Question

A satellite in a circular orbit 844.5 mi above the earth makes one complete orbit every 85.22 min. What is its linear velocity in​ mi/min? Use 3963 mi for the length of the radius of the earth and round to the nearest hundredth of a mile per minute.

Answer 1

Answer: 354.5 mi/min

Step-by-step explanation:

from the question we are given the following:

distance from the surface of the earth (s) = 844.5 mi = 1359091 m

radius of the earth (r) = 3963 mi = 6377830

time = 85.22 min = 5113.2 s

linear velocity = ?

distance of the satellite from the center of the earth (R) = 1359091 + 6377830

= 7736921 m

angular velocity =
`(θ)/(t)`

where θ = 2π

angular velocity =
`(2π)/(5113.2 )` = 0.00123
`(rad)/(s)`

linear velocity = angular velocity x distance of satellite from the earth

linear velocity = 0.00123 x 7736921

= 9507.3 m/s x 60/309.34 = 354.5 mi/min