Plan E- E for ‘Education’!

  • Swetha Srinivasan

Guidance of Tafheem Masudi and Sukant Khurana

‘Education is the passport to the future, for tomorrow belongs to those who prepare for it today’

Picture Courtesy: The Guradian

Education is the most important gift a person can ever receive, its that which stays with you for life. Education must be such that you enjoy the process of learning. Learning can be made fun and interesting via a number of techniques, all that’s needed is enthusiasm and passion. Coming specifically to complex space related topics, and conveying such content to the students, a new teaching-learning methodology must be followed, a more structured one. It will make the process easier, and uniform. The following methodology will be ideal and comprehensive-

Plan E! E for Experiments, Explanations, Effects, Extension of the idea and Educational tours.

Here are some examples of how the methodology can be put to use.

1. The Expanding Universe


Albert Einstein assumed that the universe had similar properties throughout; he assumed a static, steady-state universe. But when he applied the General Theory of Relativity to such a model, he found that space-time would have to curve in on itself, which would cause matter to move and shrink under gravity, violating the static universe assumption. To overcome this, Einstein added a cosmological constant to his equation, a mysterious cosmic repulsion force.

Albert Einstein Picture Courtesy:

But Edwin Hubble, in 1929, made a remarkable discovery. He observed that light from other galaxies seemed to be red-shifted, due to Doppler Effect, meaning that they were moving away from us. After analyzing more such red-shifts from Cepheids, he came to the conclusion that everything was rapidly moving away from everything else, the Expanding Universe theory came into place. Einstein was forced into giving up his static-universe assumption, calling the cosmological constant the ‘biggest blunder’ of his life. Even the best of minds sometimes errs (


Take an uninflated balloon, let the color be white or any other light color for clarity. Ask a student to come forth, use a marker to mark some dots on the balloon. Ensure that a few spots are such that they are very close to each other. The spots represent galaxies. The balloon itself represents the universe.

Now, inflate the balloon using a pump. And ask the students to observe what happens as the balloon expands.


As the balloon expands, the spots move away from each other. And the expansion is such that the galaxies move away from each other, not from some central point. The space between the spots seems to increase as the spots move away. This is the basic idea of the expanding universe. What’s more is that this expansion is not something we are able to observe in our immediate surroundings or even within our Solar System. This can be explained by observing the few spots that have been deliberately placed close to each other. The space between the two doesn’t really increase much, there wasn’t much distance between them to begin with. That’s why we can’t experience it, the objects within our galaxy are tied down by strong gravitational attractions. The force of gravity varies as the inverse square of distance, this means that greater the distance between two objects, lesser is the gravitational force and hence more evident will be the expansion. More far apart the dots are, the faster and farther they move apart. Now we are talking on astronomical scales here, and in such context, the distance between objects within a galaxy isn’t as much as the distances between galaxies themselves and compared to all this, the distance between planets within our Solar System is minuscule, the planets also being held tightly by the Sun. Thus, we don’t see this in day to day life around us, but we do have loads of evidence to prove this fact in the universe.

Extension of the idea:

Scientists have further come up with the theory of Inflation, to explain what happened just after the ‘Big Bang. Further extrapolation resulted in the Multiverse theory, a theory under work currently though, strongly supported by other lines of research including dark energy and string theory. If that is true, ours is not the only universe. Students can be encouraged to read it, if interested.

Picture Courtesy: Forbes

Imagine the dots on the balloons to be universes themselves. As the balloon is inflated, the universes move away from each other, the space between two universes increase. But here, the case isn’t very simple. These Universes are called bubble or pocket universes, ours is one among them. Alex Vilenkin, a cosmologist at Tufts University in Massachusetts, explained that because “the space between these bubble or pocket universes is expanding very fast, room is being made for new bubbles to form, so there will be an unlimited number of pocket universes formed in the course of inflation.” (

Picture courtesy: NBC News


Hubble provided an equation for the expanding universe. v= Hod, where v is the speed at which a galaxy moves away from us, and d is its distance. The constant of proportionality Ho is now called the Hubble constant (

The Hubble’s constant is of very high importance. Using this, various parameters have been measured. One such parameter is the age of the Universe.

The age of the Universe, t, can be approximated by the inverse (or reciprocal) of the Hubble constant H0:

t = 1/H0

Future effects of the expanding universe can be multiple, since we are debating how the Universe might end — ‘Cold death’ and ‘Big Crunch’ being popular ones. If the expansion will continue, then there will a point when our galaxy becomes totally isolated, when we cannot even see other galaxies at all. Now, that’s a grim prospect.

2. Space-time warping


Initially, Cartesian coordinates seemed most naturally adapted for our universe. Time was considered to be independent of space. Within a separately conceived space and time, from the possible states of motion one could not find an absolute state of rest. Hermann Minkowski described the Minkowski Universe where the time coordinate of one coordinate system depends on the time and space coordinates of another relatively moving system. Every event is described as ‘here-now’ points. An alteration of this geometry is used in Einstein’s general theory of relativity. Thus, came about the fabric of space-time (

General Relativity was a major intellectual revolution that has transformed the way we think about the universe. It is a theory, not only of curved space, but of curved or warped time as well. Einstein had realized in 1905, that space and time, are intimately connected with each other. One can describe the location of an event by four numbers. (Professor Stephen Hawking)

In his 1915 paper, Einstein showed that the effects of gravity could be described, by supposing that space-time was warped or distorted, by the matter and energy in it. Here, gravity itself is the warping of space-time.

Picture Courtesy: BBC


Take a big rubber sheet and stretch it around a circular frame. Ask a few students to hold up the frame. Now place a small marble on the sheet. Then remove the marble and replace it with a heavier ball. Now place another similar ball in another part of the sheet and observe what happens. Now, remove the second ball and place a marble instead. Observe.


Here, the rubber sheet represents the fabric of space-time. The marbles and the massive balls represent space-objects of varied masses. When a small marble is placed on it, there is a small depression around the marble, not much. When a more massive object is placed, there is a significant warping of the sheet around it. When two similar mass objects are placed on the sheet, it is observed that warping occurs around both the masses, and they move towards each other, attracted. Thus, it is this warping that causes attraction- more commonly known as gravity. When a marble and a massive object are kept on the sheet, the massive ball hardly moves while the marble moves towards the massive ball. This is the basic idea of space-time warping (

In the words of John Wheeler, “Matter tells space how to curve, the curved space tells the matter how to move”.

Extension of the idea:

Now, consider the mass to be huge, so huge that the gravitational well is very deep; it can be considered bottomless. What do we get then? Every object nearing that hole falls in and can never come out. Voila, we’ve got a blackhole. A black hole will be a bottomless hole in the fabric of space-time.

One of the most interesting discussions on space-time is regarding wormholes. Though a very far-fetched idea for now, it is theoretically valid and maybe super-advanced civilizations in the future may figure out a way to make the idea feasible. The idea behind wormholes is this, what if we can warp space-time so much that a small tube or wormhole is created? This would connect any two parts of space, maybe one end of the galaxy to another, and you could travel through it and come back in a jiffy. You could even manage to travel back in time with a single wormhole, if its two ends were moving relative to each other (Professor Stephen Hawking). However, to create such structures, space-time needs to warp in the direction opposite to the direction in which it normally warps, and that requires different kinds of matter and energy. Students can read up more about wormholes if interested.

Picture Courtesy: Daily Express


We can actually observe this warping of space-time, produced by the mass of the Sun, in the slight bending of light or radio waves, passing close to the Sun. The result of this is a slight shift in the apparent position of the star or radio source, when the Sun is between the Earth and the source.

3. Measurement of astronomical distances


The transit of Venus played a key role in the history of astrometry. In 1663, James Gregory, a Scottish mathematician and astronomer proposed a method to calculate the Sun’s mean equatorial parallax. It involved timing the movement of Venus across the Sun from two points that are widely separated on the Earth and using the differential. Using triangulation, the Sun’s distance from the Earth could be calculated. Knowing the distance from the Earth to the Sun, we can then figure out the distances of some stars (


This would be a small demonstration in an open field or ground. One student (say, A) must be asked to stand at a point, he/she represents the Sun. Now, draw a circle of about two feet radius around A and mark two points, one to the left of A and one to the right of A on the circle. Another student B will stand on one of these points, he/she represents the Earth. Connect the two points and draw a line segment, call it ‘c’. Draw another line on the ground, perpendicular the previous line and starting at the point of the Sun and ending at a point a suitable distance away, call it ‘d’. A student D at this end point will represent the source. Finally connect the two points on the circle to the source point and call the lines ‘a’ and ‘b’. Now, a person on Earth observes the source at a particular time of the year, the angle made by the lines ‘a’ and ‘d’ is recorded (via equipment) as α. B will now move to the opposite point (in reality, this will take 6 months), then the angle between lines ‘b’ and ‘d’ is recorded as β. α + β = p is the parallax angle, the distance ‘d’ can be measured using basic trigonometry.


The above technique forms the basic principle of measuring distances using the Parallax method. Astronomers use parallax to measure distances to nearby stars. Parallax is the apparent displacement of an object because of a change in the observer’s point of view. In the above activity, the distance between the Earth and Sun are known, and so is the parallax angle.

There is a simple relationship between a star’s distance and its parallax angle:

d = 1/p

The distance d is measured in parsecs and the parallax angle p is measured in arcseconds (

Picture Courtesy: Las Cumbres Observatory

Extension of the idea:

This technique is good for nearby stars, but for stars that are very far away, this method isn’t very accurate as the apparent shift becomes too small and the errors too large. Then, we use Cepheid Variable stars as stellar candles and yardsticks. Distances to them have been accurately found by the Hubble Space Telescope. Their brightness has also been recorded.

The apparent brightness of a light source varies inversely as the square of its distance. In other words, if the distance between an observer and a light source is doubled, the light source will appear four times as faint to the observer.

So, all we need to know is the brightness of any star. Using the inverse square law, distances to any star can be determined to a good approximation.

Another interesting topic to read about would be about Hipparcos. Launched in August 1989 Hipparcos was a pioneering space experiment dedicated to the precise measurement of the positions, parallaxes and proper motions of the stars, from 1989 to 1993. Turning slowly on its axis, the spacecraft repeatedly scanned the sky on different inclinations. Measuring angles between stars that were widely separated and recording their brightness (which varied visit to visit), lots of valuable information was collected. Each star selected for study was visited about 100 times over four years (ESA).

Hipparcos h Picture Courtesy: ESA


Using this basic technique in tandem with more advanced methods, we have calibrated Cepheid variables, we have calculated distances to various stars in space which have played huge roles in stellar studies, explanations for different phenomenon and will be of invaluable use if we ever plan on sending space vehicles to far off stars or galaxies in the future.

Thus, we can employ this method to convey complex topics to students in an interesting manner. Everyone loves a story, so the history of the innovation/discovery will be a great start. Next comes the experiment, it should be done without revealing too much about the idea, the big reveal comes in the explanation where the students grasp the idea. Then, the extension of the idea provides them with the additional knowledge to understand the magnitude of the concept, and to spark their interest. Self-reading out of interest outside the classroom is key to good learning practices. Explanation of the effects make the students understand the relevance of the concept in everyday life. This is a wholesome technique which can be customized according to the need of the teacher and student.

In addition to these techniques, educational tours must be undertaken. The goal of education is to impart knowledge and ignite the fire of learning within the student’s minds. For students to dig deeper into the subject, learn more out of interest, just classroom learning will not be enough. By seeing devices, equipment and phenomena in real life, outside the confines of books and videos, is what will ensure complete understanding and retention of knowledge. Taking students out on trips will relate to what they study better. Moreover, it is also essential for building essential life skills like teamwork, cooperation, adjustment etc. It will also provide them an opportunity to relax and enjoy.

While organizing such tours, teachers must themselves be fully aware of what the place holds, its history, importance and must be able to convey the science behind the structures with pomp, zeal and passion, such that the students get interested.

It’s about time we started working, time is ticking away and we must make the most of it.

Picture Courtesy: Franchise India