Connect HDMI Chromecast to VGA Projector

My projector has a VGA socket, but no HDMI. I'd like to connect my Google Chromecast, or other HDMI devices to it via the VGA port. I assume this can't be a simple pin-out conversion as they are completely different, but is there a relatively inexpensive way of doing this?

It is possible to buy a cheap DVD player, or some other 'box' that has a VGA/SCART output that will accept a HDMI through?

Any ideas?

Thanks

I think some HDMI sockets output the analogue RGB that VGA uses, I know DVI certainly does, I would be surprised though if the chromecast carried this signal.

On the amazon links some are just leads and some have a box on them, do the boxes actually convert anything, I doubt it.

Quick update on this - if you plan on using Chromecast with an adapter (it does work!), make sure the adapter has its own power supply. Chromecast's HDMI output doesn't provide enough power for the "unpowered" adapters.

I've tried the white box versions (branded as "MINI" in the pictures) from Amazon and both the composite video and VGA versions work for me.