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Meteor Size and Time of Arrival Calculation

-- Frank | February 7, 2021

Question:

If an 8 mile diameter meteor is approaching the earth and appears to be the same size as the moon. How far away is the meteor if use 240,000 miles as distance from earth to moon. I calculated 960 miles???

Also if an 8 mile diameter meteor is traveling 100 times the speed of sound (Sound takes 5 seconds to travel 1 mile) When you look at the meteor it appears 4 times larger than the moon 240,000 miles away.. How long until earth impact? What is the logic to explain this problem?

Thanks

-- Frank

Answer:

As your 8-mile diameter meteor appears to be the same angular size as the Moon, which is about 0.5 degrees, you can equate the angular sizes of the meteor and Moon, knowing also that the diameter and distance to the Moon are about 2159 and 238900 miles, respectively. Since angular size = diameter/distance (for small angles), you can use this equation to get the distance to the meteor.

Similarly for calculating how long until a meteor reaches Earth that appears to be 4 times larger than the Moon that is traveling at 100 times the speed of sound, which is about 1/5 mile/second, you can use the fact that the apparent size of an object is inversely proportional to its distance. In this case, the meteor appears to be 4 times larger than the Moon, so it must be at a distance of 1/4 of the Earth-Moon distance (about 238900 miles). Since you know how fast the meteor is traveling (100 times 1/5 mile/second), you can use time = distance/velocity to calculate how long it will take for the meteor to reach the Earth.

-- Jeff Mangum

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