Make the knowledge answer back.

A star has luminosity 4.0 × 10²⁶ W and is 10 pc away. Calculate its flux at Earth in W m⁻².

If the adopted distance is 10% too small, approximately how many percent too small is the inferred luminosity?

Which quantity controls a circular aperture’s diffraction scale?

Write observation, calibration, model, inference, and alternative entries for the claim “an atmosphere contains molecule X.”

Using GM☉ = 1.327 × 10²⁰ m³ s⁻² and r = 1.496 × 10¹¹ m, calculate circular speed in km/s.

A planet orbits the same star at four times Earth’s radius. What is its circular speed as a fraction of Earth’s?

At four times Earth’s orbital radius, what is the period in Earth years?

Why does a rotation speed determine total gravitating mass but not identify what that mass is made of?

A spectrum peaks near 500 nm. Estimate temperature in kelvin using b = 2.898 × 10⁻³ m K.

A 656.28 nm line is observed at 656.50 nm. Estimate radial velocity in km/s.

Why do nearly identical design-matrix columns make individual fitted depths unstable?

What does a coherent pattern in fit residuals most directly suggest?

For RJ/R☉ ≈ 0.100, calculate the transit depth in percent.

For R⊕/R☉ ≈ 0.00916, calculate transit depth in ppm.

If one transit has signal-to-noise 2, how many independent equal-quality transits are needed for signal-to-noise 8?

Explain the complete chain required to turn a transit light curve into planet density.