Man, this is a complex question these days with newer vehicles being mostly computer networks with auto parts attached instead of a mouse and keyboard. It's probably not a good idea for many vehicle electronics suites to just remove the battery cables for even a few seconds. I use a OBD-II cable attached to a battery charger to keep the car alive while messing with the starting battery. (You can buy these on EBAY, Amazon is evil.)
You would definitely want to remove the ground cable if you don't have a trickle charger installed. The car electronics usually have parasitic loads that never really turn off, and they will drain the battery enough to damage it in a few weeks. If you have an accurate and sensitive amp-meter, you can measure the parasitic load directly, although you might have to leave the meter on for more than 24 hours to get the full picture.
500-750 milliAmps seems like an appropriate amperage for a trickle charger.(1000 milliAmps = 1 Amp) The listed charging amperage is usually the maximum amount the thing can output, but most chargers are capable of reducing or tapering the charging amperage as the battery voltage increases. 2 amps is too much for continuous trickle-charging on a car battery, and may even slowly de-water the battery if it is a flooded lead acid type. But most chargers are capable of tapering the charge amps.
As Glenn's figures point out, lead acid batteries self-discharge continuously even when disconnected. The rule of thumb I learned is 10% per month. But you never want to discharge a lead-acid battery even to 50% if you can avoid it, and you immediately recharge to 100% ASAP. Batteries at less than maybe 90% of full charge (12.8 Volts) begin to sulphate up and will die young, as well as be more likely to let you down on a cold day or a hard start.
It is a lot cheaper to buy a decent battery trickle charger than replace the battery repeatedly because it has been permanently damaged from being even 20% discharged for long periods.
A sulphated battery has lost a lot of its capacity, so you may be looking for a jump start on a cold morning or wasting a lot of your PV output. A sulphated battery loses charge faster, so it is losing lifespan faster when you push it hard. It's a battery death spiral.
You can buy dedicated battery desulphators or battery chargers with desulphator functions. These can help restore batteries damaged from being stored in a discharged state, but you never get back the original full battery capacity.
Seems like putting on a good quality trickle charger, and leaving the battery connected might be the safest bet for a lot of vehicles.
A dirty/damp battery will self-discharge faster across the current path provided by the gunk. A clean battery is a happy battery!
Many people think you should never store batteries directly on the ground or concrete...
Things you can do to battle entropy and make your batteries live long and prosper, like 10+ years:
1. Buy the largest battery you can fit into the space, and buy the heaviest battery in its Group. The larger the battery, the less you discharge it in everyday use. The heavier the battery, usually the more lead in the plates and the longer it will last. (Batteries like DieHards are tuned to die just before the warranty expires. That's the data the purchase date tag carries.) That huge heavy Group 27 under the hood will start your car or keep it running a lot longer after the charging system fails on a trip and maybe save you a lot of trouble. Been there, done that.
2. Keep the battery 100% charged at all times. I use
solar battery maintainers or trickle chargers a lot, and will put a battery charger on anytime I had to discharge it much. There are newer vehicles that intentionally won't fully charge the battery for many miles after a cold start to reduce emissions and eke past some standard like ULEV or PZEV. You can't necessarily trust the car to keep the battery fully charged any more... Learn to use a voltmeter.
3. Use distilled water if needed.
4. Keep the battery and terminals clean.
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