Dynamics of
multiple system
Pluto
V. Troianskyi, O. Bazyey, V. Zhukov
Kolos, December 01 – 03, 2016
Research Objectives
Consider the evolution of the orbits of
satellites Pluto.
Search secular perturbations.
Search resonances.
2
System (134340) Pluto. Photo Space Telescope Hubble
http://hubblesite.org/newscenter/archive/releases/2012/19
3
System (134340) Pluto.
Photo spacecraft
"New Horizons"
https://www.nasa.gov/sites/default/files
4
Our orbital model is a
 Numerical integration of the equations of motion –
method Everhart’s 15th (Bazyey and Kara 2009).
 JPL planetary ephemeris DE431 (Folkner et al., 2014).
 Dynamical constants system, GM: Jovian (Folkner et al.
2014), Saturnian (Jacobson 2006), Uranian (Jacobson et al.
1992), Neptunian (Jacobson 2009), Sun and inner planets
and the Moon (Folkner et al. 2014).
 Pluto system, GM (Brozovic et al. 2015).
 State vectors for the satellites of Pluto (Brozovic et al.
2015).
5
Charon. Photo spacecraft "New Horizons"
https://www.nasa.gov/sites/default/files
6
Evolution selected Keplerian orbital
elements of the orbit of satellite Charon
a (km.)
19 596,64
19 596,63
19 596,62
19 596,61
19 596,60
0
100
200
300
400
500
600
700
800
900
1000
0
100
200
300
400
500
600
700
800
900
1000
0
100
200
300
400
500
600
700
800
900
1000
0,000058
0,000057
e
0,000056
0,000055
0,000054
i (degrees)
0,000053
96,23352
96,23351
96,23350
96,23349
96,23348
96,23347
96,23346
96,23345
96,23344
Time (years)
7
Evolution selected Keplerian orbital
elements of the orbit of satellite Charon
223,02711
223,02709
223,02708
223,02707
223,02706
223,02705
223,02704
0
100
200
300
400
500
600
700
800
900
1000
0
100
200
300
400
500
600
700
800
900
1000
356
355
354
ω (degrees)
Ω (degrees)
223,02710
353
352
351
350
349
348
347
Time (years)
8
An oblique view of the Pluto–Charon system showing
that Pluto orbits a point outside itself. Also visible is the
mutual tidal locking between the two bodies.
9
Charon and the Small Moons of Pluto. Photo
spacecraft "New Horizons"
https://www.nasa.gov/sites/default/files
10
Evolution Inclination orbits of satellites
Styx and Nix
96,30
96,25
i (degrees)
96,20
96,15
96,10
96,05
96,00
95,95
95,90
95,85
0
100
200
300
400
500
600
700
800
900
1000
0
100
200
300
400
500
600
700
800
900
1000
96,25
i (degrees)
96,20
96,15
96,10
96,05
96,00
95,95
Time (years)
11
i (degrees)
Evolution Inclination orbits of satellites
Kerberos and Hydra
96,30
96,25
96,20
96,15
96,10
96,05
96,00
95,95
95,90
95,85
95,80
0
100
200
300
400
500
600
700
800
900
1000
0
100
200
300
400
500
600
700
800
900
1000
96,20
i (degrees)
96,15
96,10
96,05
96,00
95,95
95,90
Time (years)
12
Resonance of Pluto's satellites
The resonance is described by formula (Murray and Dermot 2010):
N1 P1 N 2 P2
Ni Pi 0, i 1 n,
where N1, N2, ..., Ni – resonance coefficients, P1, P2, ..., Pi – periods/spins
Lee and Peale (2006)
found that Nix and Hydra
could be in the 3:2
mean-motion resonance.
Together with Nix and Hydra, Styx and
Kerberos complete the continuous
sequence of near-resonant orbits
(1:3:4:5:6) with respect to Pluto–Charon
orbital period (Brozovic et al. 2015).
13
Resonance of Pluto's satellites
Orbital-orbitals resonance:
11 PCharon 10 PStyx 16 PHydra 20 PNix 12 PKerberos 0.00 hour
Spin-orbital resonance:
6 S Pluto 1 PHydra 2.9175 hour
5 S Pluto 1 PKerberos 5.565 hour
4 S Pluto 1 PNix 16.6634 hour
19 S Pluto 6 PStyx 9.248 hour
1 S Pluto 1 PCharon 0.00000 hour
14
Results
We was built plutonocentrical and barycentrical
numerical model of Pluto’s system.
We was find secular perturbations in Pluto’s
satellites orbital elements.
We was calculated orbital-orbital and one of
spin orbital resonances in Pluto’s system.
15
Thanks for attention !!!
Volodymyr Troianskyi
[email protected]