Topicm1f6d22ae8fd62036_1528449000663_0Topic

How far is it to the planets, the Sun and the stars?

Levelm1f6d22ae8fd62036_1528449084556_0Level

Third

Core curriculumm1f6d22ae8fd62036_1528449076687_0Core curriculum

III. Gravity and elements of astronomy. The student:

4) describes the structure of the Solar System and its place in the Galaxy; uses the concepts of the astronomical unit and the light year.

Timingm1f6d22ae8fd62036_1528449068082_0Timing

45 minutes

General learning objectivesm1f6d22ae8fd62036_1528449523725_0General learning objectives

Explain how the distances between stars and the Sun are measured.

Key competencesm1f6d22ae8fd62036_1528449552113_0Key competences

1. Explain what the stellar parallax is.

2. Use the units of parsecparsecparsec and light‑year.

Operational (detailed) goalsm1f6d22ae8fd62036_1528450430307_0Operational (detailed) goals

The student:

- explains the method of the stellar parallaxstellar parallaxstellar parallax,

- uses in calculations the astronomical units: parsec and light‑year.

Methodsm1f6d22ae8fd62036_1528449534267_0Methods

1. Discussion.

2. Text analysis.

Forms of workm1f6d22ae8fd62036_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm1f6d22ae8fd62036_1528450127855_0Introduction

The students remind units which are commonly used to measure distances.

In what units we measure distances?

Procedurem1f6d22ae8fd62036_1528446435040_0Procedure

The teacher introduces the concept of the stellar parallaxstellar parallaxstellar parallax.

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 distance of very far objects a geometrical method is used.

Stellar parallaxstellar parallaxStellar 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.

Definition:
Stellar parallax – is the change of observed position of the celestial bodiescelestial bodiescelestial bodies due to its apparent motionapparent motionapparent motion with respect to more distant background stars.

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.m1f6d22ae8fd62036_1527752256679_0The 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.

[Interactive graphics]

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

[Illustration 1]

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 arcsec, which is the largest parallax observed for any star.m1f6d22ae8fd62036_1527752263647_0The 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 arcsec, which is the largest parallax observed for any star.

Parallax formula:

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

where: 
d - the distancedistancedistance to the star, 
p - parallax the star. 
The distancedistancedistance 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.

Definition:
1 parsec (pc) - one parsecparsecparsec corresponds to the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond.

1 parsec is equivalent to 206265 AU, or 3,26 ly, or 3,086 ∙ 10Indeks górny 13¹³ km.

Definition:
1 arcsec amounts to one sixtieth of an arcminute while an arcminute is $\frac{1}{60}$ of a degree:

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.

Definition:
Light year (ly) is the distancedistancedistance the light travels in one year.

1 ly is equivalent to 0,31 pc, or to 63270 AU.

Task 1

The star Proxima Centauri has a parallax p = 0,768 arcsec. Calculate its distance.

Answer:

1,302 pc.

Task 2

A measured parallax of a star is 0,02 arcsec. What is its distancedistancedistance?

Answer:

50 pc.

Lesson summarym1f6d22ae8fd62036_1528450119332_0Lesson summary

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

Selected words and expressions used in the lesson plan

stellar parallaxstellar parallaxstellar parallax

celestial bodiescelestial bodiescelestial bodies

parsecparsecparsec

apparent motionapparent motionapparent motion

relationrelationrelation

distancedistancedistance

digital imaging techniquesdigital imaging techniquesdigital imaging techniques