IAO 1998, Практически тур — Задача 1. The masses of the Capella's components

III International Astronomy Olympiad

Внимание: Бележка към темата

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Условие

The SAO's 6-meter telescope is one of the very few telescopes used for speckle-interferometric observations of visual close binary stars. They are aimed at direct measuring of the stellar masses. You are proposed to estimate the masses of the Capella's components using of our observing data.

Capella (Alpha Aur) is a very close visual pair. Fig. 1 shows the relative orbit of the B component which is obtained on the basis of observations carried out in various observatories, including SAO, for many years. The position of the A component is marked by a cross and is connected by a straight line with the periastron point. The radial velocity curves for the both components are shown on Fig. 2. The Capella's parallax is π=0.077′′\pi=0.077''. The orbital period of the components is P=104 dP=104\,\mathrm d.

Relative orbit of Capella B, primary-star cross, periastron line, north/east directions and 50mas scale.
Observed radial velocities and orbital solution for both Capella components, with phase and velocity axes and data-set symbols.

1 Describe a 3-dimensional model of the system taking into account the eccentricity and the inclination of the orbital plane to the line of sight.

2 Estimate the masses of the components using the Kepler's third law.

3 Specify the possible sources of errors in your estimates.

Решение

Внимание: Непълно решение

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