Equations Labeled Flashcards
(27 cards)
What is the parallax formula for distance?
d = 1 / p (p in arcseconds, d in parsecs). A smaller angle means the star is farther away.
What is the formula relating luminosity, distance, and flux?
L = 4 × π × d² × F. It shows how a star’s total brightness depends on its distance and how bright it looks from Earth.
How are apparent and absolute magnitudes related?
m − M = 5 × log₁₀(d / 10 pc). This shows how a star’s observed brightness changes with distance.
What is Wien’s Law?
λ_max × T = 2.9 × 10⁻³ m·K. Hotter stars shine at shorter (bluer) wavelengths.
What is the equation of hydrostatic equilibrium?
dP/dr = -G × m(r) × ρ(r) / r². Pressure balances gravity so stars don’t collapse.
What is the mass continuity equation?
dm/dr = 4 × π × r² × ρ(r). This tells how mass builds up as you move outward in a star.
What is the luminosity gradient equation?
dL/dr = 4 × π × r² × ρ × ε. This tells how much light is produced in each shell of the star.
What is the radiative temperature gradient equation?
dT/dr = - (3 × κ × ρ × L) / (16 × π × a × c × r² × T³). It shows how fast temperature drops due to radiation trying to escape.
What is the ideal gas law for stars?
P = ρ × k × T / (μ × m_H). This shows how particle collisions create pressure in stars.
What is the formula for mean molecular weight?
1/μ = Σ(Xᵢ / Aᵢ). It gives the average particle mass depending on composition.
What is the pressure relation for non-relativistic degenerate electrons?
P ∝ ρ^(5/3). Cold dense electron gas can still push back — applies to white dwarfs.
What is the pressure relation for relativistic degenerate electrons?
P ∝ ρ^(4/3). At extreme densities, pressure rises slower — makes white dwarfs unstable if too massive.
What is the energy released during fusion?
Q = (mass of reactants − mass of products) × c². Mass turns into energy when atoms fuse.
What is the nuclear reaction rate formula?
r = n₁ × n₂ × ⟨σv⟩. Reactions happen when particles meet often and react easily.
What is the power per unit mass formula?
ε = r × Q / ρ. This shows how much energy each kilogram of stellar material produces.
What reactions occur in the triple-alpha process?
2 He-4 → Be-8, then Be-8 + He-4 → C-12. Helium nuclei fuse into carbon in very hot stars.
Which stars undergo the CNO cycle?
Stars with mass > 1.3 M☉. They use carbon, nitrogen, and oxygen to fuse hydrogen faster.
What is the Virial Theorem?
2U + Ω = 0, so U = -Ω/2. Stars are stable when thermal and gravitational energies are balanced.
What is the dynamical timescale?
τ_dyn = √(R³ / G × M). How fast a star would collapse if pressure disappeared.
What is the Kelvin–Helmholtz timescale?
τ_KH = G × M² / (R × L). Time a star could shine using just gravity energy.
What is the nuclear timescale?
τ_nuc = ε × M / L. The time a star can shine using nuclear fusion — very long.
What triggers a Type Ia supernova?
White dwarf exceeds the Chandrasekhar limit (~1.4 M☉). It collapses and explodes from runaway carbon fusion.
What happens in a Type II supernova?
Iron core collapses, leaving a neutron star or black hole. Happens in very massive stars.
What is the solar neutrino flux at Earth?
~7 × 10¹⁴ νₑ / m² / s. Tons of neutrinos fly through you from the Sun every second.
