method

cosmic distance ladder

A sequence of methods to measure astronomical distances using standard candles and rulers.
24 related articles · 4 formulas

Description

The cosmic distance ladder is a sequence of methods used by astronomers to measure distances to celestial objects, each rung building on the previous one. It starts with nearby objects whose distances can be measured directly, then uses those to calibrate brighter or more distant standard candles and rulers. This step-by-step approach allows us to extend our reach from the solar system to the edge of the observable universe, providing the foundation for determining the scale of the cosmos and the rate of its expansion.

History

The concept was formalized in the early 20th century, with Henrietta Swan Leavitt's discovery of the period-luminosity relation for Cepheids in 1912, and Edwin Hubble's subsequent use of them to show that galaxies are receding from us, leading to the discovery of cosmic expansion in 1929.

How it works

The ladder begins with parallax, where the apparent shift of a nearby star against distant background stars is measured as Earth orbits the Sun. This gives distances to stars within a few thousand light-years. The next rung uses Cepheid variable stars, whose pulsation period is directly related to their intrinsic brightness; by comparing this to their apparent brightness, their distance can be found. These Cepheids are then used to calibrate even brighter standard candles, such as Type Ia supernovae, which can be seen across billions of light-years.

In practice

The cosmic distance ladder is essential for measuring the Hubble constant, the rate of cosmic expansion, and for mapping the large-scale structure of the universe. It is used in projects like the Hubble Space Telescope's Key Project and the Gaia mission to refine distance measurements.

Fun fact

The ladder has a built-in tension: measurements of the Hubble constant using the distance ladder (74 km/s/Mpc) disagree with those inferred from the cosmic microwave background (67 km/s/Mpc), hinting at possible new physics.

Concept graph →

Formulas

$$P \propto d^2$$
Transmitter power scales with the square of distance.
What is in the formula
PvariableTransmitter power — power watt
dvariableDistance from the transmitter — distance metre
∝operatorIndicates that the left side scales with the square of the right side — proportionality
{эиим}_{{lim}}\approxn_σ(\frac{σ_ν}{100{ян}})(\frac{d}{1{пк}})^21.2*10^{11}{вт} · 2606.04304v1
$$m - M = 5 \log_{10} \left( \frac{d}{10\,{\rm pc}} \right)$$
Relates apparent and absolute magnitudes to distance.
What is in the formula
mvariableapparent magnitude — apparent magnitude
Mvariableabsolute magnitude — absolute magnitude
dvariabledistance to the object — distance parsec
log10operatorbase-10 logarithm — logarithm base 10
m_{\rmbar}-m_{\rmbar}=5\log_{10}(\frac{d}{10{\rmpc}}) · 2606.05144v2
m-m=5\log_{10}(d/10) · 2606.26831
μ=m-m=5\log_{10}(d_l/{пк})-5 · 2607.03569
μ=m-m=5\log_{10}(\frac{d_l}{{мпк}})+25 · 2607.06959
$$r_{\text{snow}} \propto \sqrt{L}$$
Snow line distance scales with square root of luminosity.
What is in the formula
r_snowvariableDistance from star to snow line — distance metre
LvariableStellar luminosity — luminosity watt
∝operatorProportional to — proportionality
r_{{snow}}\approx2.7\sqrt{l/l_☉}{а.е.} · 2607.15144
$$D_L(z) = \frac{c(1+z)}{H_0} \times \begin{cases} \frac{\sinh\left(\sqrt{\Omega_k}\chi(z)\right)}{\sqrt{\Omega_k}} & \Omega_k>0 \\ \chi(z) & \Omega_k=0 \\ \frac{\sin\left(\sqrt{-\Omega_k}\chi(z)\right)}{\sqrt{-\Omega_k}} & \Omega_k<0 \end{cases}$$
Luminosity distance depends on redshift and cosmological parameters.
What is in the formula
D_Lvariableluminosity distance — photometric distance metre
zvariableredshift — redshift
χvariablecomoving distance — comoving distance metre
Ω_kvariablecurvature density parameter — curvature density parameter
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
H_0constantcurrent expansion rate of the universe — hubble constant = 2.2e-18 per second
sinhoperatorhyperbolic sine function — hyperbolic sine
sinoperatorsine function — sine
√operatorsquare root — square root
d_l(z)=\frac{c(1+z)}{h_0}*\begin{cases}\frac{\sinh(\sqrt{ω_k}χ(z))}{\sqrt{ω_k}}&ω_k>0\χ(z)&ω_k=0\\frac{\sin(\sqrt{-ω_k}χ(z))}{\sqrt{-ω_k}}&ω_k<0\end{cases},\qua · 2606.04216v1

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