How long does it take to get to a star?

Day 9 - Math Lesson

 

Lesson objectives:

·         Students will be able to identify what a light year is and the approximate numerical value of it.

·         Students will be able to use the distance formula to figure out the time it would take to get to a star or planet.

·         Students will be able to use the information they already know to figure out how long it takes to get to a star.

 

Content:

In this lesson students will use some of the information they already know to figure out roughly how long it would take us to reach various stars and planets. They will learn what a light-year is and will figure out how far away certain objects in space are using this type of measurement. Students will then go on to use the distance formula (d=rt) they already know from Day 5’s Distance/Scientific Notation lesson to figure out the amount of time it would take them to get to different stars or planets.

 

Materials:

·         Distance worksheet students worked on in previous classes.

·         Supplementary Worksheet (to show student work).

·         Have pictures of obvious objects displayed either on power point slides or on a standard sized piece of paper.

o   Examples of pictures to display would be: a butterfly, star, tree, bird, balloon, pumpkin, etc.

 

Lesson Introduction:

Explain to students that we are going to do an activity to see how long it takes them to see things. Explain to them that you will hold up a picture and that they will need to say what it is as soon as they have seen it. Then proceed to hold up different pictures while students identify them. After showing them several pictures and having them identify them ask them how long they think it took the light to travel from the picture to their eyes after you displayed it. (Answers should be similar to 1 sec., fraction of a sec., etc.) Ask students how fast they could get to the picture walking if they could see it in such miniscule amounts of time.  (Answers should be seconds.) Now ask students how long they think it takes the light to travel from the moon and then how long they think it takes to get to the moon. (Answers for the light travel will be seconds or minutes, answers for the time would be hours or days.) Ask students how long they think it would take light to get to us from distant stars or even galaxies. (Students most likely will not know, but that’s ok, because we’ll do some calculating about that in class today.) Can you imagine something so far away that it would take years for light to travel to our eyes? Explain to students that today they are going to figure out how many light-years away various objects are as well as how long it takes to get to a star or planet using an equation they already have.

 

Procedure:

1)      Introduce to students what a light year is.

§  A light year is often used to measure distances of stars. It is the distance that light travels in one year.

§  Light travels at 5,880,000,000,000 miles in 1 year, or 9,460,000,000,000 km. in 1 year.

2)      Explain to students that in order to convert miles or kilometers to light-years they need to set up the problem as a ratio and then cross multiply and divide the remaining number to get your answer. Do some examples as a class figuring out how to convert distance to light years.

 

 

§  Pluto is 5,925,000,000,000 km. from the sun, put this into lightyears.

                                                               i.               1 light-year           . =          X light-years         .       Answer:

9,460,000,000,000 km.         5,925,000,000 km.          0.0006263 light-years away.

§  The star Epsilon Eridani is 101,222,000,000,000 km. away from the sun, put this into lightyears.

                                                             ii.                 1 light-year          =           X light years              Answer:

9,460,000,000,000 km.   101,222,000,000,000 km.                10.7 light-years away.

3)      Use the distance worksheet from the previous lessons and have students convert the distance measurements into light-years. (NOTE: Only have students work on column titled “Distance From Sun (Light-years)”. Students will work on the other column later in lesson.)

4)      Ask students if they remember the formula they used to figure out the distance of stars. (The should respond with the equation d=rt (or d=st, depending on how you introduced it previously).

5)      Write this equation on the board and ask students if they know how they could use this equation to solve for t instead of d.

a.       Students could plug in numbers for d and r and then divide each side by r to get your answer.

b.      Students could also come up with the idea to rewrite the equation as t=d/r and then plug the numbers into the equation.

                                                               i.      This is how they should convert the equation:

1.       d=rt

2.       divide both sides by r (d/r = rt/r)

3.       so on one side you have d/r and then on the other side the r’s cancel out leaving the t by itself

4.       your final equation is t=d/r

6)      Do a few examples using light-years to find the amount of time it would take to get to different celestial objects in space.

a.       On your distance sheet you know that the distance Pluto is from the sun is 5,925,000,000 kilometers. You know that the fastest spaceship today travels at a rate of approximately 72,000 km/h. How long would it take to get there from the sun? (Round to the nearest whole number: 82,292 hours.) Take this number and convert it into days, knowing that there are 24 h/day. (Round to approximately 3,429 days.) Take the number of days and convert it into years knowing that there are 365 days/year. (Round to approximately 9.4 years.)

b.      On your distance sheet you know that the distance the star Epsilon Eridani is from the sun is 101,222,000,000,000 kilometers. You are still traveling on the fastest spaceship, so you are traveling at a rate of 72,000 km/h. How long would it take to get there from the sun? (round to the nearest whole number: 1,405,861,111 hours.) Take this number and convert it into days, knowing that there are 24 h/day. (Round to approximately 58,577,546 days.) Take the number of days and convert it into years knowing that there are 365 days/year. (Round to approximately 160,486.4 years.)

7)      Once again use the distance worksheet as well as the supplementary worksheet and have students use the distances listed to figure out how long it takes to get to various stars listed. The students should have now completed the Distance Worksheet. Collect this worksheet once students are finished.

 

Closure:

Tie this lesson into the science lesson for today and how they can figure out the time it takes for the light from celestial objects to get to us. Bring up the opening activity and talk about how they could identify the objects very quickly. Encourage students to imagine how far away something must be for it to take years for us to see. Discuss how unfathomable our universe is and therefore how unfathomable our God must be to create such a vast and amazing universe.

 

Extension:

·         Have students look through the various books on stars, galaxies, and the universe that are provided for the unit center. Have students find stars or other celestial bodies that they are interested in finding the amount of time it would take to get to them. Have students jot down the name of the celestial bodies on a sheet of paper. Have them find the distance each is from the sun using the books, but if none of the books have this information you may want to have them find out using the internet. The website http://www.cosmobrain.com/cosmobrain/res/nearstar.html may be helpful for students. They will most likely need to convert light-years into kilometers in order to solve. Have students use the same speed as they did to complete their distance worksheet. From there have students figure out how long it would take them to get to a distant celestial body traveling at the speed of a spaceship, which is about 72,000 km/h.

·         Another option would be to have students convert the hours they have found for each star or planet into days or years so that they can get a better sense of how far away these objects really are. There are 24 hrs/1 day and 365 day/1 year. Students should use these ratios to convert the time.

 

Evaluation:

1)      Collect the distance worksheets as well as the supplementary time worksheets and grade the work that the students have accomplished using both the answer key for the distance worksheet and/or the answer key for the supplementary time worksheet.

2)      Observe during lesson to make sure students understand the concept. Take notes if need be to best address students needs.

 

Resources:

1)      These websites were used to find information for the distance worksheet.

·         Carter, L. (2003, August 25). Curious about astronomy: How far is each planet from the Earth?. Retrieved November 6, 2009, from http://curious.astro.cornell.edu/question.php?number=564

·         Soares, E. (2002). The nearest stars. Retrieved November 6, 2009, from http://www.cosmobrain.com/cosmobrain/res/nearstar.html

 

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