Chapter 13, Problem 045 Your answer is partially correct. Try again. A certain s

Question

Chapter 13, Problem 045 Your answer is partially correct. Try again. A certain satellite travels in an approximately circular orbit of radius 9.4 × 106 m with a period of 5 h 23 min. Calculate the mass of its planet from this information. Uni umber [253666835400000000000ntsTkg the tolerance is +/-690 Click if you would like to Show Work for this question: Open Show Work SHOW HINT LINK TO TEXT Link to Sample Problem Link to Sample Problem Math Help By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor. Question Attempts: 2 of 3 used SAVE FOR LATER SUBMIT ANSWER

Explanation / Answer

Using force balance on satellite

Fg = Fc

G*M*m/r^2 = m*V^2/r

V = sqrt (G*M/r)

Time period is given by

T = 2*pi/w = 2*pi*r/v

T = 2*pi*sqrt (r^3/GM)

M = 4*pi^2*r^3/(G*T^2)

Using given values:

G = 6.67*10^-11

M = mass of planet = ?

r = radius of orbit = 9.4*10^6 m

T = 5 hr 23 min = 323 min = 19380 sec

So,

M = 4*pi^2*(9.4*10^6)^3/(6.67*10^-11*19380^2)

M = 1.31*10^24 kg

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