Yes, you can compost satsumas (aka mandarins or tangerines) – though there are a few things to keep in mind.
Firstly, the rind/peel is a great protective layer for the fruit – perfect for its journey to us but a hindrance to speedy composting. If for some reason you’re throwing away whole fruit, split them open to aid decomposition.
Secondly, too much citrus fruit/peel can disrupt the balance of your compost heap. If it becomes too acidic, it might cause problems for the bacteria that breaks the stuff down into compost.
Also, many types of compost heap worms or wormery worms, such as tiger worms, don’t like d-limonene, an antiseptic substance found in fresh citrus peel. The d-limonene disappears as the peel rots though so your worms will prefer it if you leave it out of the wormery/compost heap until it’s green and furry.
Basically, the odd bit of citrus fruit is fine but too much – for example if you’re making acidic juices from a lot of fruit every day – might cause problems. (Some people keep a separate compost heap/bin for problematic stuff – it’ll compost down eventually and won’t get in the way in the meantime.)