Cfp o

Fig. 4.8 Geometry of contact times. Part (a) shows the relative orbit of the secondary around the primary for inclination i = 90°. Part (b) shows a total eclipse for i = 90°; note that it is not a central eclipse. Part (c) shows a partial eclipse for i = 90°. Together parts (a), (b), and (c) illustrate that contact times alone cannot determine relative star dimensions, despite the impression given in many elementary textbooks, because the inclination ordinarily is not known ti t, t3 t4

Fig. 4.8 Geometry of contact times. Part (a) shows the relative orbit of the secondary around the primary for inclination i = 90°. Part (b) shows a total eclipse for i = 90°; note that it is not a central eclipse. Part (c) shows a partial eclipse for i = 90°. Together parts (a), (b), and (c) illustrate that contact times alone cannot determine relative star dimensions, despite the impression given in many elementary textbooks, because the inclination ordinarily is not known

8 See Section 2.8 for details on how to select star 1 and star 2.

occurs nearer to apastron is the longer one. However, it is not so easy to make firm estimates of sizes, temperatures, or luminosities as it is for circular orbits because the projected surface area involved in each eclipse is not necessarily the same. Again, for low eccentricities, the estimate is just a bit rougher than for e = 0.

3. In eccentric orbit cases, the quantities e cos œ and e sin œ may be estimated from the separation and durations (widths) of the eclipses, respectively. The relations (3.1.25) and (3.1.26) provide approximations for e and œ separately and give us tan œ

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