It is impossible to get to the moon on Pokemon Emerald version because it is not part of the gameplay or a side quest. Although there is a place called Space Center in Mossdeep City, it does not function as a means of going to the moon.
There are a number of things that can be done in Mossdeep City. These includes healing the player's Pokemon, obtain the Super Rod and obtaining the HM08 Dive. However, going to the moon is not among the things to be done in the city. The player can obtain the Sun Stone at the Space Center and likewise battle Team Magma grunts. After completing these tasks, the gameplay will take the player somewhere else, but not to the moon.