Show that the force on a star of mass m moving within a uniform cloud of dispers

Question

Show that the force on a star of mass m moving within a uniform cloud of

dispersed matter is approximately rho m r, where rho is the density of the cloud.

Show that the orbital velocity of a star in a circular orbit within this cloud varies directly as the distance of the star from the center of the distribution: v(r) ~ r.

Show that the force on a star of mass m moving within a uniform cloud of dispersed matter is approximately rho m r, where rho is the density of the cloud. Show that the orbital velocity of a star in a circular orbit within this cloud varies directly as the distance of the star from the center of the distribution: v(r) ~ r.

Explanation / Answer

Gauss law for a spherically distributed mass says that gravitational flux=4Pi G M

Gravitational field = 4pi G (4pi r^3 /3) * rho / Area

= (4 pi G r/3)*rho

Force = m x field = (4 pi G m r/3)*rho

= centripetal force = mv^2 / r

v^2 = (4 pi G rho / 3) r^2

v= sqrt((4 pi G rho / 3) r^2)

(undefined)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.