Apple iOS (iPod, iPhone, iPad, etc) supports EAP-TLS, EAP-TTLS, EAP-FAST, EAP-MSCHAPv2 (PEAP) and EAP-SIM. When connecting to spacenet via the GUI your device will probably prompt your for a username/password.
For more advanced options (like EAP-TLS (client certificate), EAP outer identity etc) you should use iPhone configuration utility: http://support.apple.com/kb/DL1466
EAP-MSCHAPv2 (PEAP) example via GUI
Select the SSID "spacenet" and fill in your username (with realm) and password.
Accept the certificate. Know what the common name is of the certificate installed on your home-RADIUS and which CA signed it.
WARNING: if you are prompted again for a certificate there is chance that someone is doing something nasty!