This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **12.87: a) There are many ways of approaching this problem; two will be given here. I) Denote the orbit radius as r and the distance from this radius to either ear as δ . Each ear, of mass m , can be modeled as subject to two forces, the gravitational force from the black hole and the tension force (actually the force from the body tissues), denoted by . F Then, the force equations for the two ears are where ϖ is the common angular frequency. The first equation reflects the fact that one ear is closer to the black hole, is subject to a larger gravitational force, has a smaller acceleration, and needs the force F to keep it in the circle of radius . δ- r The second equation reflects the fact that the outer ear is further from the black hole and is moving in a circle of larger radius and needs the force F to keep in in the circle of radius . δ + r Dividing the first equation by δ- r and the second by δ + r and equating the resulting expressions eliminates ϖ , and after a good deal of algebra,...

View
Full
Document