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physics

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the polar-orbiting 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 -

    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 -

    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.

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