If the Sun were to suddenly vanish at this very moment, the light from the Sun would continue to arrive for the next 8.5 minutes which is the travel time from the Sun to the Earth at the speed of light. There would still be a Sun in the sky even though the Sun is actually not there now. So far as we know, and so far as the little data we have can tell us, gravity and the force of gravity also travels at the speed of light. This means the Sun's gravitational force takes 8.5 minutes to cross the solar system to get to the Earth and affect the orbit of the Earth. If the Sun were to vanish, the gravitational force that it emitted before vanishing would still be on its way and would not stop coming for 8.5 minutes after the Sun had been removed. Would we see anything interesting happen to the orbits of Mercury and Venus that would alert us to the fact that the Sun had gone away? No. At least not right away. The fastest that the effects could reach us would be at the speed of light. Any effects we would see upon the other planets would take LONGER to get to us because the planets would be farther away from us than 8.5 light minutes. If Mercury were very close in the sky to the Sun, the effect would first have to get to Mercury, then the light from the planet would have to get to us. This total distance from sun to Mercury and Mercury to Earth would never be shorter than the direct travel distance of the effect to the Earth. Looking out at the sky, we would feel nothing at all as the Sun winked out except that it suddenly got a whole lot colder. Daytime would become nighttime in the blink of an eye, and as we looked at the planets Mercury and Venus over the course of a few hours or days, we would see them departing more and more from their previous orbits as they suddenly find themselves traveling 'in a straight line' tangent to their previous orbits, at the orbital speed they used to have.