What Shape is Space?

A primer for the 21st century

Giles Sparrow, Matthew Taylor

• Publisher: Thames and Hudson Ltd
• Year: 2018
• ISBN:
  9780500774403
• Topic: Physical Sciences
• Subtopic: Space Science

What Shape is Space? is a question with surprisingly far-reaching implications for our understanding of the very nature of reality and our place within it. The concepts involved may be sophisticated, but Giles Sparrows effortless prose style easily renders them understandable, allowing readers to get to grips with the overarching debates at the cutting edge of cosmology today. Infographics, diagrams and astronomical visualizations illustrate and clarify the various astonishing implications of a universe of infinite space.

1. Mapping Space

A Stellar parallax arises as Earth moves from one side to another of its orbit. When seen from either side of this 300-million-kilometre (186.5 million mi) ‘baseline’, a nearby star will shift its direction in the sky, and its apparent position compared to more distant background stars. Yet such is the scale of the Universe that the shift is tiny for even the nearest stars.

The story of our modern quest to understand the shape of space really begins in the Copernican revolution that unshackled celestial objects from the limits of crystalline spheres and allowed them to roam free in a vast gulf of space. Uprooting Earth from its hallowed place at the centre of the Universe and (for a time) elevating the Sun to cosmic pre-eminence had important and immediate implications for the distance of not only the other planets, but also of the stars themselves.

For centuries, a key argument against the heliocentric system had always been that if Earth was moving in space, the direction of the stars would surely appear to change as our point of view shifted from one side of Earth’s orbit to the other.

This effect, known as parallax, is very familiar from our everyday lives: hold up a finger at arm’s length and wink each eye in turn, and its position will appear to shift back and forth when compared to more distant background objects. Astronomers had tried and failed to detect such a parallax shift in the stars, and the lack of any evidence had weighed heavily against the idea of a moving Earth.

But as telescopic discoveries and the power of Kepler’s system brought overwhelming new evidence for Earth’s motion, the same argument flipped into reverse. If the stars did not appear to change their apparent directions even as the Earth moved some 300 million kilometres (186.5 million mi) from one side of its orbit to the other, then they must be unimaginably distant.

The quest to measure parallax occupied many astronomers through the 18th and 19th centuries. In theory, the increasing power of telescopes made the task easier, but in practice there were still major challenges to overcome in terms of ‘astrometry’ (the measurement of stellar positions). With the stars wheeling around the sky once every 24 hours and the Sun rising and setting, we cannot simply keep a telescope trained on the same point in space and observe if a star moves gently back and forth; instead we have to measure stellar positions on a fixed grid of ‘celestial coordinates’ (akin to latitude and longitude on Earth).

One early discovery was that the stars are not as fixed as they appear to be; many of them move slowly across the sky from year to year and decade to decade. This so-called ‘proper motion’ is caused by a combination of the star’s motion and that of our own solar system, and it varies considerably from star to star. Astronomers soon realized they could use this as a likely indication of which stars are closest to Earth, and focus on those for their attempts at measuring parallax.

B Proxima Centauri, the closest star to Earth, lies only 4.25 light years away – a distance at which it shows a parallax shift of 0.77 seconds of arc (about 1/2000th the width of the Full Moon) and a proper motion that sees its position shift by a Full Moon’s diameter every 450 years. Despite its proximity, it was not discovered until 1915.

C This detailed view plots Proxima Centauri’s motion against background stars through the mid-2010s (caused by a combination of both Proxima’s motion and that of Earth). The ‘loops’ in the path are due to parallax.

Nevertheless, it took many years of unsuccessful attempts before Friedrich Bessel successfully measured the parallax of a star called 61 Cygni in 1838. The yearly shift in the star’s apparent direction proved to be a tiny 1/11,500th of a degree, but this was enough to calculate that it lies some 100 million million kilometres (61 trillion mi) from Earth.

A Friedrich Bessel made these sketches of Halley’s Comet during its passage close to the Sun in 1835. He had previously made new calculations of its orbit to more precisely predict its return to the inner solar system.

Friedrich Bessel (1784–1846) This German astronomer accurately charted the positions of more than 50,000 stars. Taking into account the bending of light by the atmosphere and the slight changes in the direction of stars caused by Earth’s motion around its orbit, he finally measured parallax successfully in 1838.

Degree A unit of angular measurement. There are 360 degrees in a circle and 90 degrees in a right angle. A degree can be split into 60 ‘minutes of arc’, each of which can be subdivided into 60 ‘seconds of arc’.

Space had expanded once again, to a scale where everyday distance measurements became nonsensically huge.

Consequently, astronomers rapidly adopted the idea of measuring a star’s distance from us in terms of the amount of time its light, the fastest thing in the Universe, takes to reach us travelling at an astounding 299,792 kilometres (186,282 mi) per second; on this scale, 61 Cygni is 10.3 light years from Earth.

Light year The distance light travels through a vacuum in one year, equivalent to 9.5 million million kilometres (5.88 million million mi).

An alternative way of measuring cosmic distances is in terms of parallax seconds or parsecs. One parsec is the distance at which a star would have to lie in order to display a parallax of 1 second of arc (1/3,600th of a degree), equivalent to 3.26 light years. Modern astronomers prefer to talk of parsecs (and indeed kilo- and mega-parsecs) rather than light years because of a preference for directly measured over ‘derived’ units, but for the rest of this book we will use the more familiar terminology.

One immediate discovery arising from Bessel’s parallax measurement was confirmation that not all stars are the same. 61 Cygni is relatively faint (on the edge of naked-eye visibility, in fact), and once its distance was known, it was clear that it was far less intrinsically bright (less luminous) than the Sun. In fact, 61 Cygni is a ‘double star’, a pair of stars close together in the sky, with one slightly fainter than the other. The discovery that they both displayed the same parallax and therefore really were at the same distance also proved that these two stars must be physically different from one another because otherwise they would appear to have exactly the same brightness.

Luminosity A measure of the total energy emitted by a star or other celestial object compared to the Sun. Luminosity differences can be used crudely as an indication of relative brightness in visible light, although hot or cool stars can emit most of their energy in the invisible ultraviolet or infrared.

This and other discoveries around the same time opened the way for the science of astrophysics and our modern understanding of how stars work.

B Despite their closeness in the sky, the binary stars of the 61 Cygni system are actually separated by a distance only slightly smaller than Neptune’s orbit around the Sun, and take 659 years to orbit each other.

A Galileo published his telescopic observations of the heavens (such as the Pleiades star cluster) in 1610 in the pamphlet Sidereus Nuncius (Starry Messenger).

From the point of view of the growing scale of space, the most interesting consequence of this work was the realization that laborious parallax measurements are not always needed to estimate the true characteristics of a star; there are clues hidden in a star’s light, such as the colours of its energy output and the signatures of elements in its atmosphere, that can reveal its true physical properties. These are often enough to give a ballpark estimate of the star’s true luminosity, allowing us to estimate its distance based on its brightness as seen from Earth without direct measurement.

B Galileo’s ske...

Table of contents

• Cover
• Title Page
• About the Author and Editor
• Other titles of interest
• Contents
• Milestones
• How to Read
• Introduction
• 1. Mapping Space
• 2. The Expanding Universe
• 3. The Omega Factor
• 4. The Shape of the Multiverse
• Conclusion
• Further Reading
• Picture Credits
• Index
• Acknowledgments
• Copyright