Question

Exoplanets A and B are observed to orbit Star Xin circular orbits at distances 1.1 AU and 10.2 AU from Star X, respectively ( 1 AU = 1.5 x 1011 m). The orbital period of Exoplanet A is 244 days. What is the mass of Star X? (1 day = 86400 s.) O 1.0x 1030kg O 5.0x 1030 kg 04.0x 1030 kg 3.0 x 1030 kg O 2.5 x 1030 kg O 3.5 x 1030kg O 4.5 x 1030 kg O 2.0 x 100 kg O 1.5 x 100 kg

Answer 1

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1) The cestrepetal trepetal force of force of A is is provided by the force of gravitation between x and A. ú censtrepetal force, má mar? amma (1) mass of A my-mass of v- velocity of A re A ů جم سرا = ama NA (2)

TA-orbital V S RINA period of A 5.9797 X 1050 But velocity (tangential - (3) To sub. (3) in 22 299 cimy Max 244x864005 TA NA ? 3 ü २ = TA cz 27 l'1X1.5X10 (21 6.673x10 Nm? Kg? kg

as shown in 22 This is the relative distance the figure, d= ro-NA = 10:2-11 AU 9.1 AU 3 By the definition of angle spanned by a raclius vector (r) with length is cs) e = S 2 but here, ro d No = do do 9.1 X1.5X10m x 4-25X10 107 0.58x20lm - = 0.588106 km

= (20 1.65x86400 S 6.673x1 Nm? kg? 5.68x10²7kg =
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