About Gravity and How it Affects the Universe

 About Gravity and How it Affects the Universe

The force that organizes the universe is gravity. There are four fundamental forces in nature: of these the strong and weak forces act only over short distances; the electromagnetic force can act over great distances, but because there exist positive and negative charges, whose influences tend to cancel each other out, it is effectively insignificant over long distances. This leaves only the gravitational force. Everything in the universe exerts gravitational force and is susceptible to it. As a result, the only force that matters on the scale of the universe is gravity.

  The Heights of Mountains and the Shapes of Asteroids and Planets

Most of the major objects in the solar system the sun, the planets, and the satellites are spherical. There is, however, a group of objects that are not – the asteroids. Why are planets spherical whereas the asteroids are not? This has to do with their mass and size.  

Any fluid agglomeration of matter tends to be spherical, because that is its lowest-energy configuration. This is why bubbles and drops of water are spherical. Solid matter that we encounter in everyday life remains non-spherical because of strong inter-molecular bonds that cannot easily be deformed. When the deforming forces are strong enough, however, these bonds can break, making solids fluid-like. One consequence of this is that a mountain on a planet has a maximum possible height. If it exceeds this height, then its weight causes the molecular bonds at the bottom to deform and break, making the mountain sink into the planet.  

On Earth, this maximum height is about 10 km.  On smaller planets this maximum height is greater and on larger planets it is smaller. Thus the larger an object, the more perfectly spherical it tends to be.  On the  other hand,  if the  the object is  small enough, the “mountains” may become comparable in size to the object itself – then the object is effectively non-spherical; this is what happens in asteroids. 

The Sun and Other Stars

The star is in some sense the fundamental constituent of the universe. Stars are formed in clouds of molecular hydrogen. When a portion of a cloud reaches a certain density its own gravitational force causes it to collapse. As it collapses, its temperature increases. Ultimately, the temperature at the centre of the collapsing object becomes high enough for hydrogen fusion to occur. This in turn causes an outward pressure that, when it is balanced by gravity, produces a stable object called a star. 

Because the amount of fuel available for fusion is finite, every star has a finite lifetime, during which it remains more or less stable. How long a star lasts depends on its mass. The larger the star the shorter its lifetime!  The largest stars, which have masses a few tens of times that of the Sun, have lifetimes of the order of a few tens of millions of years. The Sun, on the other hand, as a medium-mass star, has a lifetime of about 15 billion years; one-third of its life is over. And the smallest stars, with masses about a tenth that of the Sun, have lifetimes of hundreds of billions of years. 

The end of the life of a star can be quiet or very dramatic. The smallest stars just quietly burn out. A medium-mass star expands into red giant towards the end of their life; when our Sun becomes a red giant its outer surface will swallow Mercury. Then the outer part is sloughed off as a planetary nebula while the core becomes a white dwarf. A large star undergoes a dramatic implosion followed by an explosion called a supernova, which is one of the most dramatic events in the universe; a single supernova blast can produce more light than hundred or billions of stars.

Because of the very different lifetimes of small and large stars,  a molecular cloud,  in which stars of all masses are formed, is simultaneously a nursery and a cemetery: while the smaller stars in it are still in the earliest stages of formation the larger stars are already dying.

 The Planets Around the Sun

When a portion of a molecular cloud collapses to form a star, in the initial stages the spherical core is accompanied by an equatorial disk of material (rather like the rings of Saturn). This happens because a cloud of gas typically rotates and thus has angular momentum. As it collapses, to conserve angular momentum it rotates faster, leading to the formation of a disk. Different portions of the disk then fragment and coalesce to form planets. This picture of planet formation explains why the planets all revolve in the same direction around the Sun and more or less in a plane.

As is well known, each planet revolves around the Sun in an elliptical orbit, with the the Sun at one focus. In fact the ellipticity of the orbit is very small for every planet other than Mercury – the orbits are effectively circular.

(In the theory of orbital motion we have described so far we have pretended that the Sun is stationary and unaffected by the motion of the planets. Of course that cannot be true.  If you think of a star and a single planet as a closed system, it is obvious that, because of conservation of momentum, the motion the planet must cause some compensatory motion in the star. It is very small, much smaller than the size of the star, but with modern technology one can detect this motion. It is this idea that has led to the discovery of extra-solar planets.)

As mentioned above, the planetary orbits are only slightly different from the circular. A beautiful and useful way to think of an orbit that is a slight modification of a circular orbit is as a combination of a circular orbit and a radial oscillation. A moment’s reflection will show that if the frequency of radial oscillation agrees exactly with that of the circular motion, then what we will get a figure that is very close to an offset ellipse, i.e. an ellipse with the Sun at one focus. It turns out that the agreement between the frequencies of radial oscillation and circular motion that causes the orbits to be closed ellipses is also a characteristic of a concentrated spherical mass distribution like the Sun. (By closed we mean an orbit that retraces itself repeatedly.)

The orbit of each planet would be perfectly elliptical and closed only if it is the only one orbiting the Sun. But each planet in the solar system experiences the gravitational force of the other planets as well. As a result, the orbits are not perfectly elliptical, and instead of being closed they precess. (These effects were too small to have been detected in the age of Tycho Brahe and Johannes Kepler.)

We say that the orbits undergo perturbations due to the other planets. These perturbations can be calculated using Newton’s laws of motion and his law of gravity. By the the middle of the 19th century the theory of perturbations of planetary orbits was so well understood that any deviation from any of its predictions warranted a search for a cause.

At that time the perturbations of the orbit of Uranus were not completely explained by planets then known to exist. By studying these  perturbations  two  astronomers,  Urbain  Le  Verrier  and John Couch Adams, predicted the existence of another planet in the neighborhood.   So precise were the calculations that the position of the unseen planet was predicted very precisely. Follow-up observations by Johann Gottfried Galle led to the detection of a new planet, later named Neptune. The prediction and discovery of Neptune was one of the great moments in the history of science, especially of Newton’s theories of motion and gravity.

 Einstein’s Theory of Gravity

 The Orbit of Mercury

One planet other than Uranus, it turns out, had perturbations in its orbit that could not be com- pletely explained by the known planets. Urbain Le Verrier, after his success in predicting Neptune, was convinced that another unknown planet was responsible for the residual perturbations of Mer- cury.  The truth was far more extraordinary.  Albert Einstein presented in 1911 a new theory of gravity called the General Theory of  Relativity    in  which it  was  not a  force  but the  result  of the curvature of space-time. Within the framework of this theory the orbits of the planets suffer an additional precession beyond that due to the other planets. The predicted precession due to Einstein’s theory was exactly equal to the residual perturbation seen in Mercury.

 Black Holes

One of the strangest predictions of Einstein’s theory of gravity is the black hole. A black hole is an object whose gravitational field is so strong that the escape velocity from it exceeds the speed of light. Black holes are expected to form when very large stars die.  The gravitational waves that have been observed were from the coalescence of such stellar black holes.

Another region in which black holes are thought to exist are the centres of galaxies. The best evidence we have of this is the motion of stars near the centre of our own galaxy, the Milky Way. As explained earlier, the motion of planets around a star tells us about its mass. In the same way, the motion of stars around the centre of the Milky Way tells us about the mass of the object there. It is found to be a few million solar masses. Combining this with estimations of its size lead to the conclusion that there is a black hole at the centre of the Milky Way.

The black holes in the centres of many other galaxies are much larger.  A large black hole at the centre of a galaxy leads to the formation of a disk of material around it as matter falls into it. There is tremendous friction in this accretion disk, and the electromagnetic emission from such an active galactic nucleus can be very powerful. As matter falls in through the equatorial disk, other matter is spurted out from the poles, forming huge jets which can be thousands of times the size of the galaxy itself.

All of this happens in the vicinity of a black hole but outside it. The inside and the outside of a black hole are marked not by a physical boundary but something called an event horizon; inside the warping of space-time is so severe that what happens in that region is beyond reach.

Gravitational Waves

If masses bend space-time then the motion of objects should cause the bending of space-time to propagate. And they do. The ripples in space-time are perceptible only for events like the coalescence of black holes. The recent discovery of gravitational waves by LIGO was one of the greatest achievements in the history of science.

Gravitational Lenses

In Einstein’s theory gravity is caused and felt not just by massive objects but by every form of energy. So light, which is a form of energy, is bent as it moves past a massive object. This leads to astounding images of distant galaxies with foreground galaxies or galaxy clusters acting as gravitational lenses.