Melvyn Bragg and guests discuss William Herschel (1738 – 1822) and his sister Caroline Herschel (1750 – 1848) who were born in Hanover and made their reputation in Britain. William was one of the most eminent astronomers in British history. Although he started life as a musician, as a young man he became interested in studying the night sky. With an extraordinary talent, he constructed telescopes that were able to see further and more clearly than any others at the time. He is most celebrated today for discovering the planet Uranus and detecting what came to be known as infrared radiation. Caroline also became a distinguished astronomer, discovering several comets and collaborating with her brother.WithMonica Grady Professor of Planetary and Space Sciences at the Open UniversityCarolin Crawford Institute of Astronomy, Cambridge and an Emeritus Fellow of Emmanuel College, University of CambridgeAndJim Bennett Keeper Emeritus at the Science Museum in London.Studio producer: John Goudie

Melvyn Bragg and guests discuss the simple animals which informed Charles Darwin's first book, The Structure and Distribution of Coral Reefs, published in 1842. From corals, Darwin concluded that the Earth changed very slowly and was not fashioned by God. Now coral reefs, which some liken to undersea rainforests, are threatened by human activity, including fishing, pollution and climate change. WithSteve Jones Senior Research Fellow in Genetics at University College LondonNicola Foster Lecturer in Marine Biology at the University of Plymouth AndGareth Williams Associate Professor in Marine Biology at Bangor University School of Ocean SciencesProducer Simon Tilllotson.

Melvyn Bragg and guests discuss the race to build an atom bomb in the USA during World War Two. Before the war, scientists in Germany had discovered the potential of nuclear fission and scientists in Britain soon argued that this could be used to make an atom bomb, against which there could be no defence other than to own one. The fear among the Allies was that, with its head start, Germany might develop the bomb first and, unmatched, use it on its enemies. The USA took up the challenge in a huge engineering project led by General Groves and Robert Oppenheimer and, once the first bomb had been exploded at Los Alamos in July 1945, it appeared inevitable that the next ones would be used against Japan with devastating results.The image above is of Robert Oppenheimer and General Groves examining the remains of one the bases of the steel test tower, at the atomic bomb Trinity Test site, in September 1945.WithBruce Cameron Reed The Charles A. Dana Professor of Physics Emeritus at Alma College, MichiganCynthia Kelly Founder and President of the Atomic Heritage FoundationAndFrank Close Emeritus Professor of Theoretical Physics at the University of Oxford and a Fellow of Exeter College, OxfordProducer: Simon Tillotson

Melvyn Bragg and guests discuss the remarkable diversity of the animals that dominated life on land in the Triassic, before the rise of the dinosaurs in the Jurassic, and whose descendants are often described wrongly as 'living fossils'. For tens of millions of years, the ancestors of alligators and Nile crocodiles included some as large as a bus, some running on two legs like a T Rex and some that lived like whales. They survived and rebounded from a series of extinction events but, while the range of habitats of the dinosaur descendants such as birds covers much of the globe, those of the crocodiles have contracted, even if the animals themselves continue to evolve today as quickly as they ever have.WithAnjali Goswami Research Leader in Life Sciences and Dean of Postgraduate Education at the Natural History MuseumPhilip Mannion Lecturer in the Department of Earth Sciences at University College London AndSteve Brusatte Professor of Palaeontology and Evolution at the University of EdinburghProducer Simon Tillotson

Melvyn Bragg and guests discuss the search for Longitude while at sea. Following efforts by other maritime nations, the British Government passed the Longitude Act in 1714 to reward anyone who devised reliable means for ships to determine their longitude at sea. Mariners could already calculate how far they were north or south, the Latitude, using the Pole Star, but voyaging across the Atlantic to the Caribbean was much less predictable as navigators could not be sure how far east or west they were, a particular problem when heading for islands. It took fifty years of individual genius and collaboration in Britain and across Europe, among astronomers, clock makers, mathematicians and sailors, for the problem to be resolved.WithRebekah Higgitt Principal Curator of Science at National Museums ScotlandJim Bennett Keeper Emeritus at the Science MuseumAnd Simon Schaffer Professor of History and Philosophy of Science at the University of CambridgeProducer: Simon Tillotson

Melvyn Bragg and guests discuss Laplace (1749-1827) who was a giant in the world of mathematics both before and after the French Revolution. He addressed one of the great questions of his age, raised but side-stepped by Newton: was the Solar System stable, or would the planets crash into the Sun, as it appeared Jupiter might, or even spin away like Saturn threatened to do? He advanced ideas on probability, long the preserve of card players, and expanded them out across science; he hypothesised why the planets rotate in the same direction; and he asked if the Universe was deterministic, so that if you knew everything about all the particles then you could predict the future. He also devised the metric system and reputedly came up with the name 'metre'. WithMarcus du Sautoy Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of OxfordTimothy Gowers Professor of Mathematics at the College de FranceAndColva Roney-Dougal Professor of Pure Mathematics at the University of St AndrewsProducer: Simon Tillotson

Melvyn Bragg and guests discuss the devastating mass extinctions of the Late Devonian Period, roughly 370 million years ago, when around 70 percent of species disappeared. Scientists are still trying to establish exactly what happened, when and why, but this was not as sudden as when an asteroid hits Earth. The Devonian Period had seen the first trees and soils and it had such a diversity of sea life that it’s known as the Age of Fishes, some of them massive and armoured, and, in one of the iconic stages in evolution, some of them moving onto land for the first time. One of the most important theories for the first stage of this extinction is that the new soils washed into oceans, leading to algal blooms that left the waters without oxygen and suffocated the marine life. The image above is an abstract group of the huge, armoured Dunkleosteus fish, lost in the Late Devonian ExtinctionWith Jessica Whiteside Associate Professor of Geochemistry in the Department of Ocean and Earth Science at the University of SouthamptonDavid Bond Professor of Geology at the University of HullAndMike Benton Professor of Vertebrate Paleontology at the School of Life Sciences, University of Bristol.

Melvyn Bragg and guests discuss one of the outstanding French mathematicians and natural philosophers of the 18th Century, celebrated across Europe. Emilie du Châtelet, 1706-49, created a translation of Newton’s Principia from Latin into French that helped spread the light of mathematics on the emerging science, and her own book Institutions de Physique, with its lessons on physics, was welcomed as profound. She had the privileges of wealth and aristocracy, yet had to fight to be taken seriously as an intellectual in a world of ideas that was almost exclusively male. WithPatricia Fara Emeritus Fellow of Clare College, CambridgeDavid Wootton Anniversary Professor of History at the University of YorkAndJudith Zinsser Professor Emerita of History at Miami University of Ohio and biographer of Emilie du Châtelet.Producer: Simon Tillotson

Discover the scientific importance of solar and lunar eclipses and how they provide unique opportunities for studying various phenomena. Explore the early understanding of eclipses in ancient civilizations and their shift to being seen as scientific events. Learn about observations of eclipses away from Earth and their significance in binary stars. Delve into Jules Jansen's discovery of helium during a solar eclipse and hear personal experiences and perceptions of eclipses from the speakers.

Melvyn Bragg and guests discuss Alan Turing (1912-1954) whose 1936 paper On Computable Numbers effectively founded computer science. Immediately recognised by his peers, his wider reputation has grown as our reliance on computers has grown. He was a leading figure at Bletchley Park in the Second World War, using his ideas for cracking enemy codes, work said to have shortened the war by two years and saved millions of lives. That vital work was still secret when Turing was convicted in 1952 for having a sexual relationship with another man for which he was given oestrogen for a year, or chemically castrated. Turing was to kill himself two years later. The immensity of his contribution to computing was recognised in the 1960s by the creation of the Turing Award, known as the Nobel of computer science, and he is to be the new face on the £50 note.WithLeslie Ann Goldberg Professor of Computer Science and Fellow of St Edmund Hall, University of OxfordSimon Schaffer Professor of the History of Science at the University of Cambridge and Fellow of Darwin CollegeAnd Andrew Hodges Biographer of Turing and Emeritus Fellow of Wadham College, OxfordProducer: Simon Tillotson