Instruction

1

Attempts to measure

**the distance**from the Earth to**the Sun**were made in Ancient Greece (Aristarchus of Samos), but to call them accurate was difficult. In the XVII century this**distance**was measured using the method of parallax (difference of position of an object relative to a subject based on the position of the observer). Was determined as the horizontal parallax**of the Sun**is the angle with**the Sun**located on the horizon, is visible perpendicular to the line of sight radius of the Earth. Further research was based on the length of the radius of the Earth.2

In 1672, it was determined

**the distance**from earth to Mars, who at that time was located in the diametrically opposite point of the Sun. The trigonometric laws that allow to calculate the relative distances of the planets, expressed in fractions of the distance Earth-Sun, was known, and with their help, it was computed the actual**distance**from**the Sun**to the Earth. At that time it was the most accurate value of 138.5 million kilometers.3

Subsequently, the astronomical unit was trying to determine many times, taking as a basis of computing

**the distance**from Earth to Venus, but because observers were quite a lot, and the dimensions were of high complexity, the inconsistency in the obtained values was very large. In the late nineteenth century by measuring displacement of the apparent positions of the stars was computed a more accurate value 149, 5 million kilometers.4

The second half of the XX century brought the scientific and technical revolution, and with it the development of radio. That is the radar method (in which in the direction of a celestial body send short impulse, take the reflected signal and based on the speed of propagation and the transit time of the signal in both directions to determine

**the distance**to this body) allowed to calculate the**distance**from Earth to**the Sun**as accurately as possible at different times of the year and take an average value equal to 149 597 870 km.# Advice 2 : How to determine the distance to planets

Despite the fact that most close from us

**planets**extremely far from Earth,**distance**it is of ultimate importance. And if so, it can be determined. And this was first done a long time ago – in the days of the Ancient Greek astronomer, mathematician and philosopher Aristarchus from the island of Samos proposed a method of determining the distance to the moon and its size. How can you determine**the distance**to planets? The method is based on the phenomenon of parallax.You will need

- calculator;
- - radar;
- - stopwatch;
- - Handbook of astronomy.

Instruction

1

Radar is one of the modern methods of determining the distance from Earth to the planets (geocentric distance). It is based on a comparative analysis of the sent and reflected signal.Send a radio signal in the direction of interest

**of the planet**and turn on the stopwatch. When will the reflected signal to stop the clock. By the known velocity of propagation and the time during which the signal reaches**the planet**is reflected, calculate the**distance**to**the planet**. It is equal to the product of the speed at half the stopwatch.2

Before the advent of radar to determine the distance to objects in the Solar system using the method of the horizontal parallax. The error of this method is kilometer, and the measurement error of the distance using the radar centimeter.

3

The essence of the definition of the distances to the planets by the method of the horizontal parallax is to change the direction of the object when moving the observation point (parallax) – as a base is taken maximally spaced points together: the radius of the Earth. That is, the determination of distances to

**the planets**by the method of the horizontal parallax is a simple trigonometric problem. If you know all the data.4

Multiply 1 radian (the angle formed by the arc length is equal to radius expressed in seconds (206265) on the radius of the Earth (6370 km) and divide by the amount of parallax

**of the planet**at this time. The resulting value**is the distance**to**the planet**in astronomical units.5

At an annual or trigonometric parallax (base is the semimajor axis of earth's orbit) calculate distances to very distant planets and stars. By the way, parallax equal to one second determines

**the distance of**one parsec, and 1 PS = 206265 astronomical units. Divide 206265 seconds (1 radians) on the value of trigonometric parallax. The resulting quotient is**the distance of**to the interest**of the planet**.6

Finally,

**distance**to planets can be calculated using the third law of Kepler. The calculation is quite complicated, so let's proceed to the final part.Construct the squared value of the orbital period**of the planet**around the Sun. Calculate the cube root of this value. The resulting number is**the distance**from the interest**of the planet**to the Sun in astronomical units, or heliocentric**distance**. Knowing the heliocentric**distance**and the position of the planets (angular**distance****of the planet**from the Sun), you can easily calculate the geocentric**distance**.