Yes, according to the theory of general relativity, the speed of an object can affect the way gravity acts upon it. In the theory of relativity, gravity is described as the curvature of spacetime caused by mass and energy.
When an object is in motion, its energy and momentum contribute to the curvature of spacetime around it. This curvature, in turn, affects the motion of the object itself. This phenomenon is often referred to as "gravitational time dilation" or "gravitational redshift."
As an object moves faster, its energy and momentum increase, resulting in a stronger curvature of spacetime in its vicinity. This increased curvature can affect the path of the object and how other objects are influenced by its gravitational field.
Additionally, the theory of relativity predicts that time itself can be dilated or slowed down in the presence of a gravitational field. This means that an object in motion, experiencing a stronger gravitational field due to its speed, may experience time differently compared to a stationary object.
However, it's important to note that these effects become more significant at extremely high speeds or in the presence of very massive objects. For everyday speeds and gravitational fields, the effects of motion on gravity are generally negligible and not easily observable.