As an object approaches the speed of light, its mass, as observed from a stationary reference frame, appears to increase according to the theory of relativity. However, it's important to note that this increase in mass is relative to the observer's frame of reference and does not directly impact the object's gravitational field.
According to the theory of general relativity, the gravitational field of a massive object is determined by its energy and momentum, including its rest mass energy. As an object's mass increases due to its relativistic motion, its energy and momentum also increase. Therefore, the gravitational field of the object would indeed increase, but not solely due to its increased mass.
To determine the exact magnitude of the gravitational field as measured by an object at rest, you would need to consider the full relativistic effects and solve the relevant equations of general relativity. These calculations can be complex and depend on various factors such as the mass, velocity, and distance between the objects involved.
In summary, while an object's mass appears to increase as it approaches the speed of light, the increase in its gravitational field is not solely determined by its mass. The full calculation of the gravitational field would require considering the relativistic effects and solving the equations of general relativity.