AST common mistakes
AST · Understand the traps and how to avoid them.
When asked to find the peak wavelength of a blackbody or the flux ratio between two bands, the candidate plugs numbers into Wien's law or the Planck function without first converting temperature to kelvin and wavelength to metres, then reports an answer off by orders of magnitude (e.g., angstroms treated as metres).
The constants in Wien's law and Stefan-Boltzmann carry SI units, but the problem statements habitually give temperatures in thousands of kelvin and wavelengths in nanometres or angstroms. Under time pressure, candidates pattern-match to a memorised formula and skip dimensional bookkeeping, and the arithmetic is done in a single mental step rather than written out.
What to do instead
Write the unit-conversion line explicitly before substituting: T in K, lambda in m, flux in W m^-2. Carry units through the calculation and check that the final unit matches what was asked. For ratio problems, note that unit factors cancel, which is a fast self-check on whether a conversion was even needed.
The candidate computes a star's luminosity or main-sequence lifetime from mass and radius but uses solar units inconsistently, mixing L/L_sun with L in watts, or applies the mass-luminosity relation outside its valid range (e.g., to a red giant or a very low-mass star).
Scaling relations such as L proportional to M^3.5 are memorable and easy to over-apply. Candidates learn them as universal laws rather than main-sequence fits, and the solar-normalised form invites dropping the L_sun factor when the answer is requested in SI.
What to do instead
State the relation's assumptions in one line before using it: main-sequence hydrogen burning, roughly solar composition, mass between about 0.5 and 10 solar masses. For evolved stars, compute luminosity from the Stefan-Boltzmann law using radius and effective temperature instead. Keep a running ledger of which quantities are in solar units and convert once at the end.
Given a rotation curve or velocity dispersion, the candidate estimates a galaxy's dynamical mass but forgets the gravitational constant, the factor of G, or the conversion from km/s to m/s, and reports a mass that is wrong by many orders of magnitude; alternatively, they use the virial theorem with the wrong coefficient for the geometry.
Dynamical mass formulas (M = v^2 r / G, or M = sigma^2 R / G with a geometric factor) are short and look trivial, so candidates substitute directly in mixed units. The virial coefficient depends on the assumed density profile, which is rarely stated explicitly in problems.
What to do instead
Convert velocities to m/s and radii to metres first, then divide by G = 6.67e-11 in SI. For the virial theorem, write the coefficient you are assuming and why (e.g., 5R sigma^2/G for a uniform sphere, or a stated factor of order unity for an isothermal sphere). Sanity-check the result against a known mass scale, such as 1e11 solar masses for a Milky Way-like spiral.
The candidate calculates orbital or escape velocity using the mass of the orbiting body instead of the central body, or forgets to add the radii when computing surface gravity for a close binary or a planet skimming its star.
Kepler's third law and the vis-viva equation are usually memorised as v = sqrt(GM/r) without the m1 + m2 term. When the problem involves two comparable masses, candidates default to the central-mass approximation, and for surface quantities they plug the radius alone where the separation is the sum of two radii.
What to do instead
Before substituting, identify the central or total mass and write the general form (v^2 = G(m1 + m2)(2/r - 1/a)). Check whether the secondary mass is negligible; if not, use the sum. For surface gravity or Roche geometry, confirm whether the relevant distance is a single radius or the separation between centres.
When interpreting a spectrum or spectral energy distribution, the candidate identifies a spectral line's rest wavelength but does not apply the redshift before comparing with an observed wavelength, or applies the relativistic Doppler formula where the classical one is appropriate (or vice versa) without checking the velocity regime.
Redshift is introduced early and then treated as a separate topic, so candidates see an observed wavelength and reach for a line-identification table without the (1 + z) factor. The distinction between z = v/c and the relativistic form is blurred because both reduce to the same expression at low velocity.
What to do instead
Always state the observed-to-rest relation lambda_obs = lambda_rest (1 + z) and solve for whichever quantity is unknown before consulting line tables. Check the velocity: if v is more than about 0.1c, use the relativistic Doppler formula and verify the sign convention (blueshift for approach).
The candidate estimates a molecular cloud's Jeans mass or free-fall time but uses the wrong density (number density instead of mass density), omits the mean molecular weight, or applies the isothermal Jeans criterion to a region that is clearly not isothermal.
Jeans analysis involves several conversion steps (number density to mass density via mu and m_H) that are easy to collapse or skip. The criterion is often memorised as a single formula with an unspecified constant, and candidates do not check whether the temperature and density assumptions hold.
What to do instead
Convert number density to mass density explicitly: rho = mu m_H n, with mu about 2.3 for molecular gas. Write the Jeans mass with the constant you are using and note its order-of-magnitude nature. State whether the gas is isothermal or adiabatic and why that choice is appropriate for the cloud being considered.
The candidate computes a planet's equilibrium temperature or surface gravity but uses the planet's radius where the stellar radius or orbital distance belongs, or neglects the bond albedo and greenhouse terms while presenting the result as a surface temperature.
Equilibrium temperature formulas are compact and the symbols (R_star, a, R_planet) are visually similar. Candidates also conflate equilibrium temperature with actual surface temperature, which requires an atmosphere model, and so over-interpret the number.
What to do instead
Label each symbol in the formula before substituting: T_eq depends on stellar luminosity or T_star and R_star, and on orbital distance a, not on the planet's radius. Report the result explicitly as an equilibrium (effective) temperature and state that the surface temperature requires albedo and atmospheric treatment.
When asked about telescope sensitivity or exposure time, the candidate scales exposure linearly with source flux or ignores the distinction between source-limited and background-limited regimes, and forgets that signal-to-noise grows as the square root of time.
The signal-to-noise relation is conceptually simple but candidates default to proportional reasoning. The background-limited case (S/N proportional to sqrt(t)) and the source-limited case (S/N proportional to t) look similar in formula sheets, and the noise terms (source, sky, dark, read) are often collapsed into one.
What to do instead
Write the full S/N expression with each noise term and identify which term dominates for the given conditions. Then solve for exposure time in the appropriate regime. Check the scaling: doubling exposure should improve S/N by about 1.41 in the background-limited case, not by 2.
The candidate derives a stellar structure scaling relation (e.g., central temperature or pressure from hydrostatic equilibrium) but drops a factor of order unity or a power of radius, producing a scaling that is dimensionally inconsistent or that fails a simple limiting-case check.
Order-of-magnitude derivations reward speed, and candidates treat the constants as unimportant rather than tracking them. Because the result is a scaling law, dimensional analysis alone does not catch a wrong exponent, and candidates rarely test the result against a known case such as the Sun.
What to do instead
Derive with explicit constants (e.g., dP/dr ~ -GM rho / r^2, so P_c ~ GM^2 / R^4), then check dimensions and evaluate the scaling for solar values to confirm it reproduces the known central temperature and pressure within a factor of a few. State which factors of order unity were dropped.
The candidate answers a conceptual question about energy transport, nucleosynthesis, or stellar endpoints by reciting a sequence (e.g., 'main sequence, red giant, planetary nebula, white dwarf') without conditioning on initial mass, so a 25 solar-mass star is described as ending as a white dwarf.
Evolutionary sequences are learned as a single narrative, usually anchored to the Sun. The mass-dependent branches (electron-capture supernovae, pair-instability, black hole formation) are less familiar, and under exam pressure candidates reproduce the memorised solar track.
What to do instead
Before answering, state the initial mass range and select the corresponding endpoint: below about 8 solar masses leads to a white dwarf via a planetary nebula; above about 8 to 10 solar masses leads to a core-collapse supernova and a neutron star or black hole, with the exact boundary depending on mass loss and metallicity. Make the mass dependence explicit in the answer.