We would like to compare the angular momentum of Mars about its axis of rotation with that of Earth's. The mass of Mars is 11% that of Earth, with a radius 53% that of Earth, and a rotational period 103% that of Earth. Assuming both planets to be uniform spheres calculate the ratio of the angular momentum of Mars to that of Earth.

Answer :

Manetho

Explanation:

Assume that mass of Earth is M, radius of earth orbit is R, and rotational period of Earth is T.

The angular momentum of Earth is,

 [tex]L_{z} &=M R^{2} \omega \\ &=M R^{2}\left(\frac{2 \pi}{T}\right) \\ &=\frac{2 \pi M R^{2}}{T}[/tex]

The mass of mars is, mass of Earth

=0.11 M

The radius of mars orbit is, of radius of earth

=0.53 R

The rotational period of mars is, of period of Earth

=1.03 T

The angular momentum of mars is,

[tex]L_{m}=\frac{2 \pi(0.11 M)(0.53 R)^{2}}{1.03 T}[/tex]

The angular momentum of mars is,

[tex]L_{m}=\frac{2 \pi(0.11 M)(0.53 R)^{2}}{1.03 T}[/tex]

The ratio of angular momentum of mars to that of earth is,

[tex]\frac{L_{m}}{L_{E}}=\frac{\frac{2 \pi(0.11 M)(0.53 R)^{2}}{1.03 T}}{\frac{2 \pi M R^{2}}{T}} \\ \frac{L_{m}}{L_{E}}=0.03 \\ \frac{L_{m}}{L_{B}}=3.0 \times 10^{-2}[/tex]

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