We present models of the shapes of four Kuiper belt objects ( KBOs ) and Jovian Trojan ( 624 ) Hektor as ellipsoidal figures of equilibrium and Roche binaries .
Our simulations select those figures of equilibrium whose lightcurves best match the measured rotational data .
The best fit shapes , combined with the knowledge of the spin period of the objects provide estimates of the bulk densities of these objects .
We find that the lightcurves of KBOs ( 20000 ) Varuna and 2003 EL _ { 61 } are well matched by Jacobi triaxial ellipsoid models with bulk densities 992 _ { -15 } ^ { +86 } kg m ^ { -3 } and 2551 _ { -10 } ^ { +115 } kg m ^ { -3 } , respectively .
The lightcurves of ( 624 ) Hektor and KBO 2001 QG _ { 298 } are well-described by Roche contact binary models with densities 2480 _ { -80 } ^ { +292 } kg m ^ { -3 } and 590 _ { -47 } ^ { +143 } kg m ^ { -3 } , respectively .
The nature of 2000 GN _ { 171 } remains unclear : Roche binary and Jacobi ellipsoid fits to this KBO are equivalent , but predict different densities , \sim 2000 kg m ^ { -3 } and \sim 650 kg m ^ { -3 } , respectively .
Our density estimates suggest a trend of increasing density with size .