What if Earth changed its position? Well, that would be fatal instead of pleasant, or at least dramatic changes in the environment.
The Habitable Zone
The habitable zone is where liquid water can exist on the planet’s surface. If Earth gets closer, it would have a runaway greenhouse effect. If Earth gets farther, it will be frozen. Interestingly, although Mars is in the habitable zone, it has almost no greenhouse effect so it is so cold. If it had a thicker atmosphere, water would barely stay liquid in lower latitudes.
Earth is right on the inner edge of the habitable zone and it is just right not to trigger a runaway greenhouse effect. If it gets any closer, it will be too hot. So let’s first assume it gets closer.
The Consequences of being out of the habitable zone
Outside the habitable zone, the temperature is too hot that the rate of vaporising oceans rises to a level that we can’t control. The temperature would rise uncontrollably because water vapour is a greenhouse gas and it is good at trapping heat. When all the oceans have vaporised, it would be a Venus-like hostile planet, unfriendly for life.
Then, what if Earth somehow left its orbit and visit the Asteroid Belt? First, it will get farther away quickly, and eventually reach Mars’s orbit. There would be already some fatal changes for the temperature that water in lower latitudes would freeze too. But the greenhouse effect would still keep the planet warmer than Mars.
It will finally reach the asteroid belt and it is one of the rock there. At that time, all the oceans would freeze and it would be colder than Mars. Also, more asteroids would enter its atmosphere because it is the main belt of space debris.
In the worst case scenario, 2 would both happen in the same period. We’re talking about Earth being ejected, which is next to impossible. First, to accelerate, we need to be so close to Sun that at that distance, the molten surface would be covered in magma, just like 55 Cancri e. After that, it would reach the escape velocity of the Solar System. Soon, it would be too cold for life. We would be long dead at that moment. Then, it would fly through the system, waiting for being out of the Solar System. The best case is that Earth somehow became a satellite of the giant planets or being pulled by Sun, or it would be as cold as OGLE-2005-BLG-390Lb and be a rogue planet, leaving its home permanently.
It will eventually happen in the future. A billion years later, Sun’s habitable zone will expand but move outward because of its increased luminosity. Earth would be out of the habitable zone and it will be fried although it would surely be earlier because of the carbon dioxide and other greenhouse gases produced by us.
After that, Sun will become a red giant, swallowing Mercury, Venus, Earth or even Mars. Then, when it expands to a critical point, its core becomes a white dwarf and the outer layers become a planetary nebula. If Earth somehow survived, it would be so cold because of the low luminosity of a white dwarf.