I'm told that a hardware splitter should successfully divide the output from the Apple TV for you. It's important that it's a hardware solution since a splitter cable will not work. I have not tested this solution myself but others here have posted success.
The next issue will be to connect your projector since it isn't HDMI. There are devices sold by Apple for this purpose but in order to comply with regulations they will not work with HDCP protected content.
HDCP
HDCP compliant converters will not allow you to watch HDCP protected content such as that from the iTunes Store. Non compliant converters exist but we cannot discuss them under the Terms of Use for these communities.
Resolution and aspect ratio
I'm not aware of any converters that will scale the output from the Apple TV, any TV or projector which is used will ideally need to be widescreen and support resolutions of 720p (Apple TV 2), 720p/1080p (Apple TV 3), although the Apple TV does have a number of 4:3 resolutions it supports, but these may not be available if the TV doesn't broadcast them.
DAC
Most types of HDMI to non HDMI connectors or converters won’t carry audio, in such cases you may also need to convert your optical output to an analogue signal using a DAC. If you are considering an Apple TV 4, it doesn't have an optical out so you may need another adapter to extract audio and HDMI from an HDMI source.
HDMI to HDMI + Audio (Example Only - Not a recommendation or suggestion that this is suitable in your circumstances)
DAC (Example Only - Not a recommendation or suggestion that this is suitable in your circumstances)