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See National Math Standards for this Challenge.

Q: How long after the impact happens will it be visible from Earth?

In order for you to be able to answer this question, you just need to know the following information:

1. The comet (and therefore the impact) will be 0.895 Astronomical Units (AU) away from Earth.
2. One AU is the average distance between the sun and the Earth, or roughly equal to 92,960,000 miles.
3. One mile is equal to 1.6093 km.
4. The speed of light in a vacuum is 2.998 x 108 m/sec (299,800,000 m/s).

All that remains is a matter of converting units. Good luck!

For comparison, try these questions as well. How long would it take to travel the distance between the comet at impact and Earth if you were:

1. Flying in a jet at around 300 miles per hour (480 kilometers/hr)?
2. Driving in a car at 65 miles per hour (105 kilometers/hour)?
3. Riding a horse at around 8 miles per hour (13 kilometers/hour)?
4. Taking a casual walk at around 30 feet per minute (0.5 kilometers/hour)?

A: This is a matter of unit conversion, as follows:

The first thing to do is figure out how far away the impact is from Earth in meters...

 0.895 AU × 92,960,000 miles = 83,199,200 miles 1 AU

 83,199,200 miles × 1.6093 km = 133,892,472.6 km 1 mile

 133,892,472.6 km × 1000 m = 133,892,472,600 m 1 km

And now use this distance and the given speed of light to figure out how long it will take for the light from the impact to reach Earth...

 133,892,472,600 m × 1 sec = 446.6 sec 299,800,000 m

 446.6 sec × 1 min = 7.44 min 60 sec

So, it will take 7.44 min (7 minutes, 27 seconds) for the light from the impact to reach Earth.

This is one of the reasons that the impactor spacecraft has to be able to think for itself. The only way to communicate with the spacecraft from Earth is through radio. Radio waves are just another form of light, so they take as long to travel between the area of impact and Earth as the light does.

Imagine trying to steer the impactor spacecraft from Earth. The impactor cameras notice that the impactor is off course, and send this information to Earth. The message is received 7.44 minutes later, the operator has to make a decision to adjust (say 1 minute think time?) then the operator's message takes 7.44 minutes to reach the spacecraft. Total elapsed time is around 16 minutes before a course adjustment can begin. By that time, it may be too late to correct, and any correction that the operator came up with may be wrong that much later anyway.

So, it's very important that the impactor spacecraft be able to make its own decisions about course corrections, or there may be too long a delay for something to occur. This is especially true if a decision has to be made anywhere within 15 minutes of impact. Once the impactor is that close, it's too late for any instructions from Earth to do any good.

As for the other questions for comparison, use the distance you determined (133,892,472.6 km or 133,892,472,600 m) and the given speeds to figure out the times:

1. Jet:

 133,892,472.6 km × 1 hour = 278,943 hours 480 km

 278,943 hours × 1 day × 1 year = 32 years 24 hours 365 days

2. Car:

 133,892,472.6 km × 1 hour = 1,275,166 hours 105 km

 1,275,166 hours × 1 day × 1 year = 146 years 24 hours 365 days

3. Horse:

 133,892,472.6 km × 1 hour = 10,299,420 hours 13 km

 10,299,420 hours × 1 day × 1 year = 1,176 years 24 hours 365 days

4. Walking:

 133,892,472.6 km × 1 hour = 267,784,945 hours 0.5 km

 267,784,945 hours × 1 day × 1 year = 30,569 years 24 hours 365 days

It's a good thing we have radio to communicate with. It would be a shame to have to wait so long for our data to come back!

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