Starting from ?r * ? h2=r3 = ?F(r), show that, underan attractive central force F(r) = GM=r2 + K=r3 (for some constant K), u = 1=r obeys the di?erential equation d2u d2 + u = GM h2 + Ku h2 ; and (by comparing with the usual case K = 0 and with the equation of simple harmonic motion) write down its general solution. The perihelion (point of closest approach) of a planet to the Sun is observed to `precess: its angle increases by an increment ? with every revolution. Show that this may be explained by a force of the type above, with K = h2 ® 1 ? ? 1 + ? 2ª ??2 ? : If ? is small, use the binomial expansion to show that K is approximately ?h2=ª.
Use the order calculator below and get started! Contact our live support team for any assistance or inquiry.
[order_calculator]