# Einstein\'s Gravity

Suggested Grade Level(s): 11 or 12 Physics Class

Estimated class time: 3 to 5 days depending on whether the curved space
model is done as a demonstration and how much time is spent in research.

# Summary

Students will read the 1919 edition of the Cosmic Times and respond by
raising questions to be answered with further research. They will make a
model of curved space to view the motion of spheres as explained by
General Relativity. After presentations of their research to the class
they will create an interview with Albert Einstein.

# Objectives

-   Students will be able to compare and contrast two different models
    that explain the gravitational force.

-   Students will be able to explain what is meant by gravity as
    curvature in space and time.

-   Students will be able to answer questions that are raised about
    Albert Einstein, his life, the times and his theory of general
    relativity.

-   Students will make a model of curved space.

-   Students will begin an exploration of the scientific process and how
    new ideas and technology change our understanding of the world
    around us and raise new questions to be answered.

# National Standards

**National Science Standards**

-   NS.9-12.1 SCIENCE AS INQUIRY

> As a result of activities in grades 9-12, all students should develop

-   Abilities necessary to do scientific inquiry

-   Understandings about scientific inquiry

### NS.9-12.2 PHYSICAL SCIENCE

> As a result of their activities in grades 9-12, all students should
> develop an understanding of

-   Motions and forces

-   Interactions of energy and matter

### NS.9-12.4 EARTH AND SPACE SCIENCE

> As a result of their activities in grades 9-12, all students should
> develop an understanding of

-   Origin and evolution of the earth system

### NS.9-12.7 HISTORY AND NATURE OF SCIENCE

> As a result of activities in grades 9-12, all students should develop
> understanding of

-   Science as a human endeavor

-   Nature of scientific knowledge

-   Historical perspectives

**National Language Arts Standards**

(From the National Counsel of Teachers of English)

-   NL-ENG.K-12.7 EVALUATING DATA

Students conduct research on issues and interests by generating ideas
and questions, and by posing problems. They gather, evaluate, and
synthesize data from a variety of sources (e.g., print and non-print
texts, artifacts, people) to communicate their discoveries in ways that
suit their purpose and audience.

-   NL-ENG.K-12.8 DEVELOPING RESEARCH SKILLS

Students use a variety of technological and information resources (e.g.,
libraries, databases, computer networks, video) to gather and synthesize
information and to create and communicate knowledge.

# Knowledge Prerequisite

Students should be familiar with Newton's Law of Universal Gravitation.

# Teacher Background/Notes

**Teachers\' Domain** (<http://www.teachersdomain.org/> )

Teacher's Domain is a free website offered through WGBH (public TV) in
Boston.

You must register with the site, but registration is free. See the end
of the lesson for more on the Teachers\' Domain website. Once
registered, you will find the video clip demonstration of Curved Space
by following the following submenus:

Physical Science

Fundamental Theory

Cosmology and Gravity

> Relativity and The Cosmos
>
> View
>
> Animations in box at right
>
> Space Animation

# Materials

-   Teacher's Domain (see note above)

-   Saran Wrap (NOT generic plastic wrap)

-   Support for plastic wrap -- Two interlocking 12 inch embroidery
    hoops, round trash can and tie, lids from Deli platters, etc.

-   Assorted sizes of spheres to roll

-   Black Sharpie permanent marker

# Procedure:

### I. Engagement 

1.  Read the lead article from the Cosmic Times

-   Imagine you are living in 1919.

-   Would you know who Albert Einstein was?

-   Do you know what a solar eclipse is and/or have you ever seen one?

-   What does curved space mean to you? How does it relate to gravity?

At the end of this unit you will be able to answer these questions and
some more within the context of an interview with Albert Einstein.

2.  Show the video clip of the sun warping space-time from Teacher's
    Domain.

```{=html}
<!-- -->
```
a.  How did Isaac Newton explain gravitation?

b.  How does this explain that a beam of light, which is massless, bends
    with gravity's force?

**Teachers**: This is a connection to prior knowledge, but should also
allow students to start a list of questions that they will answer later
in the lesson.

> *Answers:*

a.  *Newton explained gravitation as the interaction of two masses
    creating an attractive force.*

b.  *This does not explain the observed bending of light, which has no
    mass.*

```{=html}
<!-- -->
```
3.  Think / Pair / Share ideas

> ***Teachers**: You may want to create a list of the ideas shared for
> students to use when they try to decide what they wish to research
> further. Some classes may appreciate the guidance from this early
> point. The term [ideas]{.underline} is used here because the students
> may raise new questions or come up with ideas that are not direct
> answers to the two questions being asked.  This is the jumping off
> point for the research step and is encouraged.*
>
> **Think** -- about the Cosmic Times, the questions in #3 and the video
> clip. (The first is based on prior knowledge; the second will be a bit
> tougher, perhaps.)
>
> **Pair** -- students share their answers to the questions with a
> single partner. Share any new questions and ideas you may have.
>
> **Share** -- invite partners to share ideas with the full class. You
> may solicit new questions and ideas as well as the two answers. Make a
> list of the answers and ideas

### II. Exploration

**In Groups:**

Students should make their own model of curved space.

Equipment -- Interlocking embroidery hoops -- one per group; Metal
spheres of various sizes for each group; Saran^©^ Wrap (generic NOT
suggested) one roll in classroom.

> ***Teachers:** For students to make the model, Lycra or spandex does
> very nicely and can be reused year after year. If the teacher is
> demonstrating the model, the Saran Wrap will allow the spheres to be
> visible on the overhead projector. Do not try to reuse the Saran Wrap.
> Use a Sharpie pen to draw grid lines on the Saran Wrap to see the
> curving of the x and y directions.*

1.  Stretch a piece of Saran^©^ Wrap taut between the two hoops.

2.  Tighten the hoops.

3.  Place the hoop on a table with the Saran^©^ Wrap up and hoop down.
    This will elevate the hoop off the table by about an inch. Further
    elevation will enhance the effect. A larger demonstration can be
    made with a cheesecake pan, a three-foot wide trash can, the lid to
    a deli platter with the top cut out so only the side remains. If you
    choose one of these larger demonstrations, secure the Saran Wrap
    securely to the sides. Commercial Saran Wrap is wider than the
    standard kitchen roll.

4.  Place the larger of 2 metal spheres in the middle of the Saran Wrap.

5.  Roll a smaller sphere across the Saran^©^ Wrap at some distance
    between the center of the hoop with the larger sphere and the hoop
    itself.

6.  Students may experiment by changing the relative sizes of the two
    spheres, the speed of the rolling sphere, the starting position,
    etc. to get a nice "orbit".

> ***Teacher**: This also makes a good demonstration on an overhead
> projector if you do not have the materials or time to have groups
> explore this on their own. The hoop can be placed on an overhead
> projector supported by two pieces of wood about an inch high to
> elevate it.)*

Upon completion of the activity, students will answer the following
questions:

a.  What path does the moving sphere follow?

b.  What happens when you start the moving sphere at a faster speed?

c.  Sketch what you think would happen if there were no friction.

d.  Compare this to the orbit of a planet.

> *Answers:*

a.  *The moving sphere follows a curved path around the center sphere.*

b.  *If the moving sphere starts too fast, it will not appear to curve
    and may jump the edge of the hoop. If it starts too slow, it will
    roll right into the center sphere.*

c.  *They should have a full loop around the sphere or a path curving
    across the surface.*

d.  *The orbit of a planet is an ellipse because of the central force of
    gravity. It looks like the path of the sphere on the hoop.*

### III. Explanation

Students **[in their groups]{.underline}** will create 3 questions that
they would like to research in depth.

The groups will create a master list of questions about Einstein and/or
his theory of gravity.

> ***Teachers:***

-   *Differentiated instruction: for some groups biographical questions
    might be easier to answer than scientific questions*

-   *Use the list of ideas from the Engagement or the list of questions
    in the appenices to provide guidance to students who may be "stuck"
    at this point.*

With teacher approval, each group will research on the Internet to
answer one of their questions and make a presentation for their
classmates. Presentations may be Power Point or posters with an oral
component that involves **[all]{.underline}** group members.

### IV. Extension

-   Students may wish to expand on the information presented or answer
    new questions that were raised in their classmates' presentations.

-   Students may also create a crossword puzzle using new vocabulary
    that has rows and or columns that resemble curved space.

-   Students may view the Elevator Animation from the Teacher's Domain
    website or take an elevator ride with a spring scale and a kilogram
    to see firsthand how the apparent weight changes.

-   Students may read the Alan Lightman article, *Relativity and the
    Cosmos*, from Teacher's Domain.

### V. Evaluation 

Each student will create an interview with Albert Einstein for next
week's Cosmic Times.

Ask him 5 questions and provide the answers that he would have given
you.

You may write a script or tape the interview.

> ***Teachers:** Oral presentations of the script will be optional and
> depend on the time frame of the lesson on the whole.*

## More on the Teachers\' Domain

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