1. The problem statement, all variables and given/known data Consider a satellite in a circular, low-Earth orbit; that is, its elevation above the Earth’s surface is h ≪ R⊕. Show that the orbital period P for such a satellite is approximately P=C(1+ 3h/[2R⊕]). 2. Relevant equations P2 = (4pi2)/(GM) * a^3. (G - gravitational constant, M - mass of the earth (in this case) and a = semi-major axis) 3. The attempt at a solution Well, the semi-major axis will be: a = h + R⊕. I've also picked up that a useful representation of a will be: a = R⊕(1 + h/R⊕) This means our equation because P2 = (4pi2)/(GM) * (R⊕(1 + h/R⊕))^3. Now we just want P, so P = (2pi/√GM) * (R⊕(1 + h/R⊕))^(3/2). This obviously doesn't leave me with much. I've picked up from a few lectures that it may have something to do with Taylor series, but I'm severely stumped.