Ethernet cables do not "sort out" and treat data communications differently by any kind of categorization. They will transmit any kind of valid data, without discrimination of the source. Internet traffic is not special and does not need to be treated any differently. It just happens to come from farther away.
So you can use your one cable to have the observatory communicate to any amount of devices, from your home or from the Internet, as long as your network topology and settings are configured to do so. Most likely, yours already is. You can test this by "pinging" your observatory equipment's IP Address from the PC controller inside your home.