SVG image of the Gliese 581 system orbits. Plot of the orbits of the Gliese 581 system, including the unconfirmed planet g.

Orbit data taken from Vogt et al. (2010), "The Lick-Carnegie Exoplanet Survey: A 3.1 M⊕ Planet in the Habitable Zone of the Nearby M3V Star Gliese 581"

The configuration is given in Table 2. The 6-planet solution quoted is for circular orbits, thus eccentricities are not represented.

Assumptions:

1. It is assumed that the system is coplanar. This cannot be constrained by the radial velocity observations used to detect the planets in this system, but our solar system's planets are nearly coplanar, and both the systems of PSR B1257+12 (planets B and C) and Epsilon Eridani (planet b and the circumstellar disk) are coplanar, see Konacki and Wolszczan (2003), The Astrophysical Journal 591, L147–L150 "Masses and Orbital Inclinations of Planets in the PSR B1257+12 System" and Beust et al. (2006), The Astrophysical Journal 132, 2206–2218 "The Extrasolar Planet ɛ Eridani b: Orbit and Mass respectively, so this assumption is at least reasonable.
2. The direction of rotation around the star is assumed to be the same for each planet. Again, this cannot be constrained by the current radial velocity observations, but is a reasonable assumption since this is true for the major planets in our own solar system, and is predicted by current theories of planet formation. Under these first two assumptions, the orientation of the orbits relative to each other is correct as depicted in this diagram, however their actual orientation in 3D space with respect to external reference points (e.g. the Sun, the galactic centre) is unknown, hence such directions are not indicated on the diagram.
3. A further assumption is that the true masses of the planets are small compared to that of the star. If the masses were comparable to that of the star, the actual semimajor axis corresponding to the measured orbital period would be greater. This assumption is supported both by probability (the chance that we are observing a system which has sufficiently low inclination for this to be relevant is very low) and by dynamical stability arguments which indicate that the planets cannot have true masses much more than 1.6 times their minimum masses (Mayor et al., 2009). This effect can therefore safely be neglected.

Interpreting the diagram

The planetary orbits are drawn in orthographic projection, as viewed from directly above the plane of the system so that the orbital direction is anticlockwise. The position of each planet in its orbit is given for the specified epoch, given in the Vogt et al. (2010) paper.

While the orbits are drawn to the correct scale, the star and the planets themselves are not shown to scale as they would be too small to see on the scale of this diagram. In addition, the true radii of the planets themselves are currently unknown as no direct observation of the planets has yet been made.