Measuring the universe

The Babylonians were the first to measure the heavens with any reliable accuracy and pass on their data to future generations. Their continuing legacy is a system of angular measurement in which the celestial sphere is divided into 360 degrees, each degree into 60 minutes, and each minute into 60 seconds. Thus did the Babylonians plot position and movement of the stars as on a screen with no inkling of its distance away or the depths behind it, and so it was to remain until the revolutionary science of the 16th century.

During the 3rd Century BC, before Caesar conquered Gaul, when Northern Europe was still in the grasp of Druids, and if Roman reports are to be believed, propitiating the gods with human sacrifices, a Greek in Alexandria, Eratosthenes, was measuring the circumference of the Earth by comparing the length of the shadow cast by a stick in Aswan with that of stick in Alexandria. The logical power of geometry was revealing the size of an Earth that was still largely uncharted.

The first attempt to give depth to the heavens soon followed as Aristarchus, also in Alexandria, used the geometry of a lunar eclipse to gain a fair estimate of the distance of the moon from the Earth. Attempts, however, at determining solar distances were doomed by the tiny angular measurements involved.

When Hipparchos came to measure the stars in the 2nd century BC and compared his results with those of the Babylonians, he could identify a slight shift in the April position of the sun amongst the stars at the moment of the spring equinox. He had discovered an effect of precession, a wobble in the Earth’s spin which takes 26 000 years to complete a cycle.

Two thousand years later, the spring equinox has shifted a further 30 degrees from the constellation of Aries into Pisces, yet astrologers still cast horoscopes on the assumption that the sun is in Aries in April, a barking madness in the face of a 2000 year old science!

Alexandria remained at the centre of astronomical speculation well into the 2nd Century AD when Ptolemy developed a calculus for successfully determining the positions of sun, moon and planets amongst the stars which was valid for the next thousand years. His data was used by sailors to navigate the globe and by the Church to calculate Easter. Only in the 16th Century was his assumptions of an Earth based system questioned as accumulated errors in his calculus began to be felt.

When Copernicus rationalized Ptolemy’s system by placing the Sun at the centre of his calculations, he was driven by a mathematical sense of logic and beauty that had been the common inspiration for scientific speculation since the Babylonians. A chilling consequence of the new arrangement was that the stars were no longer fixed to a sphere circling the Earth but were unbound and distant, so distant that no shift in perspective could be seen between the stars as the Earth orbited the sun, the phenomenon of stellar parallax. The universe had been blown open but its depth was unfathomable.

The coupled circles and spheres of Copernicus were soon superseded by the more elegant ellipses of Kepler which led to a formula that at last gave a relative dimension to our solar system: the square of the period of orbit of a planet was proportional to the cube of the mean radius of its orbit, ie. Jupiter must be five times further out from the sun than the Earth.

Yet we still didn’t know how far out the Earth was, the absolute scale still eluded our grasp. This required the ability to measure a shift in perspective between the planets and the stars for observers at different positions on the Earth’s surface, the phenomenon of planetary parallax. This was finally achieved by scientists from the court of Louis XIV. Using sightings of Mars from Paris and French Guiana, a parallax shift of 24 seconds which allowed an absolute scale to be calculated for the solar system and placed the sun 140 million km away, an error of only 7% when compared with our current estimate of 150 million km, yet still further away than anyone had ever dared imagine.

Yet a more disturbing fact was emerging. When the periods of orbit of the moons round Jupiter  were compared at different times of the year, there were differences according to whether the Earth, in its annual orbit round the sun, was moving towards Jupiter or away. A discrepancy that could only be explained if the light coming from the planet was traveling at a finite speed!  The speed of light could be calculated and has been known now for over three hundred years. It was to become, under Einstein, the absolute arbiter of space and time. While the distance traveled by a light beam in one year became the standard unit for astronomical distances, with Jupiter only 35 light minutes away.

Yet we still could not estimate the distances to the stars Only in the 19th Century were instruments capable of detecting stellar parallax for the nearest stars, a fraction of a second of arc, less than one 1/60th of 1/60th of a degree (0.76 seconds for alpha centauri, the nearest star visible to the naked eye, which places it 4.3 light years away). For more distant stars, the tiny displacements placed them out of our reach. The universe was still eluding our grasp.

Until we looked more closely at starlight.

The stars are all moving, too slow to be noticed by the casual observer but creating significant angular displacements over a few years (still measured using the Babylonian system). Since the stars are moving through three dimensions, the angular displacements are also accompanied by motion towards or away from us. This distorts the light we receive. As stars approach, the light is squeezed and becomes bluer; as they move away, the light is stretched and reddens. The star doesn’t change colour since invisible infra red or ultra violet is pulled into the visible spectrum to compensate for the shift, but certain spectral signatures can be measured which reveal the phenomenon, known as the Doppler shift.

Just like parallax, the Doppler shift gave depth to the angular motion across the night sky. Not that distance could yet be measured unless we knew the general direction of motion of the star. This is easy to find when stars are clustered together since they all seem to move towards or away from a vanishing point which pins down the direction of motion. Studying star clusters has provided a window into the depths of our galaxy. The Hyades cluster which surrounds the bright red star, Aldebaran, in Taurus proved to be 650 ly away.

It was left to a woman, Henrietta Leavitt, to discover the standard beacons that would allow us to fathom deeper space: a class of stars, now known as Cepheid variables, which vary in brightness in a rhythm related to their intrinsic brightness. Once we know the intrinsic brightness we can compare it with the apparent brightness that we detect on Earth and the diminution tells us how far away the star is. The beacons needed to be standardized with known distances and that left decades of uncertainty as space seems to balloon out and shrink according to the calibration of our standard beacons.

When Shapley measured the size of the Milky Way system to be 300 000 light years across, it was thought to be so large that it must encompass the whole universe, and all the spiral nebulae that we now know to be distant galaxies were taken to be wispy shreds of gas and dust within our local star system. His was an overestimate since he had not factored in the dimming effect due to interstellar dust, a first intimation that there was more to the universe than can be seen.

However, as the dimensions of the Milky Way were reduced to 100 000 light years, spiral nebulae became independent galaxies and the universe stretched out beyond our ken. Hubble established unequivocally that the spiral nebulae were independent star systems and his discovery of Cepheid variables in them allowed the estimation of their distances. Our nearest neighbouring galaxy, the Andromeda galaxy, was estimated to be 900 000 light years away, stunning enough but later proved to be an underestimate, now believed to be 2 ¼ million light years away. With bold initiative, Hubble went beyond Cepheid variables and by assuming the brightest star in any galaxy to be the same brightness in all galaxies, he leap-frogged into deep space. And when galaxies appeared so far that individual stars couldn’t be identified, he assumed the brightest galaxies in clusters were all of the same brightness, extending our measurement to billions of light years away, distances never imagined in the speculative heat of Alexandria but now pegged by measurement.

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