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.

## Archive for November, 2017

### Slingshot Orbit to Asteroid Bennu

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

### More on Moduli

Published November 6, 2017 Occasional Leave a CommentTags: Arithmetic, Number Theory

We wrote last week on *modular arithmetic*, the arithmetic of remainders. Here we will examine a few other aspects of this huge subject. Modular arithmetic was advanced by Gauss in his *Disquisitiones Arithmeticae*. In this system, number wrap around when they reach a point known as the modulus. Numbers that differ by a multiple of the modulus are called congruent. Thus 4, 11 and 18 are all congruent modulo 7.

### Modular Arithmetic: from Clock Time to High Tech

Published November 2, 2017 Irish Times Leave a CommentTags: Arithmetic, Time measurement

You may never have heard of *modular arithmetic*, but you use it every day without the slightest difficulty. In this system, numbers wrap around when they reach a certain size called the modulus; it is the arithmetic of remainders [TM126 or search for “thatsmaths” at irishtimes.com].

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