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Distance Ladder Rungs: Parallax, P-L, Tully-Fisher, Type Ia, Hubble

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or half-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects, so parallax can be used to determine distances. To measure large distances, such as the distance of a planet or a star from Earth, astronomers use the principle of parallax. Here, the term parallax is the semi-angle of inclination between two sight-lines to the star, as observed when Earth is on opposite sides of the Sun in its orbit [a] These distances form the lowest rung of what is called "the cosmic distance ladder"; they are the first in a succession of methods by which astronomers determine the distances to celestial objects and serve as a basis for other distance measurements in astronomy, which form the higher rungs of the ladder.

Figures (10)

Parallax theory for finding naval distances. Once the triangle baseline length L and two angles at both sides of the baseline are known, all information of the triangle is determined, so the distance from the baseline to the naval object can be measured.
Stellar parallax motion from annual parallax. Half the apex angle is the parallax angle.
The blue dots (left) represent the observer. By drawing a line straight out to the star (right) from different positions and measuring the angle formed between the two (α), astronomers can measure the distance between the Earth and the star.
Intrinsic Luminosity versus Velocity Dispersion calibrated to the Virgo Cluster from the Local, M81 and M101 Groups. Data compiled from Tully & Fisher, 1977.
Baryonic Tully-Fisher relation. Data compiled from various sources.[6][7][8][9][10][11]
RS Puppis, one of the brightest known Cepheid variable stars in the Milky Way galaxy(Hubble Space Telescope)
The period-luminosity curves of classic and type II Cepheids
Illustration of Cepheid variables (red dots) at the center of the Milky Way[16]
Light curve of Delta Cephei, the prototype of classical cepheids, showing the regular variations produced by intrinsic stellar pulsations
Light curve of κ Pavonis, a Type II cepheid, recorded by NASA's Transiting Exoplanet Survey Satellite (TESS)

Key Points

  • The parallax angle is half the angle (α) formed at the star between those two lines of sight.
  • Cepheid variables are divided into two subclasses which exhibit markedly different masses, ages, and evolutionary histories: classical Cepheids and type II Cepheids.
  • Delta Scuti variables and RR Lyrae variables are not generally treated with Cepheid variables although their pulsations originate with the same helium ionisation kappa mechanism.
  • In astronomy, the Tully–Fisher relation (TFR) is an empirical relationship between the mass or intrinsic luminosity of a spiral galaxy and its asymptotic rotation velocity or emission line width.
  • Absolute magnitude M is defined as the apparent magnitude of an object when seen at a distance of 10 parsecs.

Terms

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