Illuminations: Travel in the Solar System

Travel in the Solar System


Space Shuttle

Students consider the amount of time that space travelers must spend on their journey. Students improve their concept of time and distance, while at the same time learn more about the solar system.

Learning Objectives

 
Students will:
  • apply measurement and computation to gain insight into the large numbers associated with distances in space
  • calculate the amount of time needed to travel to each of the planets

Materials

 

Instructional Plan

Mission

  • To apply measurement and computation to gain insight into the large numbers associated with distances in space
  • To plan a trip to a planet in the solar system

This lesson focuses on human travel in space. One problem associated with traveling in the solar system is the distance from on planet to another. But other problems arise. A spacecraft needs fuel to make the long journeys in space, and humans need food and water throughout the long journeys. The effects of microgravity, that is, near zero gravity, on humans over time are unknown. The probability of collisions with asteroids is uncertain, and many other aspects of long manned flights make the task of space travel very complex.

 


Image courtesy of the NASA
Human Space Flight Gallery.

 

However, publicity about unmanned flights to the planets continues to raise the question of humans' traveling in space. Research is required to increase the probability that prolonged space travel for humans can be accomplished safely. One of the NASA projects that will move us closer to space travel is the International Space Station, which will serve as a platform for many research agendas associated with living and working in space for long periods of time.

Getting Started

Begin the class by engaging students in a discussion about humans traveling through the universe. In the movies and on television, students encounter science-fiction stories about traveling at the speed of light and beyond to cross entire galaxies in a matter of seconds. Point out that most of our travel speeds are quite slow. We have not come close to traveling at the speed of light. Although radio signals can return from Mars in a short time, it takes much longer for a spacecraft from Earth to reach Mars.

Developing the Activity

Use the data about the Space Shuttle below to determine its speed in miles per hour. Remind students that the Shuttle is not designed for travel among the planets. It is designed for Earth-orbit tasks. However, its speed is helpful in judging the speeds for twentieth century spacecraft. After students have done the calculations, come to some agreement on an approximate speed for interplanetary travel. Assume that the agreement is about 50,000 miles per hour. This figure gives us a reasonable speed to use in thinking about space travel today. In the future, speeds will undoubtedly increase.

 

Space Shuttle Data:

Distance traveled by Shuttle: 4,164,183 miles

Time to travel given distance: 9d 23h 30m

 

Speed Computation:

 

Using the data sheet, The Planets at a Glance, students can determine the distance from Earth to each of the other planets. This task is not trivial. The distances in the chart are given in millions of miles. To facilitate computation and estimation, students need to translate 67.2 million miles, the distance from the Sun to Venus, into its full numeric form, 67,200,000. Before thinking about traveling to Venus, students must remember that Earth is about 93,000,000 miles from the Sun. Use the mean distance from the Sun to specified planets to calculate each distance from Earth to the targeted planet.

Alternatively, you may require your students to search for the information themselves and complete a blank The Planets at a Glance activity sheet. Students may obtain data from the NASA website.

To make this exploration manageable for middle school students, we are assuming that the planets are aligned at their mean distances. Teachers should explain to students that in actuality, this greatly simplified situation is unlikely to occur.

The students' next task is to calculate the time required to travel to each planet on spacecraft that travel from 20,000 to 100,000 miles per hour.

Group the students into their mission teams of four students. Ask them to complete a chart for travel to all the planets (and Pluto) of the solar system at the speeds shown below. They should use the mean distance of each planet from Earth.

Distribute the Speeding Through the Universe activity sheet, so students may complete the chart.

 

MPH
Mercury
Venus
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
20,000
         
30,000
         
40,000
         
50,000
         
60,000
         
70,000
         
80,000
         
90,000
         
100,000
         

 

In a typical class, students groan at the prospect of completing a chart with eighty entries. The groans provide the opportunity to challenge the teams to think of strategies for reducing the amount of calculations required to complete the chart. When patterns are used to complete entries, the teams should record them. All students in the teams should make the chart.

Discuss the patterns that teams used to complete the chart. List the patterns on the chalkboard. After all team members have shared how their patterns helped reduce their workload, ask each team how many different patterns they used.

The class now has a complete chart for travel to the solar system's planets computed in hours of travel. It is time to develop some better notions of what these times mean. Pose the Questions for Students, which require students to think about the practicality of space travel.

These questions should be posed to the mission teams. The teams should discuss the questions and agree on a team response. After students begin thinking about time questions, have each mission team make up questions for the class to solve.

Questions for Students

 
Pose questions that require students to think about the practicality of space travel:
  • If we travel at the approximate speed of the Space Shuttle, which planets can we reach in less than 10 years?
  • How fast must we be able to travel to reach Jupiter in less than 10 years?
  • Traveling to some of the planets at some of the indicated speeds would take more than a lifetime, which is about 75 years. Which planets are too far away to be reached in a lifetime?
  • We would like to make round trips. Traveling at 10,000 miles per hour, to which planets could we make a round trip in our lifetime?

Extensions

 

The students who are close followers of NASA space missions may realize that this lesson simplified at least one aspect of space travel. A spacecraft is not launched directly at a planet like a bullet from a gun to a target, and the speed of a spacecraft is not constant throughout its journey. The spacecraft will most likely orbit Earth a specified number of times before using the "sling shot" effect to transfer out of orbit. This means that a spacecraft may travel much farther than the distance between Earth and its intended target. The spacecraft must take a path so as to meet a moving target, much like throwing a football to a friend who is running. The ball is thrown to where the runner will be, not where he or she is at the moment the ball is thrown. Scientists must use very sophisticated mathematics to plan long trips in space to specific destinations.

When a spacecraft is launched into space, it may orbit Earth a specified number of times before using the "sling shot" effect to transfer out of orbit.

 

NCTM Standards and Expectations

 
Number & Operations 6-8
  1. Understand and use ratios and proportions to represent quantitative relationships.
  2. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.
  3. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.

References

 
  • Adapted from "Travel in the Solar System,", Mission Mathematics, Linking Aerospace and the NCTM Standards, 5-8, Reston, VA: NCTM/NASA, 1997. (A revised version of this book was released in 2000: Mission Mathematics II: Grades 6‑8.)
  
1 period   

NCTM Resources

Navigating through Algebra in Grades 6‑8 (with CD-ROM)

Web Sites


National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
© 2000 National Council of Teachers of Mathematics
Use of this Web site constitutes acceptance of the Terms of Use