(a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. Is it reasonable to model it as a particle?

(b) Calculate the magnitude of the angular momentum of the earth due to its rotation around an axis through the north and south poles, modeling it as a uniform sphere. Consult Appendix E and the astronomical data in Appendix F.

Astronomical Data^€ 

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Mass (kg) Orbit radius (m) Body Radius (m) Orbit period 1.99 x 1030 7.35 x 1022 3.30 x 1023 4.87 x 1024 5.97 x 1024 6.42 × 1023 1.90 x 1027 5.68 x 1026 8.68 x 1025 1.02 x 1026 1.31 x 1022 6.96 х 108 1.74 x 106 2.44 x 106 6.05 × 106 6.38 x 106 3.40 x 106 6.91 × 107 6.03 x 107 2.56 x 107 2.48 × 107 1.15 х 105 Sun 3.84 x 108 5.79 × 1010 1.08 × 1011 1.50 x 10" 2.28 x 10!1 7.78 x 10!! 1.43 × 1012 2.87 x 1012 4.50 x 1012 5.91 x 1012 Moon 27.3 d Mercury Venus 88.0 d 224.7 d Earth Mars 365.3 d 687.0 d Jupiter 11.86 y 29.45 y 84.02 y 164.8 y 247.9 y Saturn Uranus Neptune Pluto