which the bulk of the solar insolation goes into subliming ices at the surface of the
nucleus. The constants, c NGF , m NGF , k NGF , and n NGF have been determined through
fitting as in Table 1.4. Typical values for A 1 , A 2 , and A 3 are 0.3 Â 10
À8 ,
Æ0.05 Â 10
À8 , and Æ0.07 Â 10
À8 in units of [AU day
À2 ] although order of
magnitude variations between individual comets are evident. The fact that A 1 is
usually larger than A 2 and A 3 is indicative of the dominance of outgassing from the
dayside hemisphere.
It should be noted here that the formulation is symmetric about perihelion which
from inspection of Fig. 1.3 is clearly not the case. On the other hand, the formulation
can also allow for time-dependence of the A coefficients which removes this issue
(see for example Yeomans and Chodas 1989; Aksnes and Mysen 2011). The power
law form of g(r h ) should also be noted as this can be related to the power laws used to
describe the change in cometary brightness with heliocentric distance described
earlier.
The change in the orbital period resulting from the radial and transverse forces (F r
and F t , respectively) can be computed from
ΔP ¼
6π
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 À e x
2
p
M N ñ
2
e x
p L
Z P
0
F r sin f þ
F t
r h
dt
!
ð1:23Þ
where M N is the mass of the nucleus, t is the time, ñ is the mean motion, p L is the
semi-latus rectum, and, as before, e x is the eccentricity and f is the true anomaly
(Rickman 2017).
Although this approach to NGF modelling has been useful in defining the orbits
of short-period comets, one question that arises is whether something can be learnt
about the comet from the observed NGFs. One can assume that the outgassing rate is
proportional to the surface area as will be discussed below. If the total outgassing
rate can be computed in this way then the non-gravitational accelerations depend
upon the nucleus mass and if the volume can be established through observations of
the bare nucleus then the density can be derived. This idea has prompted some
authors to look at more physical approaches to determining the NGF terms in
Eq. (1.23).
The basic idea is to partially invert the problem by modelling the outgassing from
the surface accurately using heat balance equations (Sect. 2.9.3) applied to facets
describing the shape of the nucleus. Where the shape is essentially unknown, spheres
or ellipsoids can be used as approximations (e.g. Maquet et al. 2012). The water
production rate is then compared to observation (for example through ground-based
Table 1.4 Constants for the
determination of g(r) in the
standard description of
non-gravitational forces (from
Yeomans and Chodas 1989)
Constant
Value
r 0
2.808 AU (for water ice)
c NGF
0.111262
m NGF
2.15
k NGF
4.6142
n NGF
5.093
24
1 Light Curves, Orbits, and Reservoirs
nucleus. The constants, c NGF , m NGF , k NGF , and n NGF have been determined through
fitting as in Table 1.4. Typical values for A 1 , A 2 , and A 3 are 0.3 Â 10
À8 ,
Æ0.05 Â 10
À8 , and Æ0.07 Â 10
À8 in units of [AU day
À2 ] although order of
magnitude variations between individual comets are evident. The fact that A 1 is
usually larger than A 2 and A 3 is indicative of the dominance of outgassing from the
dayside hemisphere.
It should be noted here that the formulation is symmetric about perihelion which
from inspection of Fig. 1.3 is clearly not the case. On the other hand, the formulation
can also allow for time-dependence of the A coefficients which removes this issue
(see for example Yeomans and Chodas 1989; Aksnes and Mysen 2011). The power
law form of g(r h ) should also be noted as this can be related to the power laws used to
describe the change in cometary brightness with heliocentric distance described
earlier.
The change in the orbital period resulting from the radial and transverse forces (F r
and F t , respectively) can be computed from
ΔP ¼
6π
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 À e x
2
p
M N ñ
2
e x
p L
Z P
0
F r sin f þ
F t
r h
dt
!
ð1:23Þ
where M N is the mass of the nucleus, t is the time, ñ is the mean motion, p L is the
semi-latus rectum, and, as before, e x is the eccentricity and f is the true anomaly
(Rickman 2017).
Although this approach to NGF modelling has been useful in defining the orbits
of short-period comets, one question that arises is whether something can be learnt
about the comet from the observed NGFs. One can assume that the outgassing rate is
proportional to the surface area as will be discussed below. If the total outgassing
rate can be computed in this way then the non-gravitational accelerations depend
upon the nucleus mass and if the volume can be established through observations of
the bare nucleus then the density can be derived. This idea has prompted some
authors to look at more physical approaches to determining the NGF terms in
Eq. (1.23).
The basic idea is to partially invert the problem by modelling the outgassing from
the surface accurately using heat balance equations (Sect. 2.9.3) applied to facets
describing the shape of the nucleus. Where the shape is essentially unknown, spheres
or ellipsoids can be used as approximations (e.g. Maquet et al. 2012). The water
production rate is then compared to observation (for example through ground-based
Table 1.4 Constants for the
determination of g(r) in the
standard description of
non-gravitational forces (from
Yeomans and Chodas 1989)
Constant
Value
r 0
2.808 AU (for water ice)
c NGF
0.111262
m NGF
2.15
k NGF
4.6142
n NGF
5.093
24
1 Light Curves, Orbits, and Reservoirs