In any direction! The distance between the Earth and the Sun is a careful balance between the mass of the Earth, the mass of the Sun, the speed with which the Earth orbits the Sun, and the strength of gravity. If any of these things change in any direction, the orbit of the Earth would change. If the orbit of the Earth changes, then the distance between the Earth and the Sun changes.
If we kept the strength of gravity the same, and increased the mass of the Sun, the Sun would exert a stronger gravitational force on everything that orbits it, and in the absence of any other changes in the solar system, would disturb the orbits of all of the planets, pulling them closer for at least part of their orbits. Our Earth has an almost perfectly circular orbit around the sun, but that’s not required to be the case – just look at the long, looping orbits of comets around our sun. If you tug on an object once (as you would, if you suddenly increased the mass of the sun), you’ll likely pull a circular orbit into a more oval, looping orbit.
If the Earth’s mass suddenly increased, we’d have a few problems here on earth, as our bodies are calibrated to work best when we’re dealing with exactly the amount of gravitational force that we have. But on an orbital sense, the gravitational force between two objects depends on the mass of both the larger and the smaller object. So if we increase the mass of the smaller object (the Earth), that will increase the gravitational force between the Sun and the Earth, probably still pulling the Earth off of its circular orbit, but also pulling more strongly on the Sun, making the Sun wobble very slightly more as the Earth orbits around it.
It’s not hard to imagine ways of changing the distance between two objects before you get around to playing with the strength of gravity. However, changing the strength of gravity does the exact same kind of things to an orbit as changing the masses of the objects you’re interested in. Let’s say we increase the strength of gravity; that’s equivalent to making everything in the solar system more massive at once. That change would, in turn, mean that the strength of the gravitational pull between all objects gets stronger. The exact response of the orbits will depend on how different the masses are, but we can safely say that the Sun would be pulled into a more wobbly rotation around its own axis, and that the Earth would wind up closer to the Sun for at least part of the year.
If, on the other hand, we let gravity get fainter, the opposite happens. The pull between Earth and Sun grows weaker, and the planets would drift farther from the Sun, spending much more time at much greater distances from the Sun. If you’d like to play around with this more directly you can try out this solar system simulator (there are a lot of other setups you can tinker with).
So really, any change to the strength of gravity, or any change to the masses of the objects involved, would change the distance between the Earth and the Sun. However, changing the strength of gravity would have relatively catastrophic consequences for a whole series of physical processes that we currently rely on, so I wouldn’t recommend it as a scenario.
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