Posted by victoria on .
the polarorbiting environmental satellites (POES) and some military satellites orbit at a much lower level in order to obtain more detailed information. POES complete an Earth orbit 14.1 times per day. What are the orbital speed and the altitude of POES?

physics 
Damon,
period = 24 hours/14.1 = 1.702 hours
times 3600 s/hr = 6128 seconds
v = sqrt(G Me/r)
T = 2 pi r/v = 2 pi r^(1.5) /(G Me)^.5
6128/2pi=r^1.5/(6.67*10^11*5.98*10^24)^.5
975.2 = r^(1.5)/(3.989*10^14)^.5
975.2 = r^1.5 / 2*10^7
r^1.5 = 1950 *10^7
use log base 10
1.5 log r = 7 + log 1950 = 10.29
log r = 6.86
so
r = 7,244,360 m meters
or 7,244 km
subtract Re =6380km for earth radius = 864 kilometers altitude
v = 2 pi r/T
= 2 pi * 7.24*10^6 /6128
= 7423 m/second or 26724 km/hr 
physics 
tchrwill,
24/14.1 = 1.702hr = 6127sec.
T = 2(Pi)sqrt[r^3/µ]
µ = Earth's gravitational constant = 1.407974x10^16.
T = 2(Pi)sqrt[r^3/1.407974x10^16] from which r = 23,745,774ft. = 4497.3 miles or an altitude of 4497.3  3963 = 534.3 miles.
It's orbital velocity derives from
V = sqrt[µ/r] = sqrt[1.407974x10^16/23,745,774] = 24,350fps or 16,602mph.