Can Garmin Edge 500/510 and 800/810 be charged while riding?
Just verified that the 510 can be attached to power while on/in use. It continues to operate. When the external power source is removed, it will give a message to that effect, but does not power down (like the nuvi/car versions do).

Note that you (obviously) have to open the weather seal to plug in power.

Also worth noting, the 510 will go into a different mode when you plug it into a computer. Unsure if it will continue to record, but the screen shows the computer attached so suspect not.

For long trips like you describe, a device like these http://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Daps&amp;field-keywords=phone+battery+backup
should do the trick.