  The experimental data on GOES magnetic measurements and plasma measurements
on LANL geosynchronous satellites is used for selection of 169 case events
containing 638 geosynchronous magnetopause crossings (GMCs) in 1995 to 2001. We
study the necessary conditions for the geosynchronous magnetopause crossings
using scatter plot of the GMCs in the coordinate space of Psw versus Bz. In
such representation the upstream solar wind conditions demonstrate sharp
envelope boundary under which no GMCs are occurred. The boundary has two strait
horizontal branches where Bz does not influence on the magnetopause location.
The first branch is located in the range of Psw=21 nPa for large positive Bz
and is associated with an asymptotic regime of the pressure balance. The second
branch asymptotically approaches to the range of Psw=4.8 nPa under very strong
negative Bz and it is associated with a regime of the Bz influence saturation.
We suggest that the saturation is caused by relatively high contribution of the
magnetosphere thermal pressure into the pressure balance on the magnetopause.
The intermediate region of the boundary for the moderate negative and small
positive IMF Bz can be well approximated by a hyperbolic tangent function. We
interpret the envelope boundary as a range of necessary upstream solar wind
conditions required for GMC in the point on the magnetopause located mostly
close to the Earth ("perigee" point). We obtain that the dipole tilt angle and
dawn-dusk asymmetry influence on the "perigee" point location. We find that the
aGSM latitude of this point depends linearly on the dipole tilt angle with the
slope about -0.5. The aGSM longitude of the "perigee" point decreases with IMF
Bz with a rate of about 2 angular minutes per 1 nT. An empirical model
predicting the magnetopause crossing of the geosynchronous orbit in the
"perigee" point is proposed.
