It looks that you tried to start PixInsight as follows:
/opt/PixInsight/bin>./PixInsight
./PixInsight: error while loading shared libraries: libssl.so.10: cannot open shared object file: No such file or directory
/opt/PixInsight/bin>
That will not work as several libraries (*.so) are not found
/opt/PixInsight/bin>ldd ./PixInsight
linux-vdso.so.1 (0x00007ffebf740000)
libSM.so.6 => /usr/lib/x86_64-linux-gnu/libSM.so.6 (0x00007fb1e23e8000)
libICE.so.6 => /usr/lib/x86_64-linux-gnu/libICE.so.6 (0x00007fb1e21c8000)
libXi.so.6 => /usr/lib/x86_64-linux-gnu/libXi.so.6 (0x00007fb1e1fb8000)
libXrender.so.1 => /usr/lib/x86_64-linux-gnu/libXrender.so.1 (0x00007fb1e1da8000)
libXrandr.so.2 => /usr/lib/x86_64-linux-gnu/libXrandr.so.2 (0x00007fb1e1b98000)
libfreetype.so.6 => /usr/lib/x86_64-linux-gnu/libfreetype.so.6 (0x00007fb1e18e8000)
libfontconfig.so.1 => /usr/lib/x86_64-linux-gnu/libfontconfig.so.1 (0x00007fb1e16a8000)
libXext.so.6 => /usr/lib/x86_64-linux-gnu/libXext.so.6 (0x00007fb1e1490000)
libX11.so.6 => /usr/lib/x86_64-linux-gnu/libX11.so.6 (0x00007fb1e1148000)
libgthread-2.0.so.0 => /usr/lib/x86_64-linux-gnu/libgthread-2.0.so.0 (0x00007fb1e0f40000)
libgobject-2.0.so.0 => /usr/lib/x86_64-linux-gnu/libgobject-2.0.so.0 (0x00007fb1e0ce8000)
librt.so.1 => /lib/x86_64-linux-gnu/librt.so.1 (0x00007fb1e0ae0000)
libglib-2.0.so.0 => /lib/x86_64-linux-gnu/libglib-2.0.so.0 (0x00007fb1e07d0000)
libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007fb1e05b0000)
libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007fb1e03a8000)
libresolv.so.2 => /lib/x86_64-linux-gnu/libresolv.so.2 (0x00007fb1e0190000)
libcom_err.so.2 => /lib/x86_64-linux-gnu/libcom_err.so.2 (0x00007fb1dff88000)
libidn.so.11 => /usr/lib/x86_64-linux-gnu/libidn.so.11 (0x00007fb1dfd50000)
libz.so.1 => /lib/x86_64-linux-gnu/libz.so.1 (0x00007fb1dfb30000)
libssl.so.10 => not found
libcrypto.so.10 => not found
libssh2.so.1 => /usr/lib/x86_64-linux-gnu/libssh2.so.1 (0x00007fb1df900000)
libQt5Sensors.so.5 => not found
libQt5Positioning.so.5 => not found
libQt5MultimediaWidgets.so.5 => not found
libQt5Multimedia.so.5 => not found
...
...
Either start it (correctly) with:
>./PixInsight.sh
PixInsight Core 01.08.04.1198 Ripley (x64)
Copyright (c) 2003-2016 Pleiades Astrophoto
...
or by clicking on the application link which is integrated in your window manager, e.g. xfce4, gnome, etc...
The application link is created during PixInsight installation.
If you look quickly in ./PixInsight.sh you will see that the library path is there set
#!/bin/bash
appname=`basename $0 | sed s,\.sh$,,`
dirname=`dirname $0`
if [ "${dirname:0:1}" != "/" ]; then
dirname=$PWD/$dirname
fi
LD_LIBRARY_PATH=$dirname/lib:$dirname
...
...
thus the required libraries will be found.
Cheers
Thomas