File:Kuiper-belt-eccentricity.svg

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Summary

Description
English: Plot of eccentricity (e; y-axis) vs. semi-major axis (a; x-axis) of 2841 objects in the classical Kuiper belt (KBOs). Colors show the objects' main dynamical categories. The size of each dot is scaled to the size of the object, and notable objects are labeled.

For a few large objects, the diameter drawn represents actual measurements, obtained via stellar occultation, thermal emission, or direct imaging. For all others, the circles represent the assumed diameter based on the mean albedo for each dynamical category.

Based on a similar diagram by Renerpho: File:KBOs_and_resonances.png

Size data is from Johnston's Archive (15 July 2025): https://johnstonsarchive.net/astro/tnoslist.html, with the exception of (28435) 1995 SM55, which has a maximum diameter of 200 km per https://ui.adsabs.harvard.edu/abs/2024EPSC...17..556O/abstract.

Orbital data is from JPL Solar System Dynamics (18 July 2025): https://ssd.jpl.nasa.gov/tools/sbdb_query.html
Date
Source Own work
Author Thunkii
Other versions

File:Kuiper-belt-inclination.svg (inclination)

File:KBOs_and_resonances.png
SVG development
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 The source code of this SVG is invalid due to 32 errors.
 This W3C-invalid plot was created with Matplotlib.
Python source
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click to expand
import matplotlib.ticker
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib
import numpy as np
from adjustText import adjust_text
from matplotlib import font_manager

##This code creates plots of TNO dynamics and characteristics from csv data files derived from Johnston's Archive (size data) and JPL's Small Body Dynamics database (orbital data).
#A lot of things are customizable if you change the values below.

##Plotting options and parameters
#Name of the files
johnstonfile='tnos.csv'
jplfile='sbdb_query_results(1).csv'

#Font and background layout
matplotlib.rcParams['font.sans-serif'] = "Lato"
plt.rcParams['legend.title_fontsize'] = 'large'
plt.style.use('dark_background')

#Figure layout and size
fig = plt.figure(figsize=(14, 10))
ax = fig.add_axes([0.05,0.055,0.935,0.85])
colorlegendloc=[0,1]
sizelegendloc=[1,0]
titleypos=1.06

#Labels
fileout='kbos-testae-cc'
maintitle= 'The Kuiper Belt'
xlabel = 'Semi-major axis (AU)'
secxlabel = 'Period (years)'
ylabel = 'Eccentricity'
grouptitle = 'Dynamical groups'
sizetitle = 'Diameter (km)'
restitle = 'Resonances'
sizecircles=[50,100,200,500,1000,2000] #sizes of the size circles
secax = True

#Params and axis limits. Reasonable values for ylim:
#perihelion: [23.5,82], minor ticks every 5.
#eccentricity: [0,1], [0,0.4] (KBOs), minor ticks every 0.05
#inclination: [-4,115], [-2,50] (KBOs), minor ticks every 5 or 10
paramx='a_y'
paramy='e_y'
axis_doublelog=False #make a log(log(x)) axis for semi-major
xlim=[37.5,50]
ylim=[0,0.4]
xticks=[40,50,60,70,80,90,100,200,300,400,500,600,700,800,900,1000,2000,3000]
xticklabels=['40','50','60','','80','','100','200','','400','','600','','','','1,000','2,000','3,000']

secxticks=[200,300,400,500,600,700,800,900,1000,2000,3000,4000,5000,6000,7000,8000,9000,10000,20000,30000,40000,50000,60000,70000,80000,90000,100000]
secxticklabels=['200','300','400','500','600','','800','','1,000','2,000','','4,000','','6,000','','','','10,000','20,000','','','50,000','','','','','100,000']
minorxtickspace=0.5
minorytickspace=5
minorsecaxtickspace=5

#circle parameters
sizescale=np.sqrt(10)/150 #size of circles
circlewidth=1/600 #width of circle edges
maxcirclewidth=2 #maximum width
labelsize=1.8 #text size scale of labels

#Colors for the groups. If you want to label Haumeids, add a separate class_dict entry for Haumea, and change color_dict to match.
class_dict = {'Resonant TNO':'red', 'Plutino':'orange', 'Cold cubewano':'blue', 'Hot cubewano':'deepskyblue', 'Haumeid': 'mediumslateblue', 'Other TNO':'#8b2be2', 'Scattered disk':'lightgrey', 'Centaur':'lawngreen'}

#Defining the main resonances to be marked. These won't be shown if they lie outside the axis bounds.
neptuneorbit=30.07 #AU
mainres=[1,5/4, 4/3, 7/4, 5/3, 7/3, 2, 5/2, 7/2, 9/2, 3, 4, 5, 6]
minorres=[7,8,9,10,11,12,11/2,8/3,10/3,11/3,9/4,11/4,13/4,7/5,8/5,9/5,11/5,12/5,11/6,10/7,11/7,12/7,11/9]
mainresstr=['1:1','5:4','4:3','7:4','5:3','7:3','2:1','5:2','7:2','9:2','3:1','4:1','5:1','6:1']
minorresstr=['7:1','8:1','9:1','10:1','11:1','12:1','11:2','8:3','10:3','11:3','9:4','11:4','13:4','7:5','8:5','9:5','11:5','12:5','11:6','10:7','11:7','12:7','11:9']
toplabels=True

#Resonance tick/label params
restick=[0,0.006]
reslabelloc=0.008
restitleloc=[27.5,0]

#manual label adjustments go here. This is going to be different for each plot, good luck!
xoffset=[-0.5,-11.5,-0.5,-33,-1.5, 1,0,0.5,-52,2.5, -1.5,3,-90,-2.5,-43.5, 2,-42,-37,1.5]
yoffset=[-17,2,-2,-3,0.5, -8.5,-1.5,-9,-10,-8.5, -3,-10,-3,1.5,-17, -8,-1,0.5,-15.5]

#arrows: play around with shrinkB until the arrow terminates on the *outside* of the circle for readability.
arrowprops=[None for i in range(23)]
#arrowprops[7]={'arrowstyle':'-', 'color':'lightgrey', 'lw': 0.5, 'relpos': (0.1,0.2),'shrinkB':8}
#arrowprops[10]={'arrowstyle':'-', 'color':'lightgrey', 'lw': 0.5, 'relpos': (0.1,0.8),'shrinkB':9.5}
#arrowprops[21]={'arrowstyle':'-', 'color':'lightgrey', 'lw': 0.5, 'relpos': (0.3,0.2),'shrinkB':9.2}
#arrowprops[10]={'arrowstyle':'-', 'color':'#8b2be2', 'lw': 0.5, 'relpos': (0.2,0.2),'shrinkB':15}


##Main Code

pd.options.display.max_rows=100

#read in data, filter by high condition code, make sure it's in both johnston's and JPL
johnston=pd.read_csv(johnstonfile, delimiter=";",skipinitialspace=True)
johnston['pdes']=johnston['number'].str.strip(to_strip="()").fillna(johnston['provisional'])
jpl=pd.read_csv(jplfile)
tnos=pd.merge(johnston, jpl, how='inner', on='pdes')
tnofil=tnos[tnos['condition_code']<=7]

#Filter the notable TNOs that should be labeled. This is all custom.
largetnos=tnofil[(tnofil['diameter_x']>200)]
largetnos=largetnos[((largetnos['diameter_x']>700) | (~tnofil['name_x'].isna()))]
largetnos=largetnos[~largetnos['name_x'].isin(['Mbabamwanawaresa'])]
largetnos=largetnos[(largetnos['a_y']>=37.5) & (largetnos['a_y']<=50) & (largetnos['e_y']<0.4)]
#largetnos=tnofil[(tnofil['diameter_x']>210) | ((tnofil['name_x'].isin(['Alicanto'])) | tnofil['dynamics'].isin(['Sednoid']))]
#largetnos=tnofil[(tnofil['diameter']>150)]
#largetnos=largetnos[(~largetnos['dynamics'].isin(['other TNO'])) | ((largetnos['diameter_x']>499) & (largetnos['q_y']>50)) | (largetnos['diameter_x']>1000)]
#largetnos=largetnos[(~largetnos['dynamics'].isin(('cubewano-hot', 'cubewano-cold', 'Haumea', 'cubewano', 'plutino', 'SDO', 'twotino', 'Centaur', 'Nep Trj L4', 'Nep Trj L5')) & ~largetnos['dynamics'].str.contains('res')) | (largetnos['diameter_x']>600)|((~tnofil['name_x'].isna()))]
#largetnos=largetnos[(~largetnos['dynamics'].isin(['SDO'])) | (largetnos['diameter_x']>700) | ((~tnofil['name_x'].isna())) | (largetnos['a_y']>80)]
#largetnos=largetnos[(~largetnos['dynamics'].isin(('cubewano-hot', 'cubewano-cold', 'Haumea', 'cubewano', 'plutino'))|(tnofil['diameter_x']>1500))]
#largetnos=largetnos[~((largetnos['dynamics']=='SDO') & (largetnos['name_x'].isna()) & (largetnos['a_y']<85))]
largetnos['name_x']=largetnos['name_x'].fillna(largetnos['provisional'])  #add provisional desig to name to those with no names yet
print(largetnos[['name_x','provisional','diameter_x']])

#more subgroups for analysis
namedtnos=tnos[~tnos['name_x'].isna()]
p9tnos=tnofil[(tnofil['q_x']>=35) & (tnofil['a_x']>=200)]
large=tnos.sort_values(by= 'diameter_x', ascending=False)

largetnos=largetnos.reset_index()
namedtnos=namedtnos.reset_index()
#print(tnos.sort_values(by='t_jup').head(100)[['number','name_x','t_jup']])

color_dict = {'cubewano-cold': class_dict['Cold cubewano'], 'cubewano-hot': class_dict['Hot cubewano'], 'cubewano': class_dict['Hot cubewano'], 
              'plutino': class_dict['Plutino'], 'twotino': class_dict['Resonant TNO'], 'Nep Trj L4': class_dict['Resonant TNO'], 'Nep Trj L5': class_dict['Resonant TNO'],
              'res 1:3': class_dict['Resonant TNO'], 'res 1:4': class_dict['Resonant TNO'], 'res 1:5': class_dict['Resonant TNO'], 'res 1:6': class_dict['Resonant TNO'], 
              'res 1:7': class_dict['Resonant TNO'], 'res 1:8': class_dict['Resonant TNO'], 'res 1:9': class_dict['Resonant TNO'], 'res 1:10': class_dict['Resonant TNO'], 'res 1:11': class_dict['Resonant TNO'],
              'res 2:5': class_dict['Resonant TNO'], 'res 2:7': class_dict['Resonant TNO'], 'res 2:9': class_dict['Resonant TNO'], 'res 2:11': class_dict['Resonant TNO'], 
              'res 3:4': class_dict['Resonant TNO'], 'res 3:5': class_dict['Resonant TNO'], 'res 3:7': class_dict['Resonant TNO'], 'res 3:8': class_dict['Resonant TNO'], 'res 3:10': class_dict['Resonant TNO'], 'res 3:11': class_dict['Resonant TNO'],
              'res 4:5': class_dict['Resonant TNO'], 'res 4:7': class_dict['Resonant TNO'], 'res 4:9': class_dict['Resonant TNO'], 'res 4:11': class_dict['Resonant TNO'], 'res 4:13': class_dict['Resonant TNO'], 
              'res 5:7': class_dict['Resonant TNO'], 'res 5:8': class_dict['Resonant TNO'], 'res 5:9': class_dict['Resonant TNO'], 'res 5:11': class_dict['Resonant TNO'], 'res 5:12': class_dict['Resonant TNO'],
              'res 6:11': class_dict['Resonant TNO'], 'res 7:10': class_dict['Resonant TNO'], 'res 7:11': class_dict['Resonant TNO'], 'res 7:12': class_dict['Resonant TNO'], 'res 9:11': class_dict['Resonant TNO'],
               "SDO": class_dict['Scattered disk'], 'Haumea': class_dict['Haumeid'], "ESDO": class_dict['Scattered disk'], "EDDO": class_dict['Scattered disk'], "Sednoid": class_dict['Scattered disk'],
               'Centaur': class_dict['Centaur'],'Apollo': class_dict['Centaur'], 'Amor': class_dict['Centaur'], 'unusual': class_dict['Centaur'], 'Damocloid': class_dict['Centaur'], 'other TNO': class_dict['Other TNO'], 
               'Ura Trj L4': class_dict['Resonant TNO'], 'comet': class_dict['Centaur']}

colors=tuple(map(color_dict.get, tnofil['dynamics']))
largecolors=tuple(map(color_dict.get,largetnos['dynamics']))
namedcolors=tuple(map(color_dict.get,namedtnos['dynamics']))

##Plotting

#defining fancy log formatters for various stuff (those end up unused)

class myformatter(matplotlib.ticker.LogFormatter):

    def _num_to_string(self, x, vmin, vmax):

        if x > 1000000:
            s = '%1.0e' % x
        elif x < 1 and x >= 0.001:
            s = f'{x:n}'
        elif x < 0.001:
            s = '%1.0e' % x
        else:
            s = f'{x:n}'
        return s
    
def my_locs(self, locs=None):

        b = self._base
        c = np.geomspace(1, b, int(b)//int(locs) + 1)
        self._sublabels = set(np.round(c))

#Title and axis labels.
ax.set_title(maintitle,size='24',y=titleypos)
ax.set_xlabel(xlabel, size=16)
ax.set_ylabel(ylabel, size=16)


#formatter shenanigans for testing, not used in final plot

#formatter = myformatter(labelOnlyBase=False, minor_thresholds=(5, 2.5))
#formatter2 = myformatter(labelOnlyBase=False, minor_thresholds=(5, 2.5))
#fmt = matplotlib.ticker.StrMethodFormatter("{x:g}")
#ax.get_xaxis().set_minor_formatter(formatter)
#ax.get_xaxis().set_major_formatter(fmt)

#Double-log x scale and ticks for semi-major axis. 

if axis_doublelog==True:
    ax.set_xlim(xlim)
    ax.set_xscale("functionlog", functions=(
        lambda x: np.log10(np.log10(x)),
        lambda x: 10**((10**(x)))))
    ax.set_xticks(xticks, labels=xticklabels)
    #set length of minor ticks to same as major to avoid wonkiness
    ax.tick_params(which='minor', length=3.5)

else:
    ax.set_xlim(xlim)
    ax.xaxis.set_minor_locator(matplotlib.ticker.MultipleLocator(minorxtickspace))

#Linear y scale and ticks.
ax.set_ylim(ylim)
ax.yaxis.set_minor_locator(matplotlib.ticker.MultipleLocator(minorytickspace))

#Defining the secondary x scale for orbital period, with ticks and label; this will be a**(3/2).
if secax==True:
    def period(x):
        return x**(3/2)
    def invper(x):
        return x**(2/3)
    secax = ax.secondary_xaxis('top', functions=(period, invper))
    secax.set_xlabel(secxlabel)

    if axis_doublelog==True:
        secax.set_xscale("functionlog", functions=(
            lambda x: np.log10(np.log10(x**(2/3))),
            lambda x: (10**((10**(x))))**(3/2)))
        secax.set_xticks(secxticks, labels=secxticklabels)
        secax.tick_params(which='minor', length=3.5)
    else:
        secax.set_xscale("function", functions=(
            lambda x: x**(2/3),
            lambda x: x**(3/2)))
        secax.xaxis.set_minor_locator(matplotlib.ticker.MultipleLocator(minorsecaxtickspace))

#Uncomment this if you insist on using a linear scale for a. This will create reasonable ticks.
#ax.set_xticks(np.concat((np.arange(30,110,10),np.arange(150,2350,50))))
#secax.set_xticks(np.concat(([160],np.arange(200,1100,100), np.arange(1500,5500,500),np.arange(6000,11000,1000), np.arange(12000,42000,2000),np.arange(40000,115000,5000))))


#Plot the circles for each TNO
normalpoints=ax.scatter(tnofil[paramx], tnofil[paramy], s=(tnofil['diameter_x']*sizescale)**2, facecolors='none', edgecolors=colors, linewidths=np.minimum(maxcirclewidth,tnofil['diameter_x']*circlewidth))

#Plot the labels on the notable tnos
textsize=np.floor(labelsize*np.log(largetnos['diameter_x']))
diameters=largetnos['diameter_x']*sizescale*(np.sqrt(2250)/100)

#generate labels
ann=[ax.annotate(largetnos['name_x'][i],(largetnos[paramx][i], largetnos[paramy][i]),xytext=(diameters[i]+xoffset[i], diameters[i]+yoffset[i]), textcoords='offset points',size=str(textsize[i]), color=largecolors[i], arrowprops=arrowprops[i], annotation_clip=False, bbox=dict(pad=-2, facecolor="none", edgecolor="none")) for i in range(largetnos.shape[0])]

#Mark the main resonance positions
#Make resonance lines, orange for plutinos. Note it's currently given in data coordinates, but you can use axis coordinates like so to avoid confusion:
#ax.vlines([1, 2], 0, 0.2, transform=ax.get_xaxis_transform(), colors='r')
ax.vlines(neptuneorbit*(3/2)**(2/3), restick[0], restick[1], colors='orange', label='3:2')
[ax.vlines(neptuneorbit*(mainres[i])**(2/3), restick[0], restick[1], colors='red') for i in range(len(mainres))]
#[ax.vlines(neptuneorbit*(minorres[i])**(2/3), ylim[0], ylim[0]+ylim[1]/60, colors='red', lw=0.5) for i in range(len(minorres))]

#Make resonance labels (again, in data coordinates)
ax.text(neptuneorbit*(3/2)**(2/3), reslabelloc, '3:2', color='orange',horizontalalignment='center')
[ax.text(neptuneorbit*(mainres[i])**(2/3), reslabelloc, mainresstr[i], color='red',horizontalalignment='center') for i in range(len(mainres))]
if toplabels==True:
    ax.vlines(neptuneorbit*(3/2)**(2/3), ylim[1]-restick[0], ylim[1]-restick[1], colors='orange', label='3:2')
    [ax.vlines(neptuneorbit*(mainres[i])**(2/3), ylim[1]-restick[0], ylim[1]-restick[1], colors='red') for i in range(len(mainres))]
    ax.text(neptuneorbit*(3/2)**(2/3), ylim[1]-reslabelloc, '3:2', color='orange',horizontalalignment='center', verticalalignment='top')
    [ax.text(neptuneorbit*(mainres[i])**(2/3), ylim[1]-reslabelloc, mainresstr[i], color='red',horizontalalignment='center', verticalalignment='top') for i in range(len(mainres))]

#[ax.text(neptuneorbit*(minorres[i])**(2/3), ylim[0]+ylim[1]/50, minorresstr[i], color='red',horizontalalignment='center', size='small') for i in range(len(minorres))]

#Resonance text (again, in data coordinates)
ax.text(restitleloc[0], restitleloc[1], restitle, color='red',size='large')


#creating the legends
circles=[]
circle2=[]

#make some tiny circles for labeling the colors, then put the legend box in a nice place. I used 375 km circles, but you can change this.
for value in class_dict.values():
    circles.append(plt.Line2D([], [], color='None', marker='o', markersize=375*sizescale,  markeredgecolor=value,mew=np.minimum(maxcirclewidth, 375*circlewidth)))

#circles for labeling the sizes, in white
for size in sizecircles:
    circle2.append(plt.Line2D([], [], color='None', marker='o', markersize=size*sizescale,  markeredgecolor='white',mew=np.minimum(maxcirclewidth,size*circlewidth)))

legend1=ax.legend(circles, class_dict.keys(), numpoints=1, bbox_to_anchor=colorlegendloc, loc='upper left', labelcolor=class_dict.values(), title=grouptitle, frameon=False)
legend2=ax.legend(circle2, sizecircles, numpoints=1, bbox_to_anchor=sizelegendloc, loc='lower right', title=sizetitle,labelspacing=3,reverse=True, frameon=False, handletextpad=2)
ax.add_artist(legend1)
ax.add_artist(legend2)

#Save the final figures we have created, as both large png and svg (latter goes to Commons)
fig.savefig(fileout+'.svg', transparent=False)
fig.savefig(fileout+'.png',dpi=750)

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
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Captions

Orbital distribution (eccentricity vs. semi-major axis) of the main Kuiper belt, colored by its main dynamical groups.

23 July 2025

image/svg+xml

3,590,486 byte

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File history

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current00:53, 13 November 2025Thumbnail for version as of 00:53, 13 November 20251,344 × 960 (3.42 MB)wikimediacommons>ThunkiiUpdated osculating elements, some recently discovered objects added

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