# Solving Simple Problems in ASTRO 100

In the following we will show how to solve simple problems in astronomy. One of the most common type of problem in astronomy (and everyday life, for that matter) is the distance - velocity - time problem. 1. For example, suppose you are driving cross-country at an average speed of 60mph. If you drive for 12 hours how far will you get?
 A).. 5 miles B)..720 miles C).. 72 miles D)..7200 miles E)..500 miles

2. How did you solve that problem?
 A)... Multiplied the distance times the time. B)... Multiplied the speed by the time. C)...Divided the speed by the time. D)...Divided the time by the speed. E)...Added the speed to the time.

Notice that you used the basic relation that Distance = speed x time, or mathematically, D=Vt, where D is the distance you traveled, V is your average speed (more technically the velocity), and t is the time you traveled.

Now let's do a variation on that problem.

3. Suppose you are driving from Boston to New York. If you travel at an average speed of 50 mph and the distance is 250 miles, how long will the trip take?
 A)... 300 minutes. B)... 200 minutes. C)... 5 hours. D)... 5 minutes. E)... 50 hours.

Notice that you again used the basic relation D=Vt, but now in the form time = distance/speed, or mathematically, t=D/V.

Let's now do an astronomical version of this problem.

P 4. The space shuttle travels around the Earth in a circular orbit whose circumference is about 25,000 miles. The shuttle's orbital speed is about 17,000 miles/hr. About how long does it take the shuttle to complete one orbit around the Earth? (Notice this is exactly like the driving problem above.)
 A)... 1 hour B)... 1.5 minutes C)... 0.6 hours D)... 1.5 hours E)... 15 hours

Notice that in this problem none of the answers you chose from were the answer you found mathematically. Rather, you were asked to choose from rounded off answers. Such rounding off is very important in writing out answers. Generally 3 digits is accurate enough for our purposes.

For example,

5. round off 2.7248283...to three figures.
 A)... 2.72 B)... 2.73 C)... 2.71 D)... 2.74 E)... 2.70

Let's now do another astronomical distance/velocity time problem.

6. A radar pulse is sent from the Earth to an asteroid, bounces off and returns to Earth. The radar pulse travels at the speed of light (300,000 km/sec) and takes 150 seconds to travel out and return. How far away is the asteroid? (Notice that this is exactly like problem 1 above.)
 A)... 2250 km B)...4500 km C)... 45,000 km D)... 4.5x107 km E)... 2.25 x107 km

To better comprehend how much time the pulse takes, let's express the 150 seconds in minutes.

7. 150 seconds is about how many minutes? (As a quick check on your answer, will the number of minutes be more or less than the number of seconds?)
 A)... 2.0 B)... 2.5 C)... 25 D)... 0.25 E)... 0.4

You will often have to make conversions of this sort in problems. For example, suppose we ask the following: How many years does it take a ray of light to travel from a star 12x1013 km from Earth to our planet? Recall the speed of light is 3x10 5 km/sec.
In this problem you will get an answer in seconds, but you are asked for the answer in years. Thus, you need the number seconds in a year. You can figure that out by multiplying the number of seconds in a minute by the number of minutes in an hour by the number of hours in a day by the number of days in a year. In doing all that you will find that the number of seconds in a year is about 3 x 107.

8. Given this conversion factor, what is the answer to the above problem?
 A)... About 1 year B)... About 3 years C)... About 13 years D)... About 13 million years E)... About 1.3 years

If you had trouble getting this answer, check your powers-of-ten math. For example,

9. what is 10 13 divided by 10 5 ?
 A)... 108 B)... 102.6 C)...1018 D)...8 E)... 2.6

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