1."Affect" works the same as "influence", but remember that the noun is spelt with an 'e'.: "The new theory affects the scientific world" "The new theory has an effect on the scientific world". 2. "Impact" has traditionally also followed the same pattern: "The new theory impacts on the scientific world" "The new theory has an impact on the scientific world". In recent years, however, I've often seen "impact" used without a preposition e.g. "The new theory impacts the scientific world" . It sounds wrong to me to use this verb with a direct object, but it does seem to be accepted nowadays.

Re. affect/effect, also make sure not to use effect as a verb here; confusingly, 'effect' is a verb, but with a different meaning and usage Traditionally 'impact' was rarely used as a verb, ('impacted wisdom tooth', but not much else) so it wasn't similar to 'influence' at all: 'have an impact on' would be the only way to go. Common usage as a verb, with or without 'on', is quite recent, I think. For better or worse the verb is thought of variously as an Americanism (especially without 'on'), business-speak, or as a nerb (unjustly, but nerbophobia often is unjust), for which some people dislike it.