Can the acceleration of gravity be measured with a mathematical pendulum under zero gravity?

As strange as it may seem, you can. It is only necessary to judge that the pendulum is in weightlessness not by the value of the oscillation period T, but by the strangeness of the load behavior. As soon as it is noticed that the load does not hang on the thread, but floats freely relative to the suspension point, then the acceleration of gravity is zero. As soon as it ceases to be nonzero, the weight will begin to pull the thread and work like a pendulum.