Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s2/1/3/solution

Assume a central eclipse and nearly uniform projected speed during it. Let be the smaller radius and the larger. First-to-second contact requires travel , whereas the totality interval requires . With relative speed 200 km s,
The light curve has ingress, flat minimum and egress lasting 1.7, 0.8 and 1.7 hours. At the four contacts the projected center separations are . A noncentral chord would require an impact parameter and changes the inferred radii; the data alone do not fix that geometry exactly. For comparable masses in an ordinary coeval system, a component larger than its main sequence companion suggests expansion away from the main sequence, conventionally toward a subgiant/early giant track. That is a conditional evolutionary interpretation: neither effective temperature nor a bolometric flux is supplied, so a unique position on the Hertzsprung-Russell diagram cannot be inferred from these radii alone. Binary interactions and the assumed central chord also matter; these numbers do not establish an ordinary single-star evolutionary model.
Figure 1.
Central-eclipse contact geometry and schematic microwave sky components
. Details.

New to topics? Read the docs here!