Question

Example 9.5 The planet Mars has two
moons, phobos and delmos. (i) phobos has
a period 7 hours, 39 minutes and an orbital
radius of 9.4 x103 km. Calculate the mass
of Mars. (ii) Assume that Earth and Mars
move in circular orbits around the sun,
with the Martian orbit being 1.52 times the
orbital radius of the earth. What is the
length of the Martian year in days ?
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Answer 1

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Answer 2

(i) Here,

T=7hours,39minutes

              =459minutes=(459×60)s,

r=9.4×103km=9.4×106m

If m is the mass of phobos and Mm is the mass of mars, then

GMmm/r^2=mrω^2=mr4π^2/T^2

or Mm=4π^2r^3/GT^2

=[4×(3.14)^2×(9.4×106)^3]/[6.67×10−11×(459×60)^^2]

=6.48×1023kg

(ii) If r1,r2 is the distance of Earth and Mars from the sun and T1,T2 are the periods of revolution of Earth and Mars around the sun, then

T2=(r2r1)3/2×T1=(1.52)3/2×365

=684days