Israel says it intends to take control of areas from which rockets have been fired
By Jeremy Bowen
BBC Middle East editor, Jerusalem
A senior Israeli military source has said it is unrealistic to stop all the rocket fire.
But the Israeli army believes it can be decreased, and made less accurate, thanks to what he called boots on the ground. The objective, the source said, was not to recapture the Gaza Strip.
Plans had been drawn up to unseat Hamas and if the order was given it could be done, although it would be a long campaign.
The Israeli military says Hamas fighters are not engaging with them in close combat. Instead they are using mortars and improvised bombs.
Hamas' objective will be to give the Israeli army the same humiliation that the Shia movement, Hezbollah, inflicted during the 2006 war in Lebanon
Israel is trying to deflect some of the international condemnation it has had for killing civilians and using air power and ground forces in a place where 1.5m people live.
It says that the humanitarian effort has been integrated into the military planning.
That is unlikely to reassure all those who have called for an immediate ceasefire.
It is clear that Israel believes it is also sending a message to its other enemies - especially Hezbollah in Lebanon.
Israeli military sources say Hezbollah's capacities have not been decreased, but if they want another round they would pay the price.
The Israeli army was hit hard by Hezbollah in the 2006 war. Hamas will want to emulate them. Israel does not want a repeat of what happened the last time it invaded Lebanon.
Israeli troops have entered Gaza before to try to stop rocket fire - they did not succeed.
Hamas leaders have warned that a "black destiny" awaited Israeli forces
This time, after a week of air strikes, Israel believes force will work, because much more of it is being used.
The Israeli military will be concerned about casualties, but they are a very formidable and well-armed, modern force.
Its troops also know Gaza very well, having occupied the coastal territory from 1967 until September 2005.
Nevertheless, they may find it difficult when they enter the main populated areas, in which the buildings stand pretty close together. The many refugee camps are warrens of single-storey, concrete or breeze-block houses with tin roofs.
Hamas fighters, who know Gaza better than the Israeli troops, have a belief in resistance and martyrdom.
Their objective will be to give the Israeli army the same humiliation that Hezbollah inflicted during 2006.
For all their bravado, Hamas are unlikely to be as formidable as Hezbollah.
The rocky, hilly terrain of south Lebanon was not good for Israel's armour. Gaza, on the other hand, is flat and sandy.
Hamas is said to have smuggled weapons in through tunnels under the border Egypt, but it is doubtful that it has the arsenal which Hezbollah acquired.
Even so, they will be the latest heroes to those people across the Islamic world who have latched onto ideology of resistance to Israel and its American allies, which has become one of the region's most potent ideas.
For Hamas, the definition of victory will be that they can they fight on at the end of all this; for Israel it will be the stopping of rocket fire from Gaza.