where ρ V is the density of a volume element, dV, and r p is the vector from point P to
the volume element. This is illustrated in Fig. 2.5 where the gravitational acceleration at the surface of 67P is shown assuming a constant density distribution. A
minimum is seen in the neck region whilst a maximum is seen on the flat region on
the base of the body (to the right). It can be seen that this area is in a small
depression. If a uniform density can indeed be assumed, there are faster computational methods as shown by Werner and Scheeres (1997). The variation over the
surface is approaching a factor of 1.7 and this leads to the escape velocity from the
surface being strongly dependent upon position.
The gravitational field above the nucleus but within one nucleus radius of the
surface is also distorted in the neck region. This has implications for the flow
velocities of slow moving particles originating in the neck region.
2.4 Rotational Properties
So far, we have treated nuclei analytically as uniform spheres. The observations of
1P/Halley by the Halley Armada clearly established the dubiousness of this assumption and subsequent resolved observations of 19P/Borrelly and 103P/Hartley 2 have
Fig. 2.5 The gravitational acceleration at the surface of the nucleus of 67P colour coded in units of
[m s
À2
] (Courtesy of R.M. Marschall)
2.4 Rotational Properties
41
the volume element. This is illustrated in Fig. 2.5 where the gravitational acceleration at the surface of 67P is shown assuming a constant density distribution. A
minimum is seen in the neck region whilst a maximum is seen on the flat region on
the base of the body (to the right). It can be seen that this area is in a small
depression. If a uniform density can indeed be assumed, there are faster computational methods as shown by Werner and Scheeres (1997). The variation over the
surface is approaching a factor of 1.7 and this leads to the escape velocity from the
surface being strongly dependent upon position.
The gravitational field above the nucleus but within one nucleus radius of the
surface is also distorted in the neck region. This has implications for the flow
velocities of slow moving particles originating in the neck region.
2.4 Rotational Properties
So far, we have treated nuclei analytically as uniform spheres. The observations of
1P/Halley by the Halley Armada clearly established the dubiousness of this assumption and subsequent resolved observations of 19P/Borrelly and 103P/Hartley 2 have
Fig. 2.5 The gravitational acceleration at the surface of the nucleus of 67P colour coded in units of
[m s
À2
] (Courtesy of R.M. Marschall)
2.4 Rotational Properties
41