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II.2. Designations of elements and supplementary functions

Following designations of elements/ parameters are used in AMPLE.

H — photometric parameter, absolute magnitude in V band
G — photometric parameter, so called slope parameter
M — mean anomaly
Peri. — argument of perihelion
Node — longitude of ascending node
i — inclination
e — eccentricity
n — mean motion
a — semi-major axis

The angular quantities are expressed in degrees,

n — in degrees per day
a — in astronomical units (AU)

Apart conventional orbital elements AMPLE gives possibility to calculate for each minor planet the following often used functions:

q = a(1–e) perihelion distance
Q = a(1+e) aphelion distance
p = a(1–e2) orbital parameter
P = a(3/2) period of revolution in years
Peri.+ Node longitude of perihelion
L = Peri.+ Node + M mean longitude
n"= nx3600 mean motion in arcsec/day
H+5log(a(a–1)) mean opposition magnitude; for planets with q <= 1 AU the following formula is used:
    H+5log((a(e+1)+1)(a(e+1)–1)/4);
    for planets with Q <=1.1 AU this function is not calculated
Dist_AscNode =

a(1-e2)/(1+ecos(Peri.))

heliocentric distance of ascending node
Dist_DscNode =

a(1-e2)/(1-ecos(Peri.))

heliocentric distance of descending node
MOID Minimum Orbit Intersection Distance. To calculate MOID user should order the name or the number of the major or minor planet through dialog. The numbers from –1 to –9 correspond to Mercury, Venus, Earth (short designation of barycenter "Earth+Moon"), Mars, Jupiter, Saturn, Uranus, Neptune, Pluto.
MOID relative to orbit of this body is calculated for all other minor planets or their selected set.
CT=aj/a+2cos(i)sqrt(a(1-e2)/aj) Criteria of Tisserand (aj is semi-major axis of orbit of the body with respect to the criteria is calculated; a and e are the orbital elements of other body; i is the angle between the orbital planes). To calculate CT user should order the name or the number of the major or minor planet through dialog as it is proposed for MOID calculation. CT relative to orbit of ordered body is calculated for all other minor planets or their selected set
D=2.0x10(3.25–- 0.2 H) photometric diameter of minor planet
T_per time of perihelion passage as the nearest to the epoch of elements. To calculate T_per user should order the form (CD/JD - calendar/julian date).
NC Near Commensurability. As it is proposed for MOID and CT calculations, to calculate NC user should order the name or the number of the major or minor planet through dialog. NC relative to mean motion of ordered body orbit is calculated for all other minor planets or their selected set. In dialog box "Calculation range" user should order integer value "ieps" in arcsec/day. Ieps determines the range of mean motion values of selected minor planets. Selected value of ieps can change sometimes the order of commensurability, so we give possibility for user to point necessary value. At first ieps is equal to 50. When there is a near commensurability, ratio of mean motions of two bodies is equal to the ratio of two integer values, p and q. In this version of AMPLE values p,q≤9 are considered, and the values of p and q satisfy the condition abs(p-q)≤5.
T_AscNode time of ascending node passage nearest to the epoch of perihelion passage. To calculate T_AscNode user should order the form (CD/JD - calendar/julian date).
T_DscNode time of descending node passage nearest to the epoch of perihelion passage. To calculate T_DscNode user should order the form (CD/JD - calendar/julian date).

       Note.   The calculation of MOID needs more time than calculations of other functions. User should take this circumstance into account when ordering the MOID function.

To gain access to the table of elements click first on Tasks item in menu bar and then select Elements in drop-down menu. The Select elements dialog box immediately comes into view.