The *Voyager 1* and *Voyager 2* spacecraft have now left the solar system and will continue into deep space. How did we manage to send them so far? The *Voyager* spacecraft used gravity assists to visit Jupiter, Saturn, Uranus and Neptune in the late 1970s and 1980s. Gravity assist manoeuvres, known as **slingshots**, are essential for interplanetary missions. They were first used in the Soviet Luna-3 mission in 1959, when images of the far side of the Moon were obtained. Space mission planners use them because they require no fuel and the gain in speed dramatically shortens the time of missions to the outer planets.

## Posts Tagged 'Astronomy'

### Slingshot Orbit to Asteroid Bennu

Published November 16, 2017 Irish Times Leave a CommentTags: Astronomy, Mechanics

### Pedro Nunes and Solar Retrogression

Published October 12, 2017 Occasional Leave a CommentTags: Astronomy, Time measurement

In northern latitudes we are used to the Sun rising in the East, following a smooth and even course through the southern sky and setting in the West. The idea that the compass bearing of the Sun might reverse seems fanciful. But in 1537 Portuguese mathematician Pedro Nunes showed that the shadow cast by the gnomon of a sun dial can move backwards.

Nunes’ prediction was counter-intuitive. It came long before Newton, Galileo and Kepler, and Copernicus’ heliocentric theory had not yet been published. The retrogression was a remarkable example of the power of mathematics to predict physical behaviour.

### Quadrivium: The Noble Fourfold Way

Published July 20, 2017 Irish Times Leave a CommentTags: Arithmetic, Astronomy, Geometry, History, Music

According to Plato, a core of mathematical knowledge – later known as the Quadrivium – was essential for an understanding of the Universe. The curriculum was outlined in Plato’s *Republic*. The name Quadrivium means four ways, but this term was not used until the time of Boethius in the 6^{th} century AD [see TM119 or search for “thatsmaths” at irishtimes.com].

It is said that an inscription over the entrance to Plato’s Academy read “Let None But Geometers Enter Here”. This indicated that the Quadrivium was a prerequisite for the study of philosophy in ancient Greece.

### A New Window on the World

Published November 3, 2016 Irish Times Leave a CommentTags: Astronomy, Relativity

The motto of the Pythagoreans was “All is Number” and Pythagoras may have been the first person to imagine that the workings of the world might be understood in mathematical terms. This idea has now brought us to the point where, at a fundamental level, mathematics is the primary means of describing the physical world. Galileo put it this way: the book of nature is written in the language of mathematics [TM102, or search for “thatsmaths” at irishtimes.com].

### Kepler’s Magnificent Mysterium Cosmographicum

Published October 13, 2016 Occasional 2 CommentsTags: Astronomy, Geometry, History

Johannes Kepler’s amazing book, *Mysterium Cosmographicum*, was published in 1596. Kepler’s central idea was that the distance relationships between the six planets (only six were known at that time) could be represented by six spheres separated by the five Platonic solids. For each of these regular polyhedra, there is an inner and an outer sphere. The inner sphere is tangent to the centre of each face and the outer sphere contains all the vertices of the polyhedron.

Continue reading ‘Kepler’s Magnificent Mysterium Cosmographicum’

### The Search is on for Planet Nine

Published April 7, 2016 Irish Times Leave a CommentTags: Astronomy

Then felt I like some watcher of the skies

When a new planet swims into his ken.

John Keats: *On First Looking into Chapman’s Homer*

Pluto, discovered in 1930, orbits in the Kuiper Belt, a ring of asteroids and icy debris beyond Neptune. About ten years ago, it was reclassified as a “dwarf planet”, so now we have eight planets. Is there a ninth anywhere? A recent paper in the *Astronomical Journal* presents evidence of a large planet in an orbit far beyond Neptune. If confirmed, this would be a dramatic confirmation of our understanding of solar system dynamics [TM088, or search for “thatsmaths” at irishtimes.com].

### Thomas Harriot: Mathematician, Astronomer and Navigator

Published August 27, 2015 Occasional Leave a CommentTags: Astronomy, History

Sir Walter Raleigh, adventurer, explorer and privateer, was among most colourful characters of Tudor times. He acquired extensive estates in Waterford and Cork, including Molana Abbey near Youghal, which he gave to his friend and advisor, the brilliant mathematician and astronomer Thomas Harriot.

Continue reading ‘Thomas Harriot: Mathematician, Astronomer and Navigator’