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"The Achievements of the Theory of Gravity" Gravity and Space Navigation PPT High-Quality Courseware
Part One: Core Competency Goals
physical concepts
Understand the important applications of the law of gravity in astronomy.
scientific thinking
Learn how to calculate the mass and density of celestial bodies.
Scientific attitude and responsibility
Understand the role of scientific laws in human exploration of the unknown world.
Achievements in the Theory of Gravity PPT, Part 2: Pre-class Study
Knowledge Point 1 “Weighing” the Mass of the Earth
How to "weigh" the mass of the earth?
1. Idea: For an object with a mass of m on the surface of the earth, if the rotation of the earth is not taken into account, the gravity of the object is equal to the universal gravitation of the earth on the object.
2.Relationship: mg=________. (m is the mass of the earth, R is the radius of the earth)
3. Conclusion: m ground = ________, as long as the values of g, R, and G are known, the mass of the earth can be calculated.
The method of "weighing" the mass of the earth using m ground = gR2G can be extended to the determination of the mass of other celestial bodies (such as the moon), except that R should be the radius of the celestial body and g should be the gravitational acceleration on the surface of the celestial body.
Knowledge point 2: Calculate the mass of celestial bodies
1. Idea: When a planet with mass m moves in a uniform circular motion around the sun, the gravitational force between the planet and the sun provides centripetal force.
2.Relationship:
3. Conclusion: m=___________, as long as you know the period T and radius r of the planet’s movement around the sun, you can calculate the mass of the sun.
[Thinking and Judging]
(1) The gravity of an object on the surface of the earth must be equal to the earth’s gravitational pull on it. ( )
(2) If you only know the radius of a planet's circular motion around the sun, you can find the mass of the sun. ( )
(3) If you know the linear velocity and angular velocity of a planet in circular motion around the sun, you can find the mass of the sun. ( )
Knowledge Point 3: Discovering unknown celestial objects and predicting the return of Halley’s Comet
[Viewing pictures to help students]
Among the planets (or dwarf planets) in the solar system, Neptune is far away from the sun. How was it discovered?
1. Discovery of Neptune: Based on the observation data of Uranus, a student from Cambridge University in the UK and a young French astronomer named _______ used the law of universal gravitation to calculate the orbit of the "new" planet outside Uranus. On September 23, 1846, the German _______ discovered the planet - _________ near the position predicted by Le Verrier.
2. Discovery of other celestial bodies: In the past 100 years, people have discovered several larger celestial bodies such as ________ and Eris beyond the orbit of Neptune.
3. Halley’s Comet Returns
British astronomer Halley calculated that the orbits of three comets that appeared in 1531, 1607 and 1682 were exactly the same, and predicted that the comets that appeared three times were the same star with a period of about 76 years. He also predicted that it would arrive at the end of 1758 or Returned again in early 1759. The comet passed perihelion as scheduled in March 1759. Its last return was in 1986, and its next return will be around 2061.
[Thinking and Judging]
(1) Uranus was discovered based on the orbit calculated based on the law of universal gravitation. ( )
(2) The discovery of Neptune established the status of the law of universal gravitation. ( )
(3) Newton calculated the orbit of Neptune based on the law of universal gravitation. ( )
Achievements in the Theory of Gravity PPT, Part Three: Core Exploration
Core Point 1: Calculate the mass and density of celestial bodies
[Problem exploration]
The Moon is the only natural satellite of the Earth. It has been with the Earth for more than 4.6 billion years. Based on the Moon's orbital period and orbital radius, can we deduce the mass of the Moon and the mass of the Earth?
[Explore and summarize]
Calculation of the mass and density of celestial bodies
[Examination Cases]
[Example 1] (2017·Beijing Volume) Using the gravitational constant G and the following relevant data, what is ()
A. The radius of the earth and the acceleration of gravity
B. The speed and period of the artificial satellite's circular motion around the earth near the ground
C. The period of the moon’s circular motion around the earth and the distance between the moon and the earth
D. The period of the earth’s circular motion around the sun and the distance between the earth and the sun
Method summary
(1) The method of using universal gravitation to provide centripetal force can only solve for the mass of the central celestial body, but cannot find the mass of the orbiting celestial body (planet or satellite) in circular motion.
(2) Pay attention to the distinction between R and r: R refers to the radius of the central celestial body, and r refers to the orbital radius of the surrounding celestial body (planet or satellite).
In the figure, r=R+h, R is the radius of the central celestial body, r is the surrounding radius, and h is the height of the surrounding celestial body (planet or satellite) from the surface of the central celestial body.
[Example 2] On January 3, 2019, the "Chang'e-4" launched by my country achieved the first soft landing of a human probe on the back of the moon. The gravitational acceleration on the earth's surface is 6 times the gravitational acceleration on the moon's surface, and the radius of the earth is 4 times the radius of the moon. Then the ratio of the average densities of the earth and the moon is ()
A.1.5 B.4 C.6 D.24
Core Point 2: Analysis and calculation of physical quantities of celestial motion
[Problem exploration]
It is known that both the Earth and Mars revolve around the sun, and the orbital radius of Mars is 1.5 times the orbital radius of the Earth. Thinking based on the above materials:
(1) What kind of dynamic laws does the Earth and Mars follow?
(2) How to compare the linear velocity, angular velocity, period and centripetal acceleration of Mars and the Earth?
[Explore and summarize]
1.Basic idea
Generally, the motion of planets or satellites can be regarded as uniform circular motion, and the required centripetal force is provided by the universal gravitational pull of the central celestial body, that is, F direction = F million.
2. Common relationships
[Examination Cases]
[Example 3] The diameter of Mars is about half that of the Earth, and its mass is about one-tenth that of the Earth. The radius of its orbit around the sun is about 1.5 times the radius of the Earth. According to the above data, the following statement is correct ()
A. The value of gravitational acceleration on the surface of Mars is greater than that on the surface of the Earth
B. The revolution period of Mars is longer than that of the Earth
C. The linear speed of Mars’ revolution is greater than that of Earth
D. The centripetal acceleration of Mars’ revolution is greater than that of the Earth
Summary of methods: Techniques for solving celestial body motion problems
(1) Build a model
Whether they are natural celestial bodies (such as the earth, the moon, etc.) or artificial celestial bodies (such as satellites, spacecraft, etc.), as long as they are making circular motion around a certain central celestial body, they can be simplified to the uniform circular motion model of a particle to deal with the problem. .
(2) Solving a series of equations
According to the centripetal force provided by the central celestial body to the universal gravitation of the surrounding stars, a suitable centripetal force expression is listed for solution.
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"The Achievements of the Theory of Gravity" Excellent Courseware of Gravity and Space Navigation PPT:
"The Achievements of the Theory of Universal Gravity" Excellent Courseware on Gravity and Space Navigation PPT Part One Contents: Learning Objectives 1. Understand the important application of the law of universal gravitation in astronomy. 2. Understand the basic ideas of weighing the earth's mass and calculating the sun's mass, and be able to use everything lead..
"Achievements in the Theory of Gravity" Gravity and Space Navigation PPT Courseware:
"The Achievements of the Theory of Universal Gravity" Gravity and Space Navigation PPT Courseware Part One Content: Foundation of Essential Knowledge Literacy 1. Weighing the Mass of the Earth [Thinking] If the earth cannot be weighed with a balance, can it be weighed by the law of universal gravitation? Tip: Yes 1...
"Achievements in the Theory of Gravity" Gravity and Space Navigation PPT:
"Achievements of the Theory of Universal Gravity" Gravity and Space Navigation PPT Part One Content: Learning Objectives 1. Understand the important application of the law of universal gravitation in astronomy; 2. Be able to use the law of universal gravitation to calculate the mass of celestial bodies; 3. Understand and use the law of universal gravitation to deal with...