## Travel in the Solar System

• Lesson
6-8
3

This lesson affords students the opportunity to think about two aspects of the time required to complete space travel within the solar system. First, students consider the amount of time that space travelers must spend on the journey. Second, students think about what kinds of events might occur on Earth while the space travelers are on their journey. Thinking about both situations improves students' concept of time and distance as well as improves their understanding of the solar system.

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.

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.

Purpose

This lesson affords students the opportunity to think about two aspects of the time required to complete space travel within the solar system. First, students consider the amount of time that space travelers must spend on the journey. Second, students think about what kinds of events might occur on Earth while the space travelers are on their journey. Thinking about both situations improves students' concept of time and distance as well as improves their understanding of the solar system.

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. The activities in lesson 2 have reminded us 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.

Part A

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 milesTime 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.

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 10,000 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 of the solar system at the speeds shown below. They should use the mean distance of each planet from Earth.

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 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 per hour, to which planets could we make a round trip in our lifetime?

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.

Closing the Activity

Pose selected mission team questions to the entire class. The quality of the questions and the responses should indicate which students are gaining an understanding about the time required for space travel.

Extending the Activity

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.

Part B

Getting Started

The terrestrial planets are the four innermost planets in the solar system: Mercury, Venus, Earth, and Mars. They are called terrestrial because they have a rocky, compact surface like the Earth's. Jupiter, Saturn, Uranus, and Neptune are known as Jovian, or Jupiter-like, planets because they are gigantic planets when compared with Earth and have a gaseous nature like Jupiter's. Jovian planets are sometimes called the gas giants. Pluto is not a member of either group. Its composition is unknown, but it is probably composed mostly of rock, ice, and frozen gases.

Developing the Activity

Present the following scenario to students:

Since humankind wants to know more about each of our planetary neighbors, we need to plan our travel to the planets. Select one terrestrial planet and one Jovian planet. Plan trips to the two planets and to Pluto. Describe the speed of your spacecraft as well as the time required to reach the planet, stay one Earth year to explore it, and return to Earth. You may assume that advances will be made in the development of spacecraft and that speeds up to 50,000 miles per hour will be possible.

Launch day for all missions is 10 December 1999. On what date will you arrive at the targeted planet? On what date will you return from each mission?

These questions will require that students convert such time intervals as 10.2 years into years and days. When the conversion results in a part of a day, round the value to the nearest day. Students may not be familiar with thinking about a date in the year as having an ordinal value in relation to the year; for example, 1 July is the 183rd day of the year. Locate a reference calendar where the ordinal value is given along with the date. Remind students they are not beginning with 1 January, however. Launch was on 10 December. Since the year 2000 is a leap year, students need to use 366 days for that year as well as other leap years spent traveling to other planets.

Closing the Activity

Each member of the mission team should write about one of the trips to a planet. The description should include the launch date, the destination, the speed of travel, the time to reach the planet, the date of arrival, and the date the crew returned to Earth.

Each mission team should make a mission patch for one of its planned journeys. This patch can be attached to the logbook for this lesson.

Part C

Getting Started

To this point in the lesson, students have been considering space travel from the perspective of what happens to the space traveler on the journey. But while the space travelers are visiting distant planets, life continues on its usual course at home on planet Earth. Students should be familiar with the aspect of all travel from their previous experiences. While they are away from home, life goes on; on their return, they need time to catch up on all the news and events. Occasionally, an event occurs while they are gone that has a profound effect on them when they return.

Developing the Activity

Return the students to their mission teams. Tell them to imagine that their team was actually sent on a mission to their selected terrestrial planet. They know their launch data and have computed the duration of their trip and the date of their return. Although NASA kept the crew members posted on the news, they have missed many important events, both personal and public.

Each mission team serves as the ground crew for a space-traveling counterpart. The ground crew's task is to debrief the astronauts on their return to Earth.

Each ground crew makes a list of important events that the astronaut crew should know about on its return. Of course, the names and some of the events will be fictitious, but they should be plausible for the time that passed on the journey. Be certain to include the results of regularly occurring events. Such personal events as graduations for family members should be mentioned, too. Sports events, such as the Olympics, the Super Bowl, and the World Series, maybe important events for some students.

Closing the Activity

Students present the briefings they have written for the returning astronauts. These reports could take many forms. Some mission teams may make time lines. Others may present their briefing as a newscast. They might use technology to support their presentation. Another team member may make a scrapbook. Do not place limits on their creativity.

All students should take time to reflect on the mathematics of this lesson. The calendar, the time conversions, the distances in space, and the speeds required to complete space travel are all important concepts for students to think about as they construct their understanding of the world and the mathematics that describes it.

Teaching Note: For students who wish to think about the relative positions of two planets in their respective orbits, teachers may wish to refer to the modeling activities in "Scaling Up" in Mission Mathematics: Grades 9-12.

Teaching Tip: For further study, "Scaling Up" in Mission Mathematics: Grades 9-12 includes an activity on launch windows.

There are many approaches to the solution of this task, including the use of technology. All correct solutions should be accepted. Computational solutions, graphing solutions, and technological solutions are equally valid. This is an opportunity to celebrate students' originality.

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### Learning Objectives

Students will be able to:

• Apply measurement and computation to gain insight into the large numbers associated with distances in space

### NCTM Standards and Expectations

• Understand and use ratios and proportions to represent quantitative relationship.
• Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.
• Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

### Common Core State Standards – Mathematics

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, ''This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.'' ''We paid $75 for 15 hamburgers, which is a rate of$5 per hamburger.''