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5 5 - Start y Ch13 Hw - PHYS 211 Fax + V O - h X ... E → 0 A https://www.webassign.net/web/Student/Assignment-Responses/last?dep=22570931 O ☆ Tutorial 5. + 0/4 points Previous Answers OSUniPhys1 13.4.WA.031. Tutorial. My Notes + Ask Your Teacher Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 45.8 km/s, and v2 = 59.8 km/s respectively. (a) If the period of the first planet P, is 7.10 years, what is the mass of the star it orbits around? 513000000000 The gravitational force of the star on the planet supplies the centripetal force needed to keep the planet in its circular orbit. ka (b) Determine the orbital period of Pz. 318 yr Additional Materials eBook Tutorial Viewing Saved Work Revert to Last Response Submit Assignment Save Assignment Progress Home My Assignments Extension Request Copyright © 2019 Cengage Learning, Inc. All Rights Reserved o O o PDF Type here to search PDF E My * 8:49 PM 11/13/2019

Answer 1

here,

a)

the period of satellite , T = 7.1 yrs = 7.1 * 3600 * 365 * 24 s

let the radius of orbit be r1

the circumference of orbit = 2*pi*r1 = T * v1

2*pi*r1 = 7.1 * 3600 * 365 * 24 * 45.8 * 10^3

solving for r1

r1 = 1.62 * 10^13 m

let the mass of the star be M

the time period , T = 2*pi* sqrt(r1^3 /(G * M))

7.1 * 3600 = 2*pi*sqrt((1.62 * 10^13)^3 /(6.67 * 10^-11 * M) )

solving for M

M = 3.85 * 10^42 kg

the mass of star is 3.85 * 10^42 kg

b)

P2 /P1 = (r2 /r1)^3/2

P2 /P1 = ( (v2 * P2) /(v1 * P1))^3/2

(P2/P1)-1/2 = ( v2 /v1)^3/2

(P1/P2) = ( v2 /v1)^3

7.1 /P2 = (59.8 / 45.8)

P2 = 5.44 yrs

the new period is 5.44 yrs