The last time Comet C/2022 E3 (ZTF) was visible in our skies Neanderthals still roamed the Earth, 50,000 years ago, so if you don’t want to have to wait another 50 millennia, the time to see it is now. Well, maybe. But more on that later.
The comet is now just under the average limit for visibility with the naked eye, but a good pair of binoculars should allow you to see it with no problem. Luckily, over the next few nights, you’ll have a pretty big, red signpost to find it as it will be next to Mars in the sky. The Red Planet is visible to the naked eye in a westerly direction after sunset, so use it as a way to look for the green comet. For a more precise position, you can check out The Sky Live interactive page.
If you prefer a deeper look at the comet, maybe bringing out a telescope is a good idea. Many astrophotographers have snapped the peculiar space object, as have citizen scientists using Unistellar telescopes who have been collecting observations to better define the comet’s orbit. And that might be important for whether our descendants will see the comet in the future.
It's not certain that the comet will come back from the inner Solar System in 50,000 years. Current understanding of the comet tells astronomers that it is in a weakly hyperbolic orbit. That means that it should be coming back to us but a small deviation from its current path, maybe due to the gravity of the giant planets, could send it on a trajectory that would leave it away from the Solar System forever.
The comet is visible from both hemispheres but if the weather is not on your side or you do not have the right equipment, worry not. Our friends at the Virtual Telescope Project will do a live stream observation of the comet and Mars tomorrow starting at 2 pm ET.