Maybe try picking the nearest solid object, and calculating the angle difference between it and your character object (eg: GravAngle).
Then move your object at your chosen speed (eg: GravSpeed) towards this angle:
X = Character.X + GravSpeed * Cos(GravAngle - 90)
Y = Character.Y + GravSpeed * Sin(GravAngle - 90)
Might need some tinkering for calculating the angle difference, and whether or not the - 90 is required though (as this is used to move at the angle an object is facing).