I have a meatball recipe that calls for ground beef, but all I have on hand is ground pork. How might that affect the binding of the ingredients and the cooking in general?
It won't. In meatballs, pork and beef will behave pretty much the same, the flavor will just be of pork or of beef. The only real difference that you're likely to see (other than flavor) is if you are substituting ground pork for beef of a lower fat content. Ground pork in the US is not generally labeled for fat content, but tends to run about 20% fat. Ground beef is common in that range too, but a lot of people choose lower fat ground beef as it is labeled for fat content.
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Don't worry though, your meatballs will be fine.
It is the fat content of the meat that affects the outcome. Using turkey instead of pork or beef can lead to a dry meatball.