#10 a (10%) Problem 10: A geosynchnecos Earth atellite is one lie has an cebital

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#10 a

(10%) Problem 10: A geosynchnecos Earth atellite is one lie has an cebital period of peecisely 1 day Such orbits are usefal for Satelite Awerage orbital radius rom) Pered T)Irmly) unication and weather observation because the saellite remains above the same point ou Earth (iprovided it orbits in the Sen equatorial plane in the same direction as Earth's rotation 1.01xIo19 3.35x 1074 3.35x 104 000485 (1.710|319x10" ided it orfsits in the sun 1 496x 10* 7,710 4.22x 10 Europa 67x10 Ganymede 107x0 188x10 0.00972 (355) 3.210x10 00457 asa)o) 3.20×1011 theespertta.com Qa Calculate de rains of such orbit based on the dats for the moon in th-ini e in km Potential 100 atan) acotansin etailed vie DegreesRadias Hia: deduction per hnt Hts resouine 2

Explanation / Answer

Newton's version of Kepler's Third: (T² / D³)_a = (T² / D³)_b

If "a" is the moon, the table gives us T² / D³ = 1 / 1.01e19km³/y². Then

1 / 1.01e19km³/y² = (1day * 1y / 365.25day)² / D³

D³ = 7.57e13 km³

D = 42,300 km radius of geosynchronous orbit

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