In spite of the fact that the neighbors of the planet from us are madly far from Earth, **the distance** it has final value. And time so – it can be defined. And for the first time it was made long ago – at the time of Ancient Greece the astronomer, the mathematician and the philosopher Aristarkh from the island of Samos offered a way of determination of distance to the Moon and its sizes. How it is possible to define distance to planets? Parallax phenomenon is the cornerstone of a method.

## It is required to you

- - calculator;
- - radar;
- - stop watch;
- - reference book on astronomy.

## Instruction

1. A radar-location - one of modern methods of determination of distance from Earth to planets (geocentric distance). It is based on the comparative analysis of the sent and reflected radio signal. Send a radio signal in the direction of the interesting **planet** and include a stop watch. When the reflected signal comes – stop counting. On the known speed of distribution of radio waves and time for which the signal reached the planet and was reflected, calculate distance to the planet. It is equal to the work of speed on a half of indications of a stop watch.

2. Before emergence of a radar-location for determination of distance to objects of the Solar system used a method of horizontal parallax. The error of this method makes kilometer, and an error of measurements of distances by means of a radar-location – centimeter.

3. The essence of determination of distances to planets by a method of horizontal parallax consists in change of the direction on an object when moving a point of observation (parallactical shift) – as base the points which are most carried among themselves undertake: Earth radius. That is determination of distance to the planet by a method of horizontal parallax – a simple trigonometrical task. If all data are known.

4. Increase 1 radian (and divide the corner formed by an arch which length is equal to radius) expressed in seconds (206265) on Earth radius (6370 km) into the size of parallax of the planet of time at present. The received value – distance to the planet in astronomical units.

5. On year or trigonometrical parallax (the big half shaft of a terrestrial orbit is accepted to base) calculate distances to very far-out planets and stars. By the way, parallax equal to one second defines distance in one parsec, and 1 ps = 206265 astronomical units. Divide 206265 seconds (1 radian) into the size of trigonometrical parallax. The received private – distance to the interesting planet.

6. Well and at last, the distance to planets can be calculated under the third law of Kepler. Calculations are rather difficult therefore we will pass to a final part at once. Square value of a cycle time of the planet around the Sun. Calculate a cubic root from this size. The received number – distance from the interesting planet to the Sun in astronomical units, or heliocentric distance. Knowing heliocentric distance and location of planets (angular distance of the planet from the Sun), it is possible to calculate geocentric distance easily.