Question

3. The following table comes from an article "7 Earth-sized planets circle nearby star," from Science News, March 18, 2017. Planetary lineup Seven Earth-sized planets (illustrated) have been found in orbit around the ultracool dwarf star TRAPPIST-1. Astronomers already know many characteristics of these planets. (By convention, the first exoplanet discovered in a system is designated b.) Orbitdl 151 days 2.42 days 4.05 days 6.10 days 9.21 days 12.35 days -20 days sac AU 0.015 AU 0021AU 0028 AU 0.037 AU 0045 AU 006AU rt1.09 Rem 106Ru 0.77Ra02 Rer 1.04 Ru 113Reh 076 Re Distance to star radius 109 Re 1.06 Planet 0.85 | 0.85 MErt1: 1.38 MEarth I 0.41 MEarth | Ο.62 MEarth i O.68 MEarth 1.34 MEarth | Unknown 1 astronomical unit-149.6 million kilometers mass 6 SCIENCE NEWS March 18. 2017 Answer the following: a. (4 pts) The light curve from this star will have many "dips" due to the seven planet Would the dips vary greatly in size or would they vary minimally in size? Explain. b. (6 pts) Approximately, what is the mass of Trappist-1?

Answer 1

(a) The amount of dip will depend on the size of the planet, and the distance of the planet from its sun. Here we can see that the distance between the star and planets do not differ much, and also the size of the planets is almost same. Hence the dips will not vary much in size.

(b) For finding the mass of Trappist 1 we can take any data points of star. From period equation we can write, the mass of star as,

4-газ GT2 m, =

Substituting values we get, the mass of star as (Taking the first data point)

4m2 ( 0,011 x 149.6 x 106)3 G( 1.51 x 24 x 60 x 60)2-. 1091.55 x 1030 ko '