Practice Problem 6.10 Suppose we want to place a weather satellite into a circul

Question

Practice Problem 6.10 Suppose we want to place a weather satellite into a circular orbit 300 km above the earth's surface. What speed, period, and radial acceleration must it have? The earth's radius is 6380 km 6.38 x 106 m. and its mass is 5.98 x 24 kg of 1 Figure 1 Earth 6680 km 6380 km me 598 x 10 kg Part A Practice Problem: Find the speed for an earth satellite that has a period of 2.5 day (216000 s Express your answer in meters per second to three significant figures m /S Submit My Answers Give U Incorrect, Try Again, 4 attempts remaining Part B Practice Problem: Find the orbit radius for an earth satellite that has a period of 2.5 day (216000 s Express your answer in meters to three significant figures. Submit My Answers Give Up Provide Feedback Continue

Explanation / Answer

a)
we know, T^2 = 4*pi*r^3/(G*Me) (Here T is time periode and r is radius of orbit)

so, r = (T^2*G*Me/(4*pi^2))^1/3

= ((2.5*24*60*60)^2*6.67*10^-11*5.98*10^24/(4*pi^2))^(1/3)

= 7.780*10^7 m

now Apply,

orbital speed, Vo = 2*pi*r/T

= 2*pi*7.78*10^7/(2.5*24*60*60)

= 2263.110 m/s

b) we have found in the above

radius of orbit, r = 7.780*10^7 m/s

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