lass Management I Help mework 5 Begin Date: 2/15/2018 12:00:00 AM-Due Date: 3/7/
ID: 1584197 • Letter: L
Question
lass Management I Help mework 5 Begin Date: 2/15/2018 12:00:00 AM-Due Date: 3/7/2018 11:59.00 PM End Date: 3/7/2018 11:59:00 PMM (4%) Problem 18: A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite Earth Moon 3.84xI0 remains above the same point on Earth (provided it orbits in the Sun equatorial plane in the same direction as Earth's rotation). Parent Satellite Average orbital radius nkm) Period T0) 0.07481 1.000 11.86 0.00485 (1.77 3. 19x1021 0.00072 (3.55 ) 3.20x 1021 00196 (7.16 3.191021 0.0457 (16.19 6)3.20x 101 |?(km,y 101x1019 3.33x1024 Earth 1.496x10 upiter 7.783x 24 4.22x 10 lo Europa 6.71x 10 Ganymede 1.07x 10 Callisto 1.88x 10 Ctheexpertta.con Calculate the radius of such an orbit based on the data for the moon in the figure in km. Grade Summary Deductions Potential 100% cotanO asi acos( atanO acotan sinhO cosh tn cotanho+ Submissions Attempts remaining 2 00 per attemmpt) detailed vievw : Degrees Radians Submit Hint I give up Hints:-deduction per hint. Hints remamng:- Feedback: deduction per feedback.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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