What If: The Sun shot an Earth-sized fireball in a random direction once every 10 years?

I wouldn’t worry a whole lot about it.

At the distance of the Earth’s orbit, around 150 million km, the sphere around the sun would have a surface area of 4(pi)r², or 282,743 trillion square km. The Earth, being 6,371 km in radius, is a target that’s (pi)r², or 127.5 million square km in size.

Another way of looking at this, is that if you made a sphere around the sun at the distance of the Earth, you would need a sphere of about 2.2 trillion Earths to complete the sphere.

Even if you figured that the fireball had to just barely touch the Earth’s atmosphere to destroy the Earth, then your earth-sized fireball would have to hit Earth, or any of the 8 Earths touching it. So now we have any one of 9 Earths, out of 2.2 trillion, that must be hit by the sun’s 10-year fireballs. That’s about a 1 in a quarter of a trillion chance, every 10 years.

The entire life of our planet is 5 billion years old, or, 500 million sun fireballs, meaning there’s only about a 500 million in 250 billion, or a 1 in 500 chance that one of these solar fireballs had ever hit the Earth at any time in the history of our planet.

Each time the sun shoots off one of these fireballs, every 10 years, there’d be a 0.0000000004% of it hitting the Earth.