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tokens: distances. We discuss the implications of this exception in Section 4.3.4 . Inserting equation ( 16 ) into equation ( 15 ) we use equations ( 3 ) and ( 9 ) to find the ram pressure for the Isothermal Sphere, and the NFW model, where . In the above expressions, f c is the cluster gas fraction, M v,clust and R c are the virial mass and radius of the cluster, respectively, and ε is a fudge factor, added to incorporate any uncertainties in the assumptions we made in our model, e.g. motion with velocities different than the virial velocity, and which also accounts for C ram . 4.3.2 Gravitational binding We wish to compare the ram pressure to the binding gravitational force per unit area acting on the satellite gas halo and determine the amount of mass stripped from the satellite. While expressing the ram pressure is relatively simple, as shown above, deter-mining the correct form of the gravitational binding force for the appropriate mass elements affected is not so straightforward. Ideally, one wishes to construct a simple spherical approximation for the binding force at a radius l in the satellite which will lead to a definition of a stripping radius l s . One option is to find the gravitational force which binds a spherical shell of width at a given radius l, divided by the cross-section of that shell where M (l) is the total mass profile and ρ(l) is the gas density profile of the satellite. This approximation suggests that the ram pressure ‘peels’ off spherical shells, like an onion, which is incongruous with the anisotropic nature of RPS. However, if the satellite halo is rotating with respect to its direction of motion, such that all parts of the outer shell experience the ram pressure, this approach may be justified. Another option is to examine a cylindrical shell of radius l and width (), oriented in the direction of motion of the satellite, and thus the direction of the ram-pressure force. McCarthy et al. ( 2008 ) employed this method by finding the maximal value of the restoring gravitational acceleration in the direction of the motion (and, by definition, the cylinder axis) as well as an upper limit of the projected surface density, resulting in an overestimation of the binding force which ensures that one finds an upper limit to the stripping radius. For a power-law spherically symmetric density profile ρ ∝ r −α , the maximal restoring acceleration is 2 and the surface density is The upper limit of the integral is formally but can be taken to L → ∞ when the integral converges (or to some set scale otherwise) to achieve an upper limit for the surface density. The gravitational binding force is then where ν is a factor of order unity For an Isothermal Sphere profile, we find ν = π/2. Yet another option is to assume that the gas halo is in hydrostatic equilibrium within the gravitational potential of the dark matter halo of the satellite, and use the gas pressure as a proxy for the binding force per unit area. For a power-law density