i've found that you need a combination of ISO, f value and shutter speed to effectively take photos of the moon, a full moon is easy enough, a shutter speed of 1/500s @ ISO100 @ f/8.0 usually yields good photos for me, i could prolly handhold that, but for images' sake i use a tripod, i would definitely look at getting one if you don't already. for the eclipse, during totality i was using a shutter speed of 2s @ ISO800 @ f/5.6.
again it all really comes down to practise, get out with your camera and learn how it best takes the photos you want. don't be afraid to mess with the settings, experiment and you shall learn
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