Lesson 15A: The Role of Gravity in the Space System
Estimated Time
: Two forty-five minute class periodsIndicators(s): Core Learning Goal 1
1.2.7 The student will use relationships discovered in the lab to explain phenomena observed outside the laboratory.
1.4.8 The student will use models and computer simulations to extend his/her understanding of scientific concepts.
1.6.4 The student will manipulate quantities and/or numerical values in algebraic equations.
Indicators(s): Core Learning Goal 2
2.2.1. The student will explain the role of natural forces in the universe.
At least-- formation of planets, orbital mechanics, stellar evolution.
Student Outcome(s):
Brief Description:
In this lesson, students will construct a model of a satellite in orbit around the earth and calculate the velocity needed for a satellite to stay in orbit.
Background knowledge / teacher notes:
Gravitational attraction is a fundamental property of matter that exists throughout the known universe. Physicists identify gravity as one of the four types of forces in the universe. The others are the strong and weak nuclear forces and the electromagnetic force.
A microgravity environment is one in which the apparent weight of a system is small compared to its actual weight due to gravity. In practice, the microgravity environments used by scientific researchers range from about one percent of Earth’s gravitational acceleration (aboard aircraft in parabolic flight) to better than one part in a million (for example, onboard Earth-orbiting research satellites).
The effects of gravity (apparent weight) can be removed quite easily by putting anything (a person, an object, an experiment) into a state of freefall
.Kepler's discoveries about elliptical orbits and the planets' non-uniform speeds made it impossible to maintain the idea of planetary motion as a natural one requiring no explanation.
Newton asked these questions:
What keeps the planets in their elliptical orbits?
On our spinning Earth what prevents objects from flying away when they are thrown in the air? What keeps you from being hurled off the spinning Earth?
Newton said that a fundamental force called "gravity'' operating between all objects made them move the way they does. Newton developed rules governing the motion of all objects. He used these laws and Kepler's laws to derive his unifying Law of Gravity.
Gravity is the attraction between all masses dependent on distance and the object’s mass. All objects produce some amount of gravity. The more mass an object has the more gravity it produces. There is no official measure for gravity. Gravity may be described in relative terms. "Earth’s gravity is about six times that of the moon." the moon has less mass than the Earth, and so it has less gravity.
When you think of motion, you may first think of something moving at a uniform speed.
Speed = (distance traveled)/(time)
There is a direct relation between the speed and the distance: the greater the distance traveled in a given time, the greater is the speed.
To describe motion of an object, one must consider its direction and speed. Velocity includes both the numerical value of the speed and the direction something is moving.
Galileo conducted several experiments to understand how something's velocity can be changed.
He found that an object's velocity could be changed only if a force acts on the object. Newton took this as the beginning of his description of how things move, This is Newton's 1st law of motion. A force causes a change in something's velocity (acceleration).
Acceleration is a change in the speed and/or direction of motion in a given amount of time:
Acceleration = (the velocity change)/(the time interval of the change).
Something at rest is not accelerating and something moving at a constant speed in a straight line is not accelerating.
Acceleration is a change in speed. a satellite orbiting a planet is constantly being accelerated even if its speed is constant because its direction is constantly being deflected. The satellite must be experiencing a force since it is accelerating. The force is gravity. If the force of gravity is removed the satellite will move in a straight line along a path tangent to the original circular orbit.
In Newton's second law of motion, he said that the force applied = mass of an object _ acceleration. Mass is the amount of material an object has and is a way of measuring how much inertia the object has.
Newton also found that for every action force exerted on an object, there is an equal but opposite force by the object. This is Newton's Third Law of Motion.
Using Kepler's third law and his own second law, Newton found that the attractive force, gravity, between a planet and Sun a distance d apart is
Force = kp _ (planet mass) / (d)2, where kp is a number that is the same for all the planets.
In the same way he found that the amount of the gravity between the Sun and a planet is
Force = ks _ (Sun mass) / (d)2.
Using his third law of motion, Newton reasoned that these forces must be the same (but acting in the opposite directions).
The Law of Gravity:
The force of gravity = G _ (mass 1) _(mass 2) / (distance between them)2
The term G is a universal constant. If you use the units of kilograms (kg) for mass and meters (m) for distance:
G = 6.672 _ 10-11 m3 /(kg sec2).
Spherically symmetric objects such as planets, stars, moons, behave as if their mass is concentrated at their centers. When using Newton's Law of Gravity, measure the distance between the centers of the objects.
Newton stated that the law of gravity works for any two objects. It applies to motions on the Earth, and motions in space.
Gravity depends on the masses of the two attracting objects and their distance from each other. It does not depend on their chemical composition or density. Gravity is always attractive, never repulsive.
Gravity never becomes zero. Stars feel the gravity from other stars, galaxies feel gravity from other galaxies, galaxy clusters feel gravity from other galaxies, etc. Gravity acts over the huge distances in the universe.
Mass is a measure of how much material is in an object, but weight is a measure of the attraction force exerted on that material to another mass; mass and weight are proportional to each other.
In the metric system there is no confusion of terms. A kilogram is a quantity of mass and a newton is a quantity of force. One kilogram (kg) = 2.205 pounds of mass and 4.45 newtons (N) = 1 pound of force.
Lesson Description:
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ENGAGE |
Vocabulary: velocity, acceleration. Ask students to brainstorm
Education Elements: ANIMATION This JPL site is the fourteenth chapter in an on line tutorial that describes the Basics of Space Flight. It includes an animation and additional information on launching satellites into orbit. http://www-a.jpl.nasa.gov/basics/bsf14-1.html |
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EXPLORE |
Set up your equipment as shown in the picture. Around the World. p. 100. Available: http://spacelink.nasa.gov/Instructional.Matrials/NASA.Educational.Products/Microgravity/ One team member stands above the large ball and holds the end of the string. The second team member’s job is to move the small ball in different ways to answer the following questions. Draw pictures to show what happened. Draw the pictures looking straight down on the two balls. Accommodation: Provide a lab activity sheet with space for recording the sketches. Education Elements :BACKGROUND This NASA site explains gravity, Newton’s universal law of gravitation, and provides a table of gravitational accelerations throughout the solar system http://lifesci3.arc.nasa.gov/SpaceSettlement/teacher/lessons/bryan/microgravity/gravback.html |
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EXPLAIN |
Accommodation: A simple graphic organizer will be helpful to organize ideas before writing. |
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EXTEND |
Research some of the ways scientists use microgravity to investigate real world applications. pp. 13-43. The teacher may wish to assign a different topic to each group. Mathematics Connection: Calculate how fast a space shuttle orbiter and the International Space Station travel in order to orbit earth. Solve for velocity (v) using this data: V = square root of GM/r
G= universal constant of gravitation = 6.67 x 10-11m3kg/s2 M Earth = Earth's mass = 5.98 x 1024 kg r = radius of Earth + spacecraft's orbit r Earth = 6.67 x 106 m orbiter altitude = 290 km International Space Station altitude = 350 km Education Elements :BACKGROUND This NASA Space Science Biological Research Project site provides a list of questions on gravity and its relationship to biological systems. The answers to the questions are also provided. http://spaceprojects.arc.nasa.gov/Space_Projects/SSBRP/gravity.html |
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EVALUATE |
Draw a diagram that shows the effect of gravity on satellite orbiting the Earth. Include the moon and the sun and any other planets you wish in your diagram. Journal Write: Write a short paragraph to explain the diagram. |
Materials:
Large ball*
Small ball
2 meters of string
Flower pot*
* A world globe can substitute for the large ball and flower pot
Resources:
Microgravity – A Teacher’s Guide with Activities in Science, Mathematics, and Technology,
EG-1997-08-110-HQ, Around The World. Available:
http://spacelink.nasa.gov/Instructional.Materials/NASA.Educational.Products/Microgravity/ National Aeronautics and Space Administration. Office of Life and Microgravity Sciences and Applications. Microgravity Research Division. Office of Human Resources and Education. Education Division