A high-precision parallax is 0.2 arcsec. Find the simple inverse-parallax distance.
Answer and explanation
5 pc
d=1/0.2=5 pc.
Subjects
Stellar astronomy
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Sample exercises
Convert 20 milliarcseconds to arcseconds.
Answer and explanation
0.02 arcsec
Divide milliarcseconds by 1000.
For a high-precision parallax of 0.01 arcsec, find distance.
Answer and explanation
100 pc
d=1/0.01.
Which angle enters d(pc)=1/p(arcsec)?
- The telescope elevation
- Twice the parallax angle without adjustment
- Any sky angle
- The conventional parallax angle
Answer and explanation
The conventional parallax angle
The convention already incorporates the one-AU baseline geometry.
Why is a noisy parallax near zero difficult to invert?
Answer and explanation
The reciprocal is highly nonlinear and can produce extreme values; negative noisy estimates have no direct positive-distance reciprocal interpretation. A statistical distance model is needed.
Credit nonlinearity and uncertainty.
What does a distance ladder connect?
- Methods calibrated over different distance regimes
- Only physical ladders on telescopes
- The order of Moon phases
- Only planet sizes
Answer and explanation
Methods calibrated over different distance regimes
Linked calibrations extend distance estimation across scales.
Study notes
Parallax and the astronomical distance ladder
Annual stellar parallax measures a small apparent angular displacement using Earth's orbital baseline. In the conventional units, d(pc)=1/p(arcsec).
UniversityParallax and the astronomical distance ladder · revision notes
Annual stellar parallax measures a small apparent angular displacement using Earth's orbital baseline. In the conventional units, d(pc)=1/p(arcsec).
UniversityFlux, luminosity and stellar magnitudes
Luminosity is emitted power; flux is received power per area. For isotropic emission with negligible absorption, F=L/(4πd²).
UniversityFlux, luminosity and stellar magnitudes · revision notes
Luminosity is emitted power; flux is received power per area. For isotropic emission with negligible absorption, F=L/(4πd²).
UniversityStellar structure and main-sequence scaling
A hydrostatic star balances inward gravity with an outward pressure gradient. Equilibrium does not mean pressure is uniform.
UniversityStellar structure and main-sequence scaling · revision notes
A hydrostatic star balances inward gravity with an outward pressure gradient. Equilibrium does not mean pressure is uniform.
UniversityStellar evolution and compact remnants
A star's mass and composition strongly influence its lifetime and later evolution. One single life-cycle diagram is not valid for every star.
UniversityStellar evolution and compact remnants · revision notes
A star's mass and composition strongly influence its lifetime and later evolution. One single life-cycle diagram is not valid for every star.
UniversityParallax distance in parsecs
Use a positive parallax in arcseconds. Reciprocal inversion of noisy parallaxes needs additional statistical care.
UniversityParallax distance in parsecs · formula reference
Use a positive parallax in arcseconds. Reciprocal inversion of noisy parallaxes needs additional statistical care.
UniversityMagnitude difference from a flux ratio
The fluxes must refer to the same measurement band and calibration convention.
UniversityMagnitude difference from a flux ratio · formula reference
The fluxes must refer to the same measurement band and calibration convention.
UniversityDistance from an unextinguished distance modulus
This simplified model neglects extinction. Apparent and absolute magnitudes must use the same band.
UniversityDistance from an unextinguished distance modulus · formula reference
This simplified model neglects extinction. Apparent and absolute magnitudes must use the same band.
UniversityRelative luminosity of a blackbody star
Use the effective-temperature blackbody luminosity model and compare the same reference quantities.
UniversityRelative luminosity of a blackbody star · formula reference
Use the effective-temperature blackbody luminosity model and compare the same reference quantities.
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