During the Activity
Activity Sequence in Brief
Students review conditions in the early universe and discuss how the relatively smooth distribution of matter in the early universe turned into the very "clumpy" distribution of galaxies seen today.
Students use the Gravity Simulation to study the effects of gravity using a series of different scenarios.
For homework, students are instructed to write a short paragraph about the size (radius and mass) of their cosmic object.
Students discuss gravity as a force between objects that differs with the masses of the objects and the distance between them.
Teacher explains gravity as a force between two objects and shows students the equation scientists use to determine gravity.
Students investigate how differing gravitational forces would affect their weight on different planets.
Students view and discuss a video showing how gravity caused the "clumpiness" in the distribution of galaxies, the large-scale structure of the universe.
Students will be tested on this material in a quiz given at the beginning of Activity 6.1 Stellar Spectra. For homework, students read the Student Reader Article: "What Makes Galaxies Change?" and answer questions.
Engage (10 minutes)
- Review with students the highlights of events in the early history of the universe from Lesson 4, Origin of the Universe. If desired, replay the video: The Big Bang from the previous activity (this can be done with a projection system or instruct students to view the copy on the student CD). This serves to remind students of what they saw and learned earlier.
- Point out that 300,000 years after the Big Bang matter was fairly evenly distributed throughout the universe. There were areas that contained slightly more matter than others, but the differences were extremely small. (The density in any given area varied by no more than about 0.01%.) Then, approximately one billion years following the Big Bang, the first stars and galaxies began to form. By this time, matter in the universe was no longer smoothly distributed. Instead, it appeared to cluster together in clumps. Point out that the matter in the universe one billion years after the Big Bang, when the first stars and galaxies formed, was the same matter that had existed when the first atoms had formed 300,000 years after the Big Bang. No matter had been added or deleted.
- Ask students how matter in the universe could have changed from being relatively smooth 300,000 years after the Big Bang, to being "clumpy" 999,700,000 years later. (Answers may vary, but may include mention of gravity, electricity, and magnetism.) Accept all reasonable answers.
- Have students record their answers in their notes, especially their own current definition of gravity. Tell students that they will now explore whether or not gravity played a role in changing the universe from a smooth distribution of matter to one with clumps.
Explore (40 minutes)
- Divide students into teams of 2-3 so that each team has access to a computer (teams of two work the best). NOTE: If there are not enough computers, the teacher can demonstrate the simulation for the class.
- Distribute a copy of the What Is Gravity? Simulation Directions and the What Is Gravity? Student Activity Sheet to each student. Tell students that they are going to use the simulation: Gravity to explore gravity.
- Circulate and assist students as needed. Note that, during the simulation, the objects will appear white, even though the Data screen indicates that each will have a different color. When running the simulation with just two objects (Simple Orbit), the colors will not be visible. If you click the "Lines" box next to the "New" button at the bottom of the screen, the objects will appear to have colors. When the Lines box is checked, however, colored lines appear showing how each object has moved. For the simple simulations used in this activity, the use of the colored lines may confuse students and cause them to miss the actions of the objects in the simulation. We suggest you not check the "Lines" box, even if it does add color to the objects.
NOTE: Whether students can or cannot see colors for the objects at any time during the simulation depends on the type of computer and the version of browser you are using to view the curriculum. If the combination of computer and browser you are using dows not show any colors when looking at the Data screen of the simulation, substitute object #1 for yellow, object #2 for green, and object #3 for blue. During the simulation, object #1 appears at the right, object #2 appears in the middle, and object #3 appears on the left.
- The What Is Gravity? Simulation Directions can be collected and reused in other classes.
|The following represents a summary of the outcomes and concepts targeted by the Gravity Simulation. If you have students with special needs who may be unable to view the simulation, present the following:
The Gravity Simulation demonstrates seven possible combination of planets and stars: Planetary System and Comet, Chaotic Planetary System, Three Body Figure Eight, Three Mutual Orbit, Four Mutual Orbit, Three Body Elliptical Orbit, and Simple Orbit.
In all of the systems the relationship between gravity and mass, and between gravity and distance are the same:
- The strength of gravity is inversely proportional to the distance between the objects. That is, the closer the objects are to each other the greater the force of gravity, and the faster the objects move toward each other.
- When the objects are of unequal mass, the less massive object moves faster toward the more massive object than the more massive object moves toward the less massive object.
For homework, have students write a short paragraph about the size (radius and mass) of their cosmic object. They should include a description of how big it is compared to the Sun. Assign a due date that is appropriate in your particular situation. An alternative to this is to assign students the task of bringing their research materials to class on Day Two of this activity and giving them time at the end of the period to work on their paragraphs in class.
Explain (50 minutes)
- Review the Gravity Simulation results from the previous day. Ask students what happened when they decreased the distance between objects in the simulation. (Decreasing the distance increased the force of attraction between the two objects and they moved faster toward one another.) Ask students what happened when they changed the mass of an object. (Making an object more massive increased the force of attraction between the objects; the smaller (less massive) object moved faster toward the more massive one.) Ask students what factors affect the amount of attraction between two objects. (The mass of the objects and the distance between them.)
- Ask students to define gravity. (Gravity is the attraction between two objects.) Reiterate that gravity depends on the mass of the objects and the distance between them.
- Ask teams to provide the results of a scenario that supports their findings (for example, the effects of distance or mass on the gravitational attraction). Have another team provide a different result that backs up the same finding. NOTE: Allow students to use the terms "larger" and "bigger" in the discussion of changing mass, but prompt them to use "more or less massive." Correct the use of the word "heavier," which refers to weight, not mass. If desired, you can give teams a few minutes to work on this together before presenting their findings.
- Ask students if the force of gravity experienced by an object increases with distance from the Earth's surface. (No. As the distance between the Earth and the object increases, the gravitational pull between the two decreases.) Point out that this is a common misconception about gravity.
- Tell students to think back to the scenario where one object was twice as massive as the other one. Ask students:
- Did both objects move? (Yes.)
- How did each of the objects move compared to one another? (The smaller one moved more.)
- Did both objects experience an attraction or pull toward one another? (Yes.)
- Was the force of gravity the same for both objects? (Yes, although some students may say no because of the misconception that the force of gravity is not equal on both objects.)
- Show students a rubber band attached to a tennis ball and a lead ball. Pull them apart, stretching the rubber band. Ask if the rubber band pulls with the same force on both balls. (Yes. The same rubber band is attached to both, so it has to pull the same on both.) Ask what will happen to the balls when you release the rubber band. (Answers may vary.) Release the rubber band and tell students to observe the motion of the two balls. Ask them what happened. (Both balls moved toward one another, but the tennis ball moved farther and faster.)
- Ask students why the lead ball didn't move as much as the tennis ball, if the rubber band pulled with equal force on both. (The effect of the force on the lead ball, the acceleration of the ball, was less because of its larger mass.) Tell students that the rubber band is like the gravitational force between two objects. Ask if the gravitational force felt by two objects is the same. (Yes.) Ask if the effects of that force are the same. (No. If one object is more massive than the other, it will not move as much as the smaller object.) Remind students that gravity is the force of attraction between two objects. Both balls will experience the same force, although the effects of that force on the two differ.
- Have students review their initial definition of gravity in their notes from the Day One Engage section. Ask them to identify what, if anything, was lacking in their definition.
Explain (20 minutes)
- Tell students that scientists have determined that the force of gravity is proportional to the mass, and is inversely proportional to the distance squared. So, as mass increases, gravity increases. As distance increases, gravity decreases (proportional to the square of the distance). Have students write these relationships in their notes. Remind students that the relationships between gravity and mass and between gravity and distance are the same ones they saw in the simulations they worked with the first day.
- Explain that scientists have determined that the force due to gravity can be expressed by the following equation for gravitational force (write the equation on the blackboard or overhead and have students write the equation in their notes):
where F is the gravitational force, m1 is the mass of one object, m2 is the mass of the other object, and R is the distance between the two objects.
- Provide the examples below, filling in values for the masses and radius, to show how gravitational force depends on them:
- If m1 = 2 kg, m2 = 2 kg, and R = 2 m,
then F is proportional to 2 x 2 / 22 = 4/4 = 1.
- If m1 is doubled to 4kg, m2 = 2 kg, and R = 2 m,
then F is proportional to 4 x 2 / 22 = 8/4 = 2, two times higher
(since gravity is directly proportional to mass).
- Using the original masses, if R is doubled to 4,
then F is proportional to 2 x 2 /42 = 4/16 = 1/4,
which is 1/4 the original force
(since gravity is inversely proportional to the distance squared).
- Ask students if this relationship is similar to what they saw in the simulation yesterday. (Yes. When the mass of one object was increased, the force of attraction (gravitational force) between them increased. When the distance between them was decreased, the gravitational force between them increased.) Ask students to explain the relationship between gravity, mass, and distance . (Gravity is proportional to mass. The more mass an object has, the greater the gravitational pull it can exert. Gravity is inversely proportional to distance. The farther away something is from an object, the less gravitational pull it will experience from that object.) Have students write these relationships in their notes.
- Point out that gravity is mutual. It is the force of attraction between two or more objects. In the case of two objects (refer to the Scenarios 1, 2, and 3 in the simulation from the previous day), both objects experience the effects of gravity and the same force. But the intensity of the effect on the two objects can differ, depending on the mass of each object.
- Repeat the demonstration (the rubber band attached to a tennis ball and a lead ball) from the previous day.
- Ask students if they feel a gravitational pull from the Earth. (Yes.) Ask if the Earth experiences a gravitational pull from them. (Surprisingly, yes.) Ask if the gravitational force that the Earth and the student experience is the same. (Yes. This relationship is defined in the equation above, with m1 equal to the mass of the Earth, and m2 equal to the mass of each student. Since the student is standing on the surface of the Earth, R is equal to the distance between the student and the center (radius) of the Earth.)
- Ask students if the Earth and the student experience the same effects of the gravitational force between them. (No. Because the student has so much less mass than the Earth, the student is pulled toward the center of the Earth much more strongly than the Earth is pulled toward the student.) Point out that this is similar to what they observed in the simulation from the first day. When students doubled the mass of one of the objects in the simulation, they saw that the object with smaller mass moved more quickly toward the object with larger mass. Note that the student's pull toward the center of the Earth is stopped by the surface of the Earth, and that the Earth's gravity continues to hold the student to the surface.
- Remind students that the weight recorded when they step on a bathroom scale depends on two things: their mass and the strength of gravity at the surface of the Earth. Ask students how to calculate the strength of gravity at the surface of the Earth. (If students know, their answers may vary.) Explain that the strength of gravity is the amount of gravitational pull exerted by the Earth based on its mass and radius (size). It is independent of the mass of the object experiencing the pull. It is also not the gravitational force between the Earth and the object. The gravitational force between the Earth and another object (the force of attraction between the two) is defined as the strength of gravity for the Earth times the mass of the object.
- Show students that scientists determine this result by, changing one of the masses and the radius to those of the Earth in the equation for gravitational force above. The resulting equation for the gravitational force experienced between the Earth and an object of any mass, m2, is given by:
where G is the Gravitational Constant (the value of G has been determined by experiments to be 6.67 x 10-11 N m2 / kg2, where N stands for the unit "Newtons".)
The strength of gravity at the surface of the Earth can be defined as:
|Strength of gravity =
||= 9.8 meters / (second)2
When using the appropriate values for G, MEarth, and REarth, the strength of gravity on the Earth is 9.8 meters / (second)2. (Note that the strength of gravity described here is the acceleration downward that any object dropped from a height above the Earth's surface would feel because of the Earth's gravity.)
That's everything except the mass of the object. To calculate the gravitational force between the Earth and any object, simply multiply this strength of gravity by the mass of the object:
Credit for all equation images: SETI Institute
Elaborate (15 minutes)
- Ask students to imagine that they could somehow travel to another planet with their bathroom scale and weigh themselves on the planet's "surface." Would they weigh the same? Why or why not? (No. Because each planet has a different mass and radius, and therefore the strength of gravity, which depends on both, is different on each of the planets.)
- Ask students how they would calculate the strength of gravity on another planet. (Using the mass, m1, of the other planet, relative to that of the Earth, and the radius of the other planet relative to that of the Earth, use the equation for gravity above. Note that your mass, m2, remains the same no matter what planet you are on.)
- Display transparency: Gravity on Other Planets. Explain that the mass of the planets shown in the table is given in "Earth units". That means that if a planet has two times the mass of the Earth, its mass will be listed in the table as 2.00. Similarly, if a planet has half the radius of the Earth, its radius will be listed as 0.50.
- Point out that, when figuring out how much students would weigh on another planet, they have to take into account the mass of the planet in relation to that of the Earth.
- If the planet is 3 times more massive (with the same radius), the force of gravity would be 3 times higher and the students would weigh 3 times as much.
- Students must also take into account the radius squared of the planet. If the planet is 2 times bigger (with the same mass), the force of gravity would be 1/4 as large (if the mass is the same) and the students would weigh 1/4 as much.
- If the planet is 3 times more massive and the radius is 2 times bigger, then the students' weight would be 3/22 = 3/4 as much on the planet as it is on the Earth.
- For example, Mars has a mass that is 0.107 times that of the Earth, and a radius that is 0.533 times that of the Earth. To get their weight on Mars, students should multiply their weight on Earth by (0.107) / (0.533)
= 0.38. Students would weigh 0.38 times less on Mars than they do on Earth.
- Using these estimates, ask students:
- On which planet would they weight the most? (Jupiter.)
- On which planet would they weigh the least? (Pluto)
- On which planet would they weigh the closest to what they weigh on the Earth? (Venus or Saturn)
EXTENSION: Ask students to calculate the strength of gravity for the different planets. Using the transparency: Gravity on Other Planets, fill in the table. Students then calculate their actual weights on the other planets
- Remind students that mass is different than weight. Mass is a measure of the amount of matter in an object, while weight is a measure of the gravitational force that acts on the object. The students' mass will not change if they go to another planet, but their weight will. The idea that mass and weight are the same thing is a common misconception.
- Ask students what other effects they would experience on other planets, in addition to weighing more or less. (Answers may vary.) Point out that the change in weight would change the way they move around on the planet. As an example, tell students that the Moon is much less massive and much smaller in size (radius) than the Earth. As a result, the strength of gravity at the surface of the Moon is only one-sixth what it is on the Earth. When astronauts walked on the Moon in the late 1960s and early 1970s, they found that, on the surface of the Moon, they weighed one-sixth of what they weighed on the Earth. This presented some problems in moving around, since they felt much lighter than they were used to. Because they weighed so much less, they found that walking as we do on Earth was awkward. They found that a hopping motion, which on Earth would be very uncomfortable, was the easiest way to get around on the Moon.
- Display the video: Astronauts Hopping on the Moon (11 sec.). Reiterate that the effects of gravity range far beyond just determining how much we would weigh on a bathroom scale. Gravity has an impact on how we live our lives. It also has an impact on how the universe formed and on how the universe continues to evolve.
Elaborate (15 minutes)
- Remind students that in the early universe (less than 300,000 years after the Big Bang), matter was smoothly distributed. But one billion years after the Big Bang, when galaxies and stars formed, matter was clumped together. Display the image: Galaxy Distribution. Tell students that the image shows the distribution of galaxies in a slice of the universe. It's as if you were looking out from the Milky Way while turning your head and marking down where you see galaxies and where you don't, and noting how far away each galaxy is. The Milky Way is located at the bottom point of the fan-shaped slice. The numbers along the top arc represent directions in the sky. Note that the entire fan-shaped slice spans about 30° of the sky (there are 180° from eastern horizon to western horizon). The numbers along the side of the fan-shaped slice represent redshifts, and correspond to the distance away from the Milky Way. Each dot in the fan-shaped slice represents the position in the night sky of a galaxy and its distance away from the Earth.
- Ask students if the galaxies are scattered randomly or not. (No. The galaxies are not scattered randomly. They seem to lie along sheets and strings, with "voids" in between them that have very few galaxies within them.) Point out that these sheets and strings extend many millions of light years across the universe.
- Ask students how the universe could have changed from a relatively smooth distribution of matter not long after the Big Bang to the highly clumped distribution of matter we see today. (Gravity caused matter to clump together over time.) Explain that while the early universe was relatively smooth, it wasn't absolutely smooth. There were large areas that held slightly more matter in them than the surrounding regions (the density varied by no more than 0.01% from place to place). These areas with slightly greater density had slightly greater gravity because of the extra mass and, therefore, pulled even more matter toward them. As a result, they grew in mass. As their mass grew, so did their gravitational pull. Eventually, these areas grew massive enough that their gravity overcame the force of expansion of the universe from the Big Bang, and the areas began to contract, ultimately forming stars and galaxies. The large-scale distribution of galaxies that we see today is the result of gravity.
- Display the video: The Formation of Galaxies (56 sec.).
- Tell students that they will explore the formation and evolution of galaxies in more detail the next time class meets.
- For homework, have students read the Student Reader Article "What Makes Galaxies Change?"
Option 1: Display the image: What Makes Galaxies Change on your projection device or write the questions on the board or overhead. Have students write down the questions and answer them while reading the article.
Option 2: Distribute a copy of the What Makes Galaxies Change? Student Activity Sheet and have students write their answers on the handout.