T
Tom J
Guest
A particle moves under the influence of a central force given by F(r) = -k/r^n. If the particle's orbit is circular and passes through the origin, show that n = 5
I'm just not seeing the trick to this. You need circular motion so L^2/(mu*r^3) = k/r^n. I *thought* that you'd also need a finite energy which since the orbit is circular implies that
E = -1/[(n-1)*r^(n-1)] + L^2/(2*mu*r^2) = 0
since we would need the L term and the potential energy term to cancel each other.
That's not seeming to be the case though because that would imply n = 3 since we need (n-1) = 2
thx for any help you have to offer.
I'm just not seeing the trick to this. You need circular motion so L^2/(mu*r^3) = k/r^n. I *thought* that you'd also need a finite energy which since the orbit is circular implies that
E = -1/[(n-1)*r^(n-1)] + L^2/(2*mu*r^2) = 0
since we would need the L term and the potential energy term to cancel each other.
That's not seeming to be the case though because that would imply n = 3 since we need (n-1) = 2
thx for any help you have to offer.