Problema Solution
The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth) and inversely as the orbital velocity. If a satellite completes an orbit 700 miles above the earth in 9 hours at a velocity of 34000 how long would it take a satellite to complete an orbit if it is at 1600 miles above the earth at a velocity of 33,000 (Use 3960 as the radius of the earth.) Round your answer to the nearest hundredth of an hour
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let
t = the time
r = the radius of the orbit from the center of the Earth
v = the orbital velocity
R = 3,960 mi the radius of the earth
The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth) and inversely as the orbital velocity:
t = k*(r/v), where k is constant
the satellite completes an orbit 700 miles above the earth in 9 hours at a velocity of 34000:
in this case
t = 9 hr
r = 700 + R = 700 + 3960 = 4,660 mi
v = 34,000 mph
9 = k((700 + R)/34000)
k(4660/34000) = 9
by solving we find:
k = 15300/233
click here to see the step by step solution of the equation:
how long would it take a satellite to complete an orbit if it is at 1600 miles above the earth at a velocity of 33,000:
t = ?
r = 1600 + R = 1600 + 3960 = 5560 mi
v = 33,000 mph
t = (15300/233)(r/v)
t = (15300/233)(5560/33000)
t = 11.06 hr
it will take 11.06 hours for the satellite to complete an orbit if it is at 1600 miles above the earth at a velocity of 33,000 mph.