How evasive is the Earth to Catastrophic Meteors?

Google says the Earth is approximately 92.96 million miles from the Sun. It also says the suns radius is 432,474 miles.

Therefore, it is 93,392,474 miles from the Earth to the center of the Sun:

92,960,000 + 432,474 = 93,392,474 miles

I've heard the Earth's orbit is elliptical, but to keep things simple, let's just say the orbit is a perfect circle. Therefore the radius of this circle is 93,392,474 miles. This would mean the diameter of our orbit would be 186,784,948 miles:

93,392,474 x 2 = 186,784,948 miles

The circumference of a circle is π x the diameter of a circle. Therefore, the number of miles in Earth's orbit would be about 586,504,736.72 miles:

3.14 x 186,784,948 = 586,504,736.72 miles

So, the Earth travels about 586,504,736.72 miles in one year. Since there are 365 days in year, that would mean that Earth travels about 1,606,862 miles in one day.

586,504,736.72 ÷ 365 = 1,606,862.292383562

That would mean the Earth travels about 66,953 miles per hour:

1,606,862.292383562 ÷ 24 = 66952.595515982

And this would mean the Earth travels about 1,116 miles per minute:

66952.595515982 ÷ 60 = 1115.876591933

Lastly, this would mean the Earth travel about 18.6 miles per second:

1115.876591933 ÷ 60 = 18.597943199

Google says the diameter of the Earth is 7,917.5 miles. So, as fast as the Earth is traveling, a catastrophic meteor has about a 7 minute window to hit target Earth.

7917.5 ÷ 18.597943199 = 425.719119329 seconds
425.719119329 ÷ 60 = 7.095318655 minutes

What are the odds of a catastrophic meteor hitting the Earth? Or, maybe a better question: What are the odds of the Catastrophic Earth hitting a poor meteor!?

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    $\begingroup$ "What are the odds of a catastrophic meteor hitting the Earth?" You will have to specify a time limit, because over periods of millions of tears, Earth does get hit. What are the odds over the next century, perhaps? $\endgroup$ – Andy Feb 19 '16 at 9:46
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    $\begingroup$ Ok, sure. I'm interested mostly in the meteors that might kill me personally. So, lets be generous and say I have 60 more years to live if a catastrophic meteor does not curtail my life. $\endgroup$ – Lonnie Best Feb 19 '16 at 16:54
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    $\begingroup$ Ah regarding a single lifetime and a single life, then I'd say, based on actual reported injuries, virtually zero risk! (I've only heard of one suspected fatality.) But James' answer has the more scientific estimates (I've voted for that one myself) $\endgroup$ – Andy Feb 19 '16 at 17:13
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    $\begingroup$ Ha! Ok, thanks Andy. I shall now walk around with arrogance towards meteors. That won't hurt my odds, will it? Can you offend a meteor? $\endgroup$ – Lonnie Best Feb 19 '16 at 17:20

There is nothing wrong with your maths, but it isn't relevant to the question of the frequency of impact.

Now you ask about comets, but do you also want to include asteroids, since these are rather more common.

You also ask about catastrophic, and this is a poorly defined word. A Tunguska scale event is a local disaster, but has no significant global effects.

The Torino scale classifies objects according to their threat. A "10" on the Torino scale signifies a object carrying an energy of more than 10000 Megatons of TNT and capable of causing a global catastrophe. Such events occur, on average of less than once in 100,000 years.

Within the next 100 or so years the probability is considerably lower than $10^{-5}$ in each year, as many of the potentially hazardous objects have been observed, and their orbits shown not to intersect with Earth. So while a naive estimation would suggest that the chance of an impact in the next 100 years is about 1 in 1000, the actual probability is rather less than that.

If you restrict to only comets, the probability is reduced further.

  • $\begingroup$ Thanks for the more precise terminology (I agree those terms much better than "catastrophic"). To me, anything that hits the Earth (whether it is a comet, asteroid, or something else) is of interest and these things become a "meteorites" (from Earth's perspective) upon impact. That might not be proper terminology either though. $\endgroup$ – Lonnie Best Feb 19 '16 at 16:44

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