Low power + Logging motion detection Scenario: I would like to monitor my closet's door as I highly suspect a family member is opening and using my items without permission. To respect privacy and also because my closet is nowhere near a power mains, I don't need video nor audio recording. I also do not need indicator lights etc because I intend to turn it on when I go to work and check the logs on the SD card when I return home. A typical day would require the device to run for 12 hours minimally.

Aim: Is it possible for Arduino to achieve the following,


Run on batteries for at least 1 month
Detect motion
Logging the detection motion onto a text file in a SD card


Or do I have to look elsewhere for this functionality?

Current understanding: I am aware Arduino can run on batteries though I've never been able to get it to last more than 3 hours. Probably has to do with me not using the low power mode or something and that my batteries were being stepped up. I also know that Arduino has some PIR motion sensors though I don't quite remember how power hungry these sensors are. I have NEVER tried logging onto an SD card using Arduino. This sums up my experience with Arduino.

Any advice would be much appreciated. Thank you.
You would be better off with a bare ATmega chip than an Arduino - you want to eliminate extraneous circuitry like a USB converter, regulators with quiescent current draw, and any resistors pulling signals against their usual state.  Fortunately the ATmega chip has a fairly wide voltage range, especially at 8 MHz or below, so you can use something like 3 cells, alkaline or rechargeable, over most of their range.

An SDcard is neither necessary, nor a good idea.  If your circuit won't be discovered you can probably hold the data in static ram while the ATmega sleeps; if not, the quantity of data would probably not exceed the on-chip EEprom and would certainly not exceed that of a 4 megabyte SPI flash. Either of these will be far more robust (and low power) in a battery powered situation than an SD card.  They will also be simpler to support in software.  Either an SPI flash or an SDcard will probably have a narrower supply range the the ATmega and require a regulator - you may be able to enable that only when you need to access the memory.

Your main power consumption win however will be sensors.  If you can use a contact sensor - either a direct switch, or a magnetic reed one, that will result in the lowest power consumption.  Your next option might well be an accelerometer chip, specifically if you choose one which can run in a micropower mode and fire a wakeup interrupt to the MCU when it detects that a door it is mounted on is being opened.  Anything with light is likely to have much higher power consumption and could well be impractical, unless you figure out how to operate it in short bursts with a lengthy inactive time in between.