Build solar powered Arduino with RTC support

We want to have Arduino or any low power board running on solar energy(with good battery backup). Ardunio should wake up on absolute time using RTC like 1:00 AM, 2:00 PM, and is configurable(it can be running on every hour's 1st minute). Once it wakes up it should perform a routine(around 10 sec) and go back to sleep for low battery consumption. Deliverables: 1) Arduino with RTC integration and solar-powered with battery backup. 2) Capacity plan of battery and calculation about how long it would run in worst condition(no sun for two weeks or so in monsoon). The expectation is to make it durable and long-lasting. 3) Once done can discuss about enclosure and PCB making if required. (optional)