There is no way to identify the machines that will be spun up in an EKS cluster, before they are created.  However, all of the traffic from a saturn deployment comes from an Internet Gateway  that lives inside your VPC.

If you contact support, we'd be happy to find your IP for you.   However you can also find it yourself inside your AWS console.

On the EC2 Dashboard, you can click on "Elastic IPs" on the left hand menu.

Look for an Elastic IP labeled saturn-cluster-${company-name}-vpc .  The IP Address listed there is the Public IPv4 address that all data services you run will see when users of Saturn are trying to connect.

You can confirm this in the Jupyter notebook, 

import urllib.request
external_ip = urllib.request.urlopen('').read().decode('utf8')

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