Read Binary Orbits: Use the Separation in Kepler's Law
A binary system follows Kepler's third law using the separation of the two stars and their total mass. Both stars share one angular period.
Motion and force questions become simpler when direction, starting condition, time and the acting forces are marked first.
Start with the condition
Use T² = 4 π squared d³/[G(M1 plus M2)]. The individual orbital radii affect speeds, not the common period once separation is known.
Build the governing relation
Keep astronomical units and solar masses in the solar-system form of Kepler's law consistently.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Calculating two different periods for the two stars confuses their different orbit radii with their shared angular motion.
Ready to try the pattern?
100% coverage across the linked question.
Practise the linked question