## Just How Big is this Place? |

- Examine ways of measuring distance
- Make inferences regarding space travel
- Identify the distance relationship between Earth and other objects in the Universe
- Develop formulas and procedures for determining measurements to solve problems
- Chose the appropriate metrics units and tools
- Calculate using the appropriate metrics units

Students often have difficulty comprehending just how immense the Universe actually is. In an effort to help them grasp this abstract concept, this lesson develops a path along which they encounter increasingly larger numbers. This script allows them to correlate distance to the more tangible concept of time. If you tell a student a planet is 10,000,000,000 kilometers away, it doesn't mean as much as when you tell them it would take a car traveling at 100 km/hr 100,000,000 hours to make the journey. The point is really made when the student realizes that is 4,166,667 days or 11,415.5 years!

To introduce the lesson, have the students complete the Just How Big Is This Place? worksheet. This activity will allow them to start associating typical sizes to objects and ranking them in order from smallest to largest. The next part of the lesson will be where the students manipulate the actual numbers involved in exploring the Universe.

In today's world, travel is made easy by jet aircraft, high-speed trains, and interstates on which cars may travel at high rates of speed. If you have relatives in a city 200 kilometers away, you can be at their house in only 2 hours by car if you travel at a speed of 100 kilometers per hour. How do we know this? By using the formula t = d/r (where t = time, d = the distance traveled, and r = the rate at which we travel), we can calculate our travel time.

The following questions/problems can be posed to students to take them to the ever-larger numbers encountered in our Universe.

What if those relatives lived 400,000 km away on the Moon; how long would it take to get to their house if you traveled by car at 100 km/hr? 4000 hrs.

The distance that you must travel to get to a lunar relative's house is nothing compared to the distance you must cover in order to visit a relative on Pluto. Pluto is 6,000,000,000 km from Earth. If you travel at 100 km/hr, just how long would it take you to reach our most distant planet? 60,000,000 hrs. There are only 8760 hours in a year. How many years would it take you to reach Pluto? 6849.3years -- I hope you like these relatives a lot!

Perhaps we could reach Pluto in a more reasonable amount of time if we journey by jet. A jet travels at 1000 km/hr. At this faster speed, what is our travel time to Pluto? 6,000,000 hrs. How many years will it take us? 684.9 years

Once you get outside of our solar system, the distances between objects
become absolutely astronomical! It would be very difficult to do
mathematical calculations using such large numbers. Scientists therefore
rely on a unit called a light year to describe the distance between the
farthest objects in our Universe. A light year is equal to
9,500,000,000,000 km and is the distance that light travels
in one year. A light year can be expressed as 9.5 trillion km or in scientific notation as 9.5
x 10^{12} km.

The star outside of our solar system that is closest to Earth is Alpha Centauri C. It is 40,000,000,000,000 (40 trillion) km away. How many light years is that? 4.21 light years If we hopped aboard our jet, how long would it take us to get to Alpha Centauri C? 40,000,000,000 hours How many years would that take? 4,566,210.0 years Are you packed yet?

As an extra challenge, calculate the time it would take to reach
Betelgeuse, a red giant located 600 light years away. First convert light
years into kilometers. 5.7 x 10^{15} km Traveling at
1000 km/hr. by jet,
how long would it take to reach Betelgeuse? 5,700,000,000,000 hrs. How
many years is that? 650,684,931.5 years Did you know that by the time
you got there, Betelgeuse would no longer be the red giant we know today?
Betelgeuse is in the dying phase of its lifecycle. With a mass 1000 times
that of the Sun, if Betelgeuse was put in the middle of our solar system
it would extend all the way out to Jupiter's orbit! As a supermassive
star, the next step in Betelgeuse's lifecycle will be a supernova. This is expected to occur within
the next 10,000 years.
So forget your trip to Betelgeuse because by the time you get there you
won't be able to see it.

EXTENSIONS:

(1) For extra practice working with large distances, have the students go to The Facts page of each planet (or dwarf planet) in the Solar System section of StarChild. There they will find the average distance of each object from the Sun. Have the students calculate the time it would take to travel to each planet by car (100 km/hr.) or by jet (1000 km/hr). For a real challenge, have the students calculate travel time using the speed of the Space Shuttle (27,200 km/hr.) at main engine cut-off which occurs 112 km above Earth's surface.

(2) To further examine the lifecycle of a medium, massive, or supermassive star, have the students go online and explore the "Stars" pages in StarChild. "Stars" can be found in the Universe section in both levels of StarChild.