Four Fates for Humanity

The Earth is doomed. Sometime in the future, a giant asteroid or comet will strike it, or a gravitational anomaly will eject it from the solar system, or the Sun will expand and engulf it, or a black hole will gobble it up, or ...

The Earth is doomed. Humanity with it, unless we conquer space; or evolve into / create a species that can do so.

I can imagine four fates for humanity:

Easter Earth
============
We bumble along, burning oil and ripping up forest and breeding uncontrollably etc., until the Earth is as barren as the once forested and prosperous Easter Island is now. Civilisation collapses as resources run out. At best, we have to start all over again, but without fossil fuels. At worst, we cease any meaningful evolution, and die out with (or more likely, before) the Earth.

Bio Earth
=========
We adjust to climate change and the current demographic challenge, and go on to bio-engineer our further evolution. It becomes possible to regrow amputated limbs, for example. Artificial wombs enable the first substantial increase in cranial capacity since Homo Sapiens. Efficient means of space travel are invented, and genetic engineering makes it tolerable for biological life forms. Homo Sapiens might be exterminated, being dangerous, or preserved on a museumed Earth.

Info Earth
=======
We adjust to climate change and the current demographic challenge, then go on to create "artificial minds"; i.e. robots. Having external reproduction, distributed consciousness, mental cloning, etc. makes them a quantum evolutionary leap. "Eating" only energy and minerals, "excreting" only heat and dust, they are ideally suited to space. As for the fate of their progenitors, we will probably be exterminated, being dangerous, and of no practical importance.

Nano Earth
========
Whether biological or infocanical, the Earth becomes a single colony of nano engineered particles. Over some (probably extensive) period of time, the atmosphere and oceans are withdrawn into an artificial interior, and a giant column begins to rise. Eventually, using just the rotation of the Earth, blobs begin flying off the tip of the column, as spores to colonise space.