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recent studies suggest that most stars are formed in groups and clusters ( ( * ? ? ?
* lada & lada 2003 ) ) .
the evolution of star clusters is driven by internal ( e.g. two - body relaxationi , mass loss by stellar evolution ) , as well as external processes ( e.g. tidal forces of a galaxy ) ( ( * ? ? ?
* spitzer 1987 ) , ( * ? ? ?
* elson et al . 1987 ) ) . since these mechanisms finally lead to the dissolution of clusters they have a finite life time .
so , if our sun has been born in an open star cluster , the solar planetary system may also have formed before the dissolution of its parent star cluster .    observations of exoplanets have been possible since the early 1990s . as of december 2014
, more than 1,800 exoplanets have been discovered , among which are 473 multi - planet systems like our own solar system ( http://exoplanet.eu ) .
nevertheless , most exoplanets are found in the solar neighborhood ; very few exoplanets ( e.g. kepler-66 , kepler-67 ) are found in star clusters .
star clusters , especially cores of globular clusters , are characterized by high density of stars and high velocity dispersions , which results in frequent close encounters .
current observations suggest that formation of planetary systems in dense regions of star clusters .
this could be due to instability against external gravitational perturbations , though there may also be some instrumental biases due to detection limits .
previous studies include direct @xmath0-body simulation ( ( * ? ? ?
* spurzem et al . 2009 ) ) and monte - carlo simulations ( ( * ? ? ?
* hao et al . 2013 ) ) .
we present numerical simulations to investigate the dynamical stability of planetary systems in star clusters .
coupling planetary system with star cluster dynamics is a multi - scale problem , due to time scales ranging from @xmath1 for planetary orbits to @xmath2 years for stars orbiting in the cluster .
full direct coupled simulations are expensive , though not impossible ( see e.g. ( * ? ? ?
* spurzem et al . 2009 ) ) ; but frequently monte carlo approaches are used ( see e.g. ( * ? ? ?
* hao et al . 2013 ) ) .
the amuse framework is a convenient toolbox to study such a problem ( ( * ? ? ?
* portegies zwart et al . , 2013 ) ;
* portegies zwart et al . , 2009 ) ) . within amuse
we integrate star cluster dynamics directly with nbody6++ ( ( * ? ? ?
* spurzem 1999 ) ) , while the planets are integrated with mercury6 ( ( * ? ? ?
* chambers 1999 ) ) .
the perturbations are implemented with the bridge scheme ( ( * ? ? ?
* fujii et al . , 2007 ) ;
* pelupessy et al , . 2013 ) ) .
all coupling is done within amuse framework .
for the initial setup of our system we follow the previously cited papers ( plummer sphere for stellar density , @xmath3 and @xmath4 stars , virial radius @xmath5 pc ; ( a ) current gas giant configuration or ( b ) equal mass and mutual hill radii separation for the planets ) . for case
( b ) the inner planet has @xmath6 and @xmath7 au .
we distribute 50 ( 100 ) planetary systems randomly across the @xmath3 ( @xmath4 ) cluster , to sample different positions and environments of planetary systems in star clusters .
figure  [ fig : aeplot ] shows the @xmath8 space ( semi - major axis verses eccentricity ) at the end of the @xmath4 simulation ( corresponding to @xmath9 myr ) .
the evolution of semi - major axes and eccentricities of saturn in the @xmath3 simulation are shown in figures  [ fig : ecc ] and  [ fig : semi ] , respectively .    0.32   space at @xmath10 kyr of a simulation ; ( b ) eccentricity evolution of saturn in one of the planetary systems ; ( c ) corresponding semi - major axis evolution of saturn in the same planetary system as ( b).,title="fig : " ]    0.32   space at @xmath10 kyr of a simulation ; ( b ) eccentricity evolution of saturn in one of the planetary systems ; ( c ) corresponding semi - major axis evolution of saturn in the same planetary system as ( b).,title="fig : " ]    0.32   space at @xmath10 kyr of a simulation ; ( b ) eccentricity evolution of saturn in one of the planetary systems ; ( c ) corresponding semi - major axis evolution of saturn in the same planetary system as ( b).,title="fig : " ]
our simulations show that generally planetary systems have difficulty surviving within dense cluster environments , but some compact ones are sheltered in the potential well of their hosts from disruption .
we acknowledge support by naoc cas through the silk road project and ( rs ) through the chinese academy of sciences visiting professorship for senior international scientists , grant number 2009s1 - 5 .
we are grateful for the supports from the amuse team , especially simon portegies zwart , inti pelupessy , arjen van elteren and nathan de vries for various useful discussions .
mxc and mbnk acknowledge the amuse team for supporting their visits to leiden , and michiko fujii for useful discussions .
in the solar neighborhood , where the typical relaxation timescale is larger than the cosmic age , at least 10% to 15% of sun - like stars have planetary systems with jupiter - mass planets . 
 in contrast , dense star clusters , charactered by frequent close encounters , have been found to host very few planets . 
 we carry out numerical simulations with different initial conditions to investigate the dynamical stability of planetary systems in star cluster environments .