Jak daleko jest do planet, Słońca i gwiazd?

Before you start, answer the question.

• In what units we measure distances?

DistancedistanceDistance is the most important and most difficult quantity to measure in astronomy. Distances are key variables for estimating physical sizes of the celestial bodiescelestial bodiescelestial bodies, their true motion through the cosmic space, their masses and emitted energy.

To measure the distancedistancedistance of very far objects a geometrical method is used.

Stellar parallax

Stars located closer to the observer appear to move with respect to more distant stars. The effect is a result of the motion of the Earth around the Sun.

The position of a star noticed by an observer on the Earth in December with respect to the background stars will be different in June. This is caused by the change of the position of the Earth on its orbit around the Sun. In the geometrical representation, as seen from the Earth, the nearby star appears to sweep through the angle shown on the drawing. The parallax, p, is the half of this angle.

As the distancedistancedistance to a star increases, then its parallax decreases. Closer stars have larger parallaxes while distant stars have smaller parallaxes.

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Na rysunku przedstawiony jest dwa razy schemat opisujący zjawisko paralaksy. Na obydwu schematach pokazane jest Słońce (żółte koło), orbita Ziemi i jej dwie pozycje (niebieskie punkty), z których obserwowana jest gwiazda. Górna część rysunku przedstawia gwiazdę leżącą bliżej słońca, której paralaksa jest większa; na dolnym gwiazdę leżącą dalej, której paralaksa jest mniejsza. Na rysunkach liniami ciągłymi zaznaczona jest: odległość niebieskiego punktu leżącego nad Słońcem do do gwiazdy, odległość Słońca do gwiazdy, odległość punktu leżącego pod Słońcem do gwiazdy. Zaznaczony jest kąt paralaksy p.

The distances to the closest stars are enormous, as compared to terrestrial scales; therefore the largest measured parallaxes are very small. They are usually less than an arcsecond, e.g. the nearest star, called Proxima Centauri, has the parallax of 0,768 arcseconds, which is the largest parallax observed for any star.

Parallax formula

The relationrelationrelation between the parallax and the distancedistancedistance to the star can be calculated using a simple formula:

where d is the distance to the star and p is its parallax. The distance is expressed in parsecs and the parallax in arcseconds.

The fundamental relationrelationrelation in astronomy says that a star with a parallax of 1 arcsecond has a distance to the Sun of 1 parsecparsecparsec.

In the past, measuring of parallax was very arduous occupation. Nowadays we use digital imaging techniquesdigital imaging techniquesdigital imaging techniques to measure it. To avoid blurring due to the Earth’s atmosphere the measurement are done from space.

Other, very often used especially in the popular science, astronomical unit is the light year.

Remember

• The distances of stars from the Sun are measured using the stellar parallaxstellar parallaxstellar parallax method.

Exercises

Glossary

Keywords

stellar parallaxstellar parallaxstellar parallax

celestial bodiescelestial bodiescelestial bodies

parsecparsecparsec

apparent motionapparent motionapparent motion