Find Kirkwood Gaps in the Asteroid Belt

Query for the orbital semimajor axis for asteroids in the asteroid belt:

In[1]:=

semimaj=EntityValue[EntityClass["MinorPlanet",{"SemimajorAxis"Between[Quantity[{2,3.5},"AstronomicalUnit"]]}],"SemimajorAxis"];

Group the orbital semimajor axis values in bins of width 0.005 AU to observe the reduced number of asteroids at certain distances:

In[2]:=

hist=Histogramsemimaj,{Quantity[.005,"AstronomicalUnit"]},



Out[2]=

Define a simplified form of Kepler's third law valid for orbit period in years and semimajor axis in AU:

In[3]:=

kepler[p_Quantity]:=QuantityMagnitude[p,"Years"]^(2/3)

Get the orbit period of Jupiter:

In[4]:=

jupperiod=

Jupiter

PLANET

["OrbitPeriod"]

Out[4]=

11.862615

a

Important resonances are found at several important fractions of Jupiter's orbit period:

In[5]:=

gaps={1/#,kepler[jupperiod#]}&/@{1/3,2/5,3/7,1/2}

Out[5]=

{3,2.5017142},

5

2

,2.8250438,

7

3

,2.9580171,{2,3.2781730}

The histogram can be annotated to label the important resonances and label them as a ratio to Jupiter's orbit period:

In[6]:=

Showhist,



Out[6]=

Related Symbols