The age of the earth and the age of the universe have been twin
holy grails of science since before science became a formal series
of disciplines. Strangely enough, the first scientific stab
at determining the age of the earth came from a religious man,
Archbishop James Ussher of ireland. Ussher came up with the
date 4004 B.C. in the Seventeenth Century. The date is
wildly underestimated, but Ussher at least used what he thought was empirical evidence to arrive at it. He tracked biblical generations all the way back to Adam and Eve, compared different translations of the Bible, and made somewhat plausible assumptions about ambiguous lines such as "the earth was without form and void" and "the evening and the morning were the first day."
Ussher's chronology started gracing subsequent editions of the Bible, and were generally accepted until the Jesuits penetrated China, where they discovered credible Chinese astronomical observations of regularly-appearing celestial objects (comets) that stretched back before the earth's putative beginning. Other flies in the biblical ointment kept cropping up as well: fossil forms of decreasing complexity the deeper one dug, and anomalies in terrain that cast doubt on the ubiquity of Noah's global flood.
The first true geologists emerged at the end of the Eighteenth
Century, and began comparing structures like Hadrian's Wall, whose
building date was known, with more greatly eroded natural
formations like mountains. If Hadrian's Wall had barely
changed in over a millennium, yet a volcanic rock like Arthur's
Seat in the heart of Edinburgh showed great signs of erosion,
Arthur's Seat must have been around for a much longer time. Scotsman James Hutton concluded that the earth was a dynamic engine, constantly churning and remodeling itself, with "no vestige of a beginning, no prospect of an end."
By the mid-Nineteenth Century, science had developed sets of rules that were assumed applicable in any physical situation. Giants like William Thompson (later Lord Kelvin) came up with 100 million years as an age for the planet, based on simple laws of thermodynamics. Kelvin's calculations held sway until a new source of heat and energy was discovered by those intrepid few who had cracked the secrets of atomic structure. In radioactive decay, a built-in time clock was present, and samples of the first coalesced planetary fragments, long since subducted on the earth, were found in lunar samples and in fallen meteorites. The current scientific best-estimate for the age of the earth is 4.3 billion years.
Dating the age of the universe was impossible until it had been
firmly established that there had indeed been a beginning at
all. The discovery of a universal cosmic microwave
background radiation in 1965 confirmed the Big Bang as the most
likely cosmological creation theory, and increasingly more
powerful telescopes pushed the human gaze further and further into
space. Of course, the deeper one looked, the older things were, because the speed of light is a constant, a speed limit over which nothing can exceed. Other complex problems had to be solved, like the conundrum caused by observing the red shift in distant stars and galaxies. The universe wasn't just expanding, but was accelerating in that expansion. Once that rate of
acceleration could be established, back calculations could be made to that point in the distant past when the entire universe was contained in an almost unimaginable singularity, the explosive beginning of time popularly known as the Big Bang. Scientists now estimate the Big Bang to have taken place 13.4 billion years ago, give or take a few hundred million years.
Doubtless, minor corrections will emerge for these two defining
numbers as more sophisticated dating techniques and more powerful
telescopes are created, but the reasoning behind these numbers,
and their essential truth, is now as accepted in science as the
germ theory of disease, or the structure of the atom, both
controversial when they first appeared, but now
almost universally accepted. Gorst tells the story in MEASURING ETERNITY in more detail than time allows here, and does so elegantly and persuasively.
Dialogue on favorite books with Deane Rink before and during his latest trek to Antarctica, with a note from Bill Ransom and a digression about Frank Herbert (a.k.a Bookbabble 101) -- a very long and rapidly growing document: