Binary Orbits: Two-Body Dance

Name: ________________________________ Section: __________ Date: __________

Station: __________ Group members: ________________________________________________

Goal: Use the demo to make a claim supported by (1) at least one number/readout and (2) at least one sanity check.

Station card: Binary Orbits (6–8 minutes) Controls: mass ratio $m_2/m_1$, separation $a$ (AU)
Readouts: barycenter offset from $m_1$ (AU), orbital period $P$ (yr)

Your station artifact (fill in):

1. Observation: Compare an equal-mass case ($m_2/m_1=1$) to an unequal-mass case (try $m_2/m_1=5$). What happens to the barycenter offset from $m_1$?
2. Rule: Write a relationship between orbit sizes and masses (in words or a ratio).
3. Prediction: If the total mass increases while separation stays the same, what happens to the period (bigger/smaller, and why)?
4. Data artifact: Record two snapshot rows (equal vs unequal) and compare the readouts.
5. Connection sentence: “This connects to another course idea because…”

Word bank + sanity checks Word bank:

• Barycenter: the center of mass; both bodies orbit this point.
• Mass ratio: if one mass is larger, the barycenter sits closer to that body.
• Orbit size about the barycenter: the more massive body has the smaller orbit.
• Kepler scaling: at fixed separation, higher total mass means a shorter period.

Key relationship (mass vs orbit size):

$$\frac{a_1}{a_2}=\frac{M_2}{M_1}$$

Sanity checks:

• If $M_1=M_2$, both orbits should be the same size (mirror symmetry).
• Increasing $m_2/m_1$ moves the barycenter farther from $m_1$.
• Increasing total mass (at fixed $a$) decreases the period ($P \propto (M_1+M_2)^{-1/2}$).