Damping apparatus and exposure apparatus

An assembly comprising:

• a stage apparatus that includes a first stage, a second stage, a first motor that moves the first stage and the second stage along an X axis, and a second motor that moves the second stage along a Y axis that is orthogonal to the X axis;
• a base plate that supports the stage apparatus;
• a first mount, a second mount, a third mount and a fourth mount that are spaced apart and that cooperate to support the base plate in a vertical direction;
• and
• a control system that controls the first, second, third, and fourth mounts, the control system includes a thrust calculating unit that utilizes an equation as provided below to calculate at least a portion of a thrust value for the first mount:
• F
• A
• =
• W
• 4
• -
• W
• 2
• ⁢
• L
• X
• ⁢
• X
• -
• W
• Y
• 2
• ⁢
• L
• Y
• ⁢
• Y
• +
• W
• Y
• L
• X
• ⁢
• L
• Y
• ⁢
• XY
• where (i) FA is a thrust value for the first mount;
• (ii) W is a force that the first stage and the second stage exert upon the base plate as a result of gravity;
• (iii) WY is a force that the second stage alone exerts on the base plate as a result of gravity;
• (iv) X is a position of a center of gravity of the second stage along the X axis, (v) Y is a position of the center of gravity of the second stage along the Y axis, (vii) LX is a distance between the first mount and the second mount in an X direction, and (viii) LY is a distance between the first mount and the third mount in a Y direction.