Mainstream has it that gravitational force travels with the speed of light. Thus if the gravitational force between the Sun and Earth were suddenly to disappear by the vanishing of the Sun, it would take about 8 minutes for the effect to be experienced on the Earth. The Earth would then fly off along a tangent to its original curved path.
Against the mainstream is that gravitational force is instantaneous in a static field. Thus when the Earth is moving around the Sun, the attraction of the Earth is toward the instantaneous position of the Sun and not where the Sun had been. If the Sun’s position was retarded by the 8 minute delay of light speed the pull of gravity would be toward the optical and not the actual position of the Sun.
A gravimeter (gravitational force detector) employed during the lunar eclipse of 28th Sep 2015 might have provided the answer to the opposing views. So when the eclipse occurred visually, if the maximum gravitational force of Sun-Earth with reference from Earth had shifted 5.7x10-3 degrees east, the gravitational force would be acting instantly. Fig1.
Zhu, Yin (2011). “Measurement of the speed of Gravity” arXiv:1108.3761
Also regarding the film ‘Event Horizon’, where the ship uses gravity drive:
Zhu, Yin (3 June 2016). Can we use the Gravitational field?