Question

Question 16 Exoplanets A and Barberved to orbe Star Xin circular orbits a distances 11 AU and 102 AU from Star X respectively ( 1 U - 15 x 10" Theor period of Exoplanet Ais 24 days. What is the mass of Star X11 day 400 50x10 45x10 150 20x10 1010 35.10 40x10 30.10 2.510

Answer 1

Here is the solution provided below in the hand written mode. Hope you will find it helpful.

Here Kepler's 3rd law is used but in a modified form due to exoplanet condition.

Variation in the star's mass 0 Solution : For our solar sy stem and planet around stars our sun, that states , ow with the some mass as R is a a planets distance where R=T3 from the sun in in Astronomical Units Cau), and Tis the planet's orbital mas period in years For exoplanets, we must modify the formula to compared with our 1. So, ... R = 3/7²ms sum .() where, Ms the stars mass in relation to sun's mass. ours Here given, Radius of arebit...of explanet, A., , 1 RA= 1.1 AU - 10.2 AV exoplanet B B, RB Radius of orbit of Orbital period of exoplanet, A, T = 244 days 0.67 years

So from equation @, R= 35T? Ms . 다. R² = TYMs = ) Ms R- T2 10:25 3 . (0.67) -> Ms. 2.96 Hence, the mass of star X. is 2.96 times the Sun. mass of 1 yl mass of star X x, My 2.96 X solar mass 72196 X 1.989 X10 kg 30 [since, 1 solar mass - 1.989x10 30 kg 30 5.88 x 10 ка Hence, option (i) is correct