. (You can measure this yourself using the photograph above – trace the moon and shadow and complete the moon and shadow circles. Now draw a line to cut each circle in half and measure them. I get about 1.3cm for the moon and 3.5cm for the shadow indicating that the earth is about 2.7 times larger than the moon). In order to calculate the distance between the earth and the moon, Aristarchus used his knowledge of the angular size of the moon. Angular size is a fancy term for how big an astronomical object appears to someone on earth. On a full moon night, you can measure this yourself as follows: extend your arm and hold up your pinky (or whatever finger is big enough) such that your finger eclipses the moon. Then measure the length of your arm, all the way from your chin down to your fingertips, and the width of your pinky. The ratio of the width of your pinky to that of your arm is the angular size of the moon. So in my case, the length of my arm is about 75cm and the width of my pinky is 1cm. So I get the angular size of the moon to be about 0.013 radians which is 0.7 degree. (In actuality, the angular size of the moon is 0.5 degree or 0.01 radians). Now we return to geometry to get the answer:

In the figure above, theta is 0.013 radians (let’s use our highly approximate measurements), r is the distance between the earth and moon, and d is the diameter of the moon. In the limit of small theta, we have: tan(theta/2) = (theta/2) = d/2r, yielding r = diameter of earth / (2.7*theta), or r = 28*diameter of earth. Aristarchus knew that the diameter of the earth was 7636 miles thanks to Eratosthenes. So we have the distance between the earth and moon as 213818 miles. The correct answer as we know today is 238857 miles, so we are off by only about 10%. Aristarchus’ simple approach and our very approximate methods yield an astonishingly close answer.

Simple methods such as these were the first steps in mankind’s journey to understand the scale of the universe. Aristarchus attempted to find the distance between the earth and sun using simple geometric methods and figured out that the sun is atleast seven times as large as the earth. So logically, it made sense that the earth (the smaller body) was orbiting the sun (larger body) than the opposite belief that was prevalent at that time. However, due to the lack of accurate instruments required to measure small angles, Aristarchus was quite a bit off in his measurements.

Next week, we will fast forward several centuries to the early 17th century AD when a couple of breakthroughs came about that would crack open the scale of the solar system. The first breakthrough was the development of one of the more accurate theories of planetary motion – i.e. rules that define the motion of a planet around the sun. This theory was proposed by astronomer Johannes Kepler and showed that all the distances in the solar system were linked to each other. In other words, if you knew one distance (say that between the earth and the sun) you would immediately know the distance between every other planet and the sun! However, no such distance was known during that time until the second breakthrough came about that would yield the distance between Mars and the sun. With this measurement, the scale of the solar system was finally no longer a mystery.

Science Tuesday :: What is the universe made of?

My older daughter is asking me a lot of questions about the world – how did it come into existance? How were planets formed? How did we (humans) come to being? These questions have made me think beyond the boundaries of everyday life as I attempt to answer her questions. They have also made me realize how woefully inadequate my education was when I was her age. I cannot think of a single book or person who inspired me to wonder about these things. I am also ecstatic that she has gone beyond the iGadget disease and finds something other than a flickering LCD screen fascinating. Every week, I will attempt to answer a question that I have been asked by curious minds about the world we live in and the vastness beyond. The idea is to get to the basics so a child can understand them.

So without ado, let us begin. How did the universe come to being? Before we answer that question properly, we need to understand what the universe, as we know it today, is made of.

What is the universe made of?

http://www.universe-galaxies-stars.com/Universe.html

Close your eyes and let your imagination run wild.  Our solar system, a lot of stars that you can see on a clear night? How about more planets? How many stars and planets are there? It turns out that there are a lot of stars in the universe, an unimaginably large number. To begin to answer this question, let’s start with a galaxy. We know that lots and lots of stars make a galaxy, a hundred billion stars to be more precise. That’s 100000000000 stars in a galaxy. How many galxies are there in the universe? At least 100 billion! That is to say there are as many galaxies as there are stars in a given galaxy. So the total number of stars is at least 10000000000000000000000 – or 10 billion trillion!!! What about planets? It was  estimated by the famous cosmologist, Carl Sagan, that there are about 10 billion trillion planets in the universe. Our solar system with it’s eight planets is ridiculously small when compared to to the grand scale of the universe.

How do we know this? It is impossible to “see” every star and planet in the universe. It is possible to see but a teeny tiny slice of of the universe at a given time using powerful telescopes. Here’s how the astronomers figure out how many planets and stars there are. Imagine that you took a few fistfuls of sugar and scattered the grains across the floor of your room such that the floor was covered with a fine layer of the sugar. Finding out how many stars there are in the universe is like finding out how many grains of sugar are on your floor. A relatively quick way to do it would be to count how many grains there are in a 1×1 foot square. Now if your room was 10 x 10 feet square, you would simply multiply the number of grains in the 1×1 square by 100 to estimate the total number of grains of sugar on the floor.

A telescope can be used to take a snapshot of a tiny sliver of the universe. Astronomers estimated that there are about a few thousand galaxies in one such snapshot taken by the  Hubble telescope. If we know the size of the universe, we can estimate the number of galaxies.  More about the size of the universe next week. We can use a similar method to estimate the number of stars in a galaxy.

What else exists in the universe? We know that earth has a companion, the moon. Jupiter has 63 moons. There are about 170 moons in our Solar System. Then there is a lot of gas and rock that makes up what is called the intergalactic space, or the space between galaxies. Now, here’s a funny thing – the word space has a very different meaning when you talk about outer “space”. What is space? Nothing, right? Wrong! Brace yourself for this: all the billions of stars and planets, gas, rocks, moons etc. that we talked about makes up a measly 5% of the stuff of the universe. That is, if the universe were to fit in your room, the planets and stars would occupy a couple of drawers in your closet. The rest of the space in your room is a mysterious “thing” that you cannot see. Hence it is called dark matter and dark energy. Scientists know very little about the dark stuff of the universe. They predicted that it must exist to explain some very strange goings on that we will talk about later.

So to wrap up, here is the composition of the universe, as we know it today.