Download TechnoogyEducation-HOSKINS-Discover of Neptune

Course: Technology Education
Submitted By: Tracy Hoskins, CATE TECHED, Tulsa Public Schools
Project Name: Discovery of Neptune
Situation or Problem: Developments in mathematics often stimulate innovations in
science and technology. Students will explain why the development of scientific
knowledge depends on mathematical concepts such as the use of measurement,
symbols, estimation, accuracy, and the idea of scaling and proportion. They will
describe the role of technology in the confirmation of mathematical predictions.
Students will address open-ended questions in verbal and written form. This activity will
allow them to contribute to a group endeavor by offering useful ideas, supporting the
efforts of others, and focusing on the task. They will actively participate in group
discussions, ideation exercises, and debates; demonstrate curiosity, exhibit motivation
for learning, and use class time effectively; and, exhibit and refine inherent personal
qualities such as creativity and resourcefulness.
Project Description and Purpose: To familiarize students with the relationship
between technology, mathematics, and science by examining mathematical concepts,
scientific laws, and the process of innovation.
Performance Specifications:
Technology Standards
1. Students will develop an understanding of the relationships among technologies
and connections with other fields of study. (ITEA-STL 3)
2. Students will develop an understanding of the nature of mathematics. (AAAS-BSL)
3. Students will develop an understanding of the nature of technology. (AAAS-BSL)
Mathematics Standards – Unit 2 and Unit 4
4. Students will develop an understanding of mathematics processes. (Process
Standard Connections 4.1) (NCTM)
5. Students will develop an understanding of mathematics processes. (Process
Standard Communications 2.1 and 2.3) (NCTM)
6. The student will use measurement to solve problems in a variety of contexts. (4.3a)
7. The student will use data analysis and statistics to interpret data in a variety of
contexts. (5.1 and 5.3)
Language Arts Standards – Unit 1 and Unit 2
8. The student will interact with the words and concepts in a text to construct an
appropriate meaning. (3.1a, 3.1b, 3.3a, 3.5a, 3.5c, 3.2a and 3.4a)
9. The student will conduct research and organize information. (5.2d)
10. The student will read, construct meaning, and respond to a wide variety of literary
forms. (4.2b)
Project Based Activity – Technology Education – Discovery of Neptune - 1
Instructions and Parameters:
1. Explain why the development of scientific knowledge depends on mathematical
concepts such as the use of measurement, symbols, estimation, accuracy, and the
idea of scaling and proportion.
2. Describe the role of technology in the confirmation of mathematical predictions.
3. Explain that developments in mathematics often stimulate innovations in science
and technology.
4. Address open-ended questions in verbal and written form.
5. Contribute to a group endeavor by offering useful ideas, supporting the efforts of
others, and focusing on the task.
6. Actively participate in group discussions, ideation exercises, and debates.
7. Demonstrate curiosity, exhibit motivation for learning, and use class time effectively.
8. Exhibit and refine inherent personal qualities such as creativity and resourcefulness.
Engagement
Engaging question – How do you think the planet Neptune could be discovered using
a mathematical process instead of the use of a telescope?
1. The teacher will assess prior knowledge and possible misconceptions related to the
relationship between technology, mathematics, and science.
2. The teacher will show students a picture of our solar system and then a picture of
the planet Neptune.
3. The teacher will state that the planet Neptune was discovered through the
application of mathematical processes and not the use of a telescope.
Exploration
1. The teacher will explain that a vignette is a presentation of material providing a
description of people, circumstances, processes and/or events that represent an
illustrative example within a particular area or topic of study.
2. Students will read “The Discovery of Neptune” vignette found at the end of this
lesson.
3. Students will complete the exercises at the end of the reading.
Explanation
1. The students will present their answers for the exercise and state their questions.
2. The teacher will define perturbation as a disturbance in the regular elliptic or
motion of a heavenly body, produced by some force additional to that which
causes its regular motion, as the perturbations of the planets are caused by their
attraction on each other.
3. The teacher will explain that:
a. The study of perturbations has led to important discoveries in astronomy.
b. Within the solar system, the existence and position of Neptune was
predicted because of the deviations of Uranus from its computed path.
c. Neptune was discovered in 1846, after being predicted by two
mathematicians who found that Uranus was not moving in a perfectly
elliptical path.
d. By calculating the gravitational tug necessary to pull Uranus in its orbit,
they were able to tell astronomers where to point their telescopes to
discover Neptune.
e. Likewise, Pluto was discovered by its effect on Neptune.
Project Based Activity – Technology Education – Discovery of Neptune - 2
f. Beyond the confines of the solar system, perturbations in the orbits of
stars caused by the gravitational forces of orbiting bodies have led to the
discovery of a number of extra solar planetary systems.
4. Students will restate any questions that were not answered in the teacher’s
lecture and clarify any unresolved issues.
Lesson
1. Students will read the vignette “Gravitational Perturbations and the Prediction of
New Planets” and complete the exercise at the end.
2. The teacher will review the exercise questions with the class.
Evaluation
Students’ knowledge, skills, and attitudes will be assessed using selected response
items and rubrics for class participation, group work, brief constructed responses, and
extended constructed responses summarizing the lesson. The rubrics will be presented
in advance of the activities to familiarize students with the expectations and
performance criteria. They will also be reviewed during the activities to guide students in
the completion of assignments. The teacher may wish to develop a collection of
annotated exemplars of student work based on the rubrics. The exemplars will serve as
benchmarks for future assessments and may be used to familiarize students with the
criteria for assessment.
Project Based Activity – Technology Education – Discovery of Neptune - 3
Vignette 1
The Discovery of the New Planet Neptune
In 1846, the planet Neptune was discovered after its existence was predicted because
of discrepancies between calculations and data for the planet Uranus. Astronomers
found the new planet almost exactly at the position predicted by the calculations.
The situation is illustrated schematically in the adjacent diagram.
The dominant interaction
between Uranus and the Sun
is indicated with the heavy
line, but some perturbations
associated with other masses
are indicated by thin lines. By
using Newton’s laws to
calculate the perturbations on
the orbit of Uranus by a
hypothesized new planet,
mathematicians were able to
predict where the planet had
to be in order to cause the
observed deviations in the
position of Uranus. Once
astronomers took this
calculation seriously, they
found the new planet within
hours of turning their
telescopes on the region of
the sky implicated by the calculations. This precise prediction of the new planet and its
location was striking confirmation of the power of Newton’s theory of gravitation.
Later, similar calculations on supposed perturbations of the orbits of Uranus and
Neptune suggested the presence of yet another planet beyond the orbit of Neptune.
Eventually, in 1930, a new planet, Pluto, was discovered, but we now know that the
calculations in this case were also in error because of an incorrect assumption about
the mass of the new planet. It is now believed that the supposed deviations in the orbits
of Neptune and Uranus were errors in measurement because the actual properties of
Pluto would not have accounted for the supposed perturbations. Thus, the discovery of
Pluto was a kind of accident.
Exercise
1. When was Neptune discovered?
2. What do you think the word perturbation means?
3. List three questions you have about this vignette.
Project Based Activity – Technology Education – Discovery of Neptune - 4
Vignette 2
Gravitational Perturbations and the Prediction of New Planets
Computing the orbit of the earth as an ellipse around the center of mass for the earthsun system assumes that they are the only two masses in the universe. In reality, the
Universal Law of Gravitation implies that the earth interacts gravitationally not only with
the sun, but with every other mass in the Universe: the moon, the other planets,
asteroids and comets, the distant stars.
The Two-Body Approximation
However, from the form of the gravitational force, we see that the interactions are
largest when two situations are fulfilled:
1. The product of the masses of the two objects is large, which maximizes the
numerator of the expression for the strength of the gravitational force and,
2. The objects are near each other, which minimizes the denominator of the force
equation. The two-body approximation that the orbits of the planets are
determined only by the gravitational interaction between the sun and the planet is
possible because:
a. The sun is so massive compared with every other object in the solar
system.
b. Objects outside the solar system, such as stars, are so distant that the
distance squared factor in the denominator renders their gravitational
interactions with the planets negligible. For example, the sun is about
300,000 times more massive than the earth, and about 1000 times more
massive than the largest planet.
Thus, the product of the mass of a planet and the mass of the sun is always much
larger than the product of the masses of any two planets, and it is a good initial
approximation to neglect all interactions except that of the planet and the sun.
Gravitational Perturbations
However, the small deviations from this ideal picture have consequences if careful
measurements are made. These small deviations from the simplified picture are called
perturbations. They can be calculated systematically using Newton’s laws of motion and
gravitation from the positions of the known masses in the solar system. If we account
carefully for all known gravitational perturbations on the motion of observed planets, and
the motion of the planet still deviates from the prediction, there are two options:
1. Newton’s Law of Gravitation requires modification.
2. There is a previously undetected mass that is perturbing the orbits of the
observed planets.
Exercise
1. What happens to the gravitational
force if the distance between
objects is increased?
2. The interactions between two
bodies is greatest when what two
situations are fulfilled?
3. Compare the products of the
masses of the Sun and Mars with
Project Based Activity – Technology Education – Discovery of Neptune - 5
the product of the masses of Mars and the earth.
Project Based Activity – Technology Education – Discovery of Neptune - 6