What were each side objective going into battle gettyburg and Vicksburg?

Answer 1

The garrison commander, John C. Pemberton, would certainly like to have known the answer to that question, as he was at the mercy of conflicting orders. The Confederate president told him his orders were to hold the town at all costs, while his local area commander, Joseph E. Johnston, was urging him to evacuate the place and save his army.

On the Union side, it was a simpler matter. Grant's aim was simply to capture Vicksburg and liberate the Mississippi.

Answer 2

Once retreated into the entrenched camp of Vicksburg, general Pemberton aimed to carry on a passive defense of the fortress waiting for a relief army led by gen Joseph Johnston to come.
Once succeeded in encircling Vicksburg, general Grant managed to completely isolate the fortress and built a second line of circumvallation to prevent his army from being attacked from the back by the Confederate Army that Joseph Johnston was attempting to set up for this purpose. Furthermore Grant intensified the bombardements both from the land and river's sides, which led to the surrendering of the fortress and the capture of the whole besieged Pemberton's Army.

Answer 3

Gettysburg: Lee hoped to destroy the Federal forces in a Decisive Battle that would free him to threaten northern cities and cause the Union government to sue for peace. Meade's more limited objective was to force Lee to give up his invasion, then, if possible, destroy his army.

Vicksburg: Grant hoped to close the Mississippi to enemy traffic, to choke off reinforcement and supplies between southern states and turn the river into a Northern supply line and communications conduit. Pemberton hoped to hold out until a relief force could break Grant's siege.