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Theme E — Nuclear and Quantum Physics

E.5.7 Stellar Parallax — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 44 of 45 1 quiz

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E.5.7 Stellar Parallax — IB PHYSICS SL notes: Use the parallax angle to find the distance to nearby stars and define the astronomical unit, light-year and parsec.Astronomical unit (AU) = the mean distance from the centre of the Earth to the centre of the Sun.1 AU = 1.496 × 1011 m…

  • Light-year (ly)
  • Parsec (pc)
  • The AU suits the solar system
  • Milli-arcseconds (mas) must be divided by 1000 first
  • Observe the star six months apart
  • Distant stars appear fixed

Part 1 of 7Units of astronomical distance

1Astronomical unit (AU)
Astronomical unit (AU) the mean distance from the centre of the Earth to the centre of the Sun.
  • 1 AU = 1.496 × 1011 m, about 1.5 × 1011 m.
  • Earth's orbit is elliptical — 1.471 × 1011 m in January and 1.521 × 1011 m in July.
2Light-year (ly)
Light-year (ly) the distance travelled by light in one year.
  • 1 ly = 3 × 108 m s-1 × 3.15 × 107 s, about 9.5 × 1015 m.
3Parsec (pc)
Parsec (pc) the distance at which a star has a parallax angle of one arcsecond, with a baseline of 1 AU.
  • 1 pc = 3.09 × 1016 m = 3.26 ly.
4The AU suits the solar system
  • The AU suits the solar system the ly and pc suit interstellar distances.

Part 2 of 7Angle units

11 degree
60 arcminutes — and 1 arcminute = 60 arcseconds.
21 degree
3600 arcseconds — so 1 arcsecond = 1/3600 degree = 4.85 × 10-6 rad.
3Notation
  • 1′ is one arcminute and 1″ is one arcsecond.
4Milli-arcseconds (mas) must be divided by 1000 first
  • Milli-arcseconds (mas) must be divided by 1000 first p = 50 mas is 0.050″.

Part 3 of 7Stellar parallax

1Stellar parallax
Stellar parallax the apparent shift of a nearby star against distant background stars, seen from different positions in Earth's orbit.
2Observe the star six months apart
  • Observe the star six months apart the Earth is at opposite ends of a 2 AU baseline.
3Distant stars appear fixed
  • Distant stars appear fixed the nearby star appears to shift.
4
The nearer the star, the larger the shift.
5The parallax angle p
The parallax angle p the angle subtended at the star by 1 AU — half of the total shift between the two observations.

Part 4 of 7Parallax equations

1tan p
1 AU / d — where d is the distance to the star.
2For small angles in radians
  • For small angles in radians tan p ≈ p, so p = 1 AU / d.
3With d in parsecs and p in arcseconds
  • With d in parsecs and p in arcseconds d = 1 / p.
  • A star with p = 0.50″ is 2.0 pc away; p = 0.05″ gives 20 pc.
  • Proxima Centauri has p = 0.768″, so d = 1.30 pc, about 4.2 ly.
4
Fractional uncertainty in distance equals fractional uncertainty in p.

Part 5 of 7Limits of parallax

1Accurate up to about 100 pc
  • Accurate up to about 100 pc beyond that the angles are too small to measure.
  • At 100 pc p = 0.01″, near the limit for ground-based telescopes because of atmospheric blurring.
2Space telescopes (Hipparcos, Gaia) measure micro-arcsecond angles
  • Space telescopes (Hipparcos, Gaia) measure micro-arcsecond angles giving distances to several thousand parsecs.
3Parallax is a direct geometric method
  • Parallax is a direct geometric method it is the base of the cosmic distance ladder.
4
Other methods, such as standard candles, are calibrated against parallax of nearby objects.

Part 6 of 7Using the distance

Using the distance
Apparent brightness b
L / (4πd2) — so luminosity L = 4πd2b once d is known.
Position on the HR diagram follows from L and T
  • Position on the HR diagram follows from L and T and radius from L = 4πR2σT4.
Parallax links position measurements to the physical properties of a star.

Part 7 of 7More from the specification

Spectroscopic parallax and energy levels
  • Spectroscopic parallax and energy levels spectral line broadening indicates stellar luminosity classes, reflecting quantum atomic transitions across electronic energy levels.
Stellar parallax and distance measurement
  • Stellar parallax is the apparent angular displacement of a nearby star against distant background stars as Earth orbits the Sun: d = 1 / p.
Stefan-Boltzmann law and stellar luminosity
  • Total power radiated by a star depends on surface area and absolute surface temperature: L = 4 pi R2 sigma T4.
Hertzsprung-Russell diagram classification
  • Plotting stellar luminosity against surface temperature organizes stars into distinct evolutionary stages: main sequence, giants,
  • and white dwarfs.
Main sequence core fusion
  • Main sequence core fusion hydrogen nuclei fuse into helium within hot stellar cores, releasing radiant energy that generates outward thermal radiation pressure.
Equilibrium in stellar interiors
  • Equilibrium in stellar interiors gravitational collapse pressure is counteracted by outward thermal gas and radiation pressure, maintaining stable main sequence stellar diameters.
Stellar emission and absorption spectra
  • Stellar emission and absorption spectra analysing spectral absorption lines in a star's electromagnetic spectrum reveals core surface temperature and elemental chemical composition.
Energy level
  • A discrete energy an electron in an atom can have
Continuous spectrum
  • Spectrum with no gaps between the regions.
Radiation
  • Transfer by electromagnetic waves, requiring no medium
Photon
  • A quantum of electromagnetic energy, E = hf
    What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Wavelength
  • Distance between a point on one wave and the same point on the next wave
White dwarf
  • Small, hot, dense core left by a low-mass star.
Radiation pressure
  • The pressure exerted on a surface by absorbed or reflected radiation because photons transfer momentum.
Surface temperature
  • Effective temperature of the star's radiating surface.
Binding energy
  • The minimum energy required to separate the nucleons of a nucleus to infinity.
Emission spectrum
  • The set of discrete wavelengths emitted by excited atoms of an element.
Fusion
  • Joining of light nuclei into a heavier one.
Temperature
  • Measure of the average kinetic energy of the particles.
Pressure
  • Force per unit area, P = F/A.
    What the symbols mean: p = pressure (Pa = N m−2) · F = force acting at right angles to the surface (N) · A = area (m2)
Spectrum
  • Range of colours in white light.
Helium
  • Product of the fusion of hydrogen in stars.
Nucleus
  • Small, dense, positively charged centre of the atom.
Absorption
  • The conversion of wave energy to internal energy of the medium.
Reaction
  • The partner force acting on the other object.

Key terms

TermMeaning
Parallax angleHalf the apparent angular shift of a star over six months.
Astronomical unitMean Earth–Sun distance, 1.50 × 1011 m.
ParsecDistance at which the parallax angle is one arcsecond, 3.09 × 1016 m.
Light-yearDistance light travels in one year, about 9.5 × 1015 m.
Arcsecond1/3600 of a degree.
Apparent brightnessIntensity of starlight received, in W m-2.

Avoid these mistakes

1
Using the total shift between two observations as the parallax angle — use half.
2
Thinking a larger parallax means a larger distance — they are inversely proportional.
3
Confusing the parsec with the light-year — 1 pc is 3.26 ly.
4
Leaving the parallax angle in degrees in d = 1/p — it must be in arcseconds.
5
Assuming parallax works for any distance — the angle becomes too small.

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