Hydrostatic Equilibrium Explorer

Name: ________________________________ Section: __________ Date: __________

Station: __________ Group members: ________________________________________________

Goal: Use the demo to justify one claim about how gravity, pressure scale height, and the ideal gas law set a star’s inferred core temperature.

Station card: Hydrostatic Equilibrium Explorer (8-10 minutes) Artifact: one completed support-chain table + one claim backed by a readout and a sanity check.

1. Start from the solar-like baseline and record the readouts for $g$, $H_P$, and $T_c$.
2. Increase the mass at fixed radius. Record what happens to the pressure gradient and $H_P$.
3. Shrink the radius at fixed mass. Decide whether the star becomes more or less steeply supported.
4. Change the mean molecular weight $\mu$ and note how the ideal-gas temperature estimate responds.
5. Classify the state as under-supported, balanced, or over-supported, then explain your choice.
6. Write one claim sentence:
   • “This star needs a hotter interior because ____; evidence: ____.”

Data table

Case	$M$ ($M_\odot$)	$R$ ($R_\odot$)	$\mu$	$g$ (cm s$^{-2}$)	$H_P$ (cm)	$T_c$ (K)	Support state
Baseline
Higher $M$
Smaller $R$
Higher $\mu$

Claim + Evidence

• Claim:
• Evidence number(s):
• Sanity check:

Word bank

• Hydrostatic equilibrium: inward gravity and outward pressure balance locally.
• Pressure scale height $H_P$: the distance over which pressure changes by a factor of $e$.
• Mean molecular weight $\mu$: average particle mass in units of $m_u$; larger $\mu$ means fewer particles for the same mass density.
• Ideal gas closure: pressure depends on temperature, density, and composition.

Sanity checks

• If $g$ increases at fixed $P$, then $H_P$ should get smaller.
• If $\mu$ increases at fixed $P$ and $\rho$, then $T$ should increase.
• Hydrostatic equilibrium does not mean zero pressure; it means the pressure gradient balances gravity.
• A core-temperature estimate should scale upward with $M/R$.