Gravitomagnetic Force

we know that the field exerted by a static charge is different from that of a moving charge. also a moving charge exerts magnetic effect but a static charge can not. also the gravitational field is very much similar to electric field. but why moving mass can't create a different field than a moving mass? is there any weak field be created due to a moving mass like magnetic field?
- shantonu mukherjee (age 19)
hooghly/west bengal/India

That's a very perceptive question.  There's an argument based on Special Relativity that requires the existence of the velocity-dependent magnetic force to accompany the electrical force. A similar argument applies to any force. So yes, there's a velocity-dependent component of the gravitational force. The full expression of it requires General Relativity, but so long as the gravity is weak one can draw a close analogy between the magnetic effect for electricity and this gravitomagnetic effect.

This effect has recently been measured by the Gravity Probe B experiment.

A Wikipedia article goes into more detail:
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Mike W.

(published on 09/22/2012)