Assuming that the filenames do not contain spaces, tabs or newlines, using one-liner and bash and awk would be simple:
ls -rt | awk -F "." '{print $0 " object" sprintf("%03d",NR) "." $NF }' | xargs -lL 1 mv
The xargs -l command execute mv for each line. Before executing command execute the following command and check that target and source file names are correct:
ls -rt | awk -F "." '{print $0 " object" sprintf("%03d",NR) "." $NF }'
should output something like:
melon.foo object001.foo
cookie.foo object002.foo
pie.foo object003.foo
apple.foo object004.foo