Calculate the following for the moon and earth. Potential energy of the moon by

ID: 2250987 • Letter: C

Question

Mm-mass of moon=7.35 x 10^22 kg r-radius of moon=1.74 x 10^6 m

Me-mass of Earth=5.97 x 10^24 kg R-radius of Earth=6.4 x 10^6 m

D-distance between earth and Moon=3.84 x 10^8 m

Wm-ang. velocity of moon=1 rot/27days= 2Pi rad/27 days= 2.69 x 10^(-6) rad/s

We-ang. velocity of earth=1rot./24hrs=2Pi/24 rad/hr=7.27 x 10^(-5) rad/s.

1) P.E of moon by earths ravity= Mm x g x D=(7.35 x 10^22 kg)x(9.8 m/s^2)x(3.84 x 10^8 m)

= 2.77 x 10^32 J

2)Rotational inertia of moon by its spinning

Im=(2/5)xMmx r^2=(2/5)(7.35x10^22)[(1.74 x 10^6)^2]=8.9x 10^34 kg m^2

3)Rotational inertia of earth by its spinning

Ie=(2/5)xMex R^2 = (2/5)(5.97 x 10^24)[(6.4 x 10^6)^2]=9.78 x 10^37 kg m^2

4)Rotational K.E of moon's spinning= 0.5 Im x [(Wm)^2]=0.5 x (8.9x 10^34)x(2.69 x 10^(-6))^2

= 3.22 x 10^23 J

5)Rotational K.E of earth's spinning=0.5 Ie x [(We)^2]=0.5x(9.78 x 10^37)x(7.27 x 10^(-5) )^2

=2.58 x 10^29 J

6)Location of centre of mass of Moon Earth System(from Earths centre)

= [(Me)(0)+(Mm)(D)]/(Me+Mm)

= (7.35 x 10^22)(3.84 x 10^8)/(5.97 x 10^24 +7.35 x 10^22)

= 4.67 x 10^(6) m

7)Rotational inertia of moon about centre of mass

=(Im of moon)+(Mm x (Dm)^2) where Dm is distance from centre of mass to moon.

= (8.9x 10^34)+(7.35 x 10^22 x [(3.84 x 10^8 - 4.67 x 10^6)^2]

= 1.06 x 10^40 Kg m^2

8) Rotational inertia of earth about centre of mass

= (Ie of earth)+(Me x (De)^2) where De is the distance from centre of mass to earth

= (9.78 x 10^37)+(5.97 x 10^24 x(4.67 x 10^(6))^2 )

= 2.28 x 10^38 Kg m^2

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