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Newton's laws of motion

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He believes that the earth is stationary and the sun, planets, and stars are rotating around the earth.

Riebeek, H., (2009, July 7).
Planetary Motion: The History of an Idea That Launched the Scientific Revolution. NASA Earth Observatory.
https://earthobservatory.nasa.gov/features/OrbitsHistory

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force acting on a planet to be the product of its mass and the acceleration

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Newton's First Law of Motion states that every moving item in space will move in a straight line at the same speed at all times, unless acted upon by an outside force, in this case, the sun's gravitational pull is the outside force pulling them toward it.

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He adapted the Ptolemaic model of the universe (geocentric), that all celestial bodies revolve around the Earth.

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Isaac Newton first introduced the concept of gravitational force as the reason for falling bodies and astronomical movements. Newton's universal law of gravitation states that 'every object in the universe attracts every other object with a force that is directed along a line joining them.' It is said that force has a direct relationship with the product of the objects' masses and has an inverse relationship to the square of the distance between them (Urone, et al., 2020).

Urone, P. P., & Hinrichs, R. (2020). Physics. Houston, Texas: OpenStax. Retrieved from https://openstax.org/books/physics/pages/7-2-newtons-law-of-universal-gravitation-and-einsteins-theory-of-general-relativity

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Developed an explanation of planetary motion using the same physical laws that apply on Earth. He knew through an experiment that a moving body will continue in a straight path in the absence of an external force. Planets, on the other hand, travelled in elliptical orbits because of the gravity.

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Galileo used his telescope to observe the night sky. With his discoveries, he proved that the planets were orbiting around the sun.

Riebeek, H., (2009, July 7).
Planetary Motion: The History of an Idea That Launched the Scientific Revolution. NASA Earth Observatory.
https://earthobservatory.nasa.gov/features/OrbitsHistory

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Kepler's first law: Planets move in a loop/ellipse, sun is the focus point that is slightly offset from the center.

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Aristotle's view seems to be that planetary motions are partly independent, and partly dependent on the motion of other spheres.

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Aristotle's view seems to be that planetary motions are partly independent, and partly dependent on the motion of other spheres.

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Johannes Kepler is recognized as the "Father of Planetary motion" due to his three laws of planetary motion. His laws of motion are the law of orbits, the law of areas, and the law of periods.

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Galileo Galilei opposed Aristotle's view on what astronomical bodies revolve around in the Solar system. He introduced the concept of heliocentrism wherein the planets revolve around the sun.

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Kepler's Laws of Planetary motion consists of: (1) All planets move about the Sun in elliptical orbits, having the Sun as one of the foci. (2) A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time. (3) The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.
Britannica, T. Editors of Encyclopaedia (n.d.). Kepler's laws of planetary motion. Encyclopedia Britannica. https://www.britannica.com/science/Keplers-laws-of-planetary-motion

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Aristotle, on the other hand, believed that the sun and other planets revolve around the earth. Thus, the geocentric view was born.

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Tycho Brahe backed up Johannes Kepler's results and strengthened them since he was able to make a comprehensive and exact observation of the planet's location.

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They describe how (1) planets move in elliptical orbits with the Sun as a focus, (2) a planet covers the same area of space in the same amount of time no matter where it is in its orbit, and (3) a planet's orbital period is proportional to the size of its orbit (its semi-major axis).

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Tycho Brahe believes that the Sun revolves around the earth while the other planets revolve around the Sun.

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Developed three laws of planetary motion:

1. The planets move in elliptical orbits with the sun at a focus.

2. In their orbits around the sun, the planets sweep out equal areas in equal times.

3. The squares of the times to complete one orbit are proportional to the cubes of the average distances from the sun.

Kepler was the first to state clearly that the way to understand the motion of the planets was in terms of some kind of force from the sun.

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Aristotle believed that the earth is stationary, and the planets including the sun rotated around the earth.

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According to Physics Classroom (n.d.), Newton became a part of the Gravity Hall of Fame not because he discovered gravity but rather, because he discovered that gravitation is universal. Gravity is universal in such a way that with a force of gravitational attraction, attraction exist between all objects. Accordingly, newton is responsible for the development of a mathematical formulation of gravity. In this formula, it is showed that the force of gravitational attraction is in direct relationship with the masses of both objects and is in an indirect relationship with the square of the distance between the two objects.

https://www.physicsclassroom.com/class/circles/Lesson-3/Newton-s-Law-of-Universal-Gravitation

https://sciencing.com/newton-explain-planetary-motion-20884.html

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Gave the three fundamental laws of planetary motion:
1. Each planet's orbit about the Sun is an ellipse.  The planet to Sun distance is constantly changing as the planet goes around its orbit.
2.   A planet is moving fastest when it is at perihelion(point nearest to the sun) and slowest at aphelion (point farthest).
3. The period for a planet to orbit the Sun increases rapidly with the radius of its orbit, which were instrumental in Isaac Newton deriving his theory of universal gravitation.

Source:
https://solarsystem.nasa.gov/resources/310/orbits-and-keplers-laws/

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He first discovered that moons orbited around Jupiter. He also saw the different phases of Venus, thereby proving that planets orbit around the sun. Accordingly, he was also the first one to observe that objects are pulled towards the Earth’s center

http://zebu.uoregon.edu/disted/ph121/l3.html

https://earthobservatory.nasa.gov/features/OrbitsHistory

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Although Johannes Kepler was known for the findings of planetary motion, he was known for defining the laws regarding the planetary motion. One Kepler Law is that every planet's orbit is an ellipse with the Sun at a focus.

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Johannes Kepler created his three Laws of Planetary Motion

1. The planets move in elliptical orbits with the sun at a focus.

2. In their orbits around the sun, the planets sweep out equal areas in equal times.

3. The squares of the times to complete one orbit are proportional to the cubes of the average distances from the sun.

Fowler, M., (n.d.). Tycho Brahe and Johannes Kepler. https://galileoandeinstein.phys.virginia.edu/lectures/tycho.htm

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Aristotle believed on a geocetnric worldview. He said that the Earth is stationary and is at the center of the revolving universe.

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Galileo Galilei supported heliocentrism when he observed the moons of Jupiter. Galileo also observed the phases of Venus, proving that planets orbit the sun.

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Brahe gathered detailed astronomical data in order to support his theory, which Kepler later utilized to verify heliocentrism and compute the orbital equations. Tycho Brahe presented a solar system theory that combined parts of both the Ptolemaic and Copernican systems.

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Kepler’s Three Laws of Motion

- Planets move in elliptical orbits with the Sun as a focus

- A planet covers the same area of space in the same amount of time no matter where it is in its orbit

- A planet’s orbital period is proportional to the size of its orbit

NASA. (2019). Orbits and Kepler’s Laws | NASA Solar System Exploration. Retrieved from: https://solarsystem.nasa.gov/resources/310/orbits-and-keplers-laws/

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Brahe believed in a model of the Universe with the Sun (rayed disk) orbiting the Earth (black dot), but the other planets (symbols) orbiting the Sun. In an attempt to prove his theory, Brahe compiled extensive astronomical records, which Kepler eventually used to prove heliocentrism and to calculate the orbital laws.

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Brahe believed in a model of the Universe with the Sun (rayed disk) orbiting the Earth (black dot), but the other planets (symbols) orbiting the Sun. In an attempt to prove his theory, Brahe compiled extensive astronomical records, which Kepler eventually used to prove heliocentrism and to calculate the orbital laws.

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When it comes to masses, Galileo is the one who mentions one of the first exact laws of motion. He was able to prove that all bodies, regardless of size or mass, may accelerate at the same pace. His discovery of how things resist change in motion, or inertia, was particularly significant.

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Aristotle's geocentric model touches upon the idea that the Earth is the center of the universe where the Sun, Moon, planets, and all stars are revolving around the planet.

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Aristotle believed that the planets and the Sun orbited Earth. There was no sign that the earth was in motion because there was no perpetual wind that blew over the surface of the earth and a ball thrown straight up into the air doesn’t land behind the thrower.

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Newton's 3 laws of motion developed an explanation for the sun's influence around planets and other bodies surrounding it. For instance, the gravitational pull of the sun is influenced by its mass and distance thus, predicting the motion of the planets.

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He believed that the Sun, together with the planets, orbited Earth. He did not discover proof that tells that the Earth moves. Therefore, Aristotle had a premise that the Earth has to be stationary and instead, is the other planets, the Sun, and the fixed dome of stars that rotate around the Earth.

https://earthobservatory.nasa.gov/features/OrbitsHistory

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Newton's First Law of Motion states that unless acted upon by an external force, a body in motion will remain in motion. Similarly, if it is not moving, it will remain so until a force acts on it. The planets move in roughly circular orbits around the sun due to the force of gravity.

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Johannes Kepler introduced the three Laws of Planetary Motion: (1) The orbit of each planet is an ellipse with the sun, (2) planets move to cover out equal areas at equal times, and (3) the ratio of the squares of the periods of any two planets is equal to the ratio of cubes of the distances from the sun.

Urone, P. P., & Hinrichs, R. (2020). Physics. Houston, Texas: OpenStax. Retrieved from https://openstax.org/books/physics/pages/7-1-keplers-laws-of-planetary-motion

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Section Learning Objectives

By the end of this section, you will be able to do the following:

Explain Kepler's three laws of planetary motion

Apply Kepler's laws to calculate characteristics of orbits

Teacher Support

The learning objectives in this section will help your students master the following standards:

(4) Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to:
(C) analyze and describe accelerated motion in two dimensions using equations, including projectile and circular examples.

In this section students will apply Kepler's laws of planetary motion to objects in the solar system.

[BL] [OL] Discuss the historical setting in which Kepler worked. Most people still thought Earth was the center of the universe, and yet Kepler not only knew that the planets circled the sun, he found patterns in the paths they followed. What would it be like to be that far ahead of almost everyone? A fascinating description of this is given in the program Cosmos with Carl Sagan (Episode 3, Harmony of the Worlds).

[AL] Explain that Kepler's laws were laws and not theories. Laws describe patterns in nature that always repeat themselves under the same set of conditions. Theories provide an explanation for the patterns. Kepler provided no explanation.

Section Key Terms

aphelion

Copernican model

eccentricity

Kepler's laws of planetary motion

perihelion

Ptolemaic model

Concepts Related to Kepler's Laws of Planetary Motion

Examples of orbits abound. Hundreds of artificial satellites orbit Earth together with thousands of pieces of debris. The moon's orbit around Earth has intrigued humans from time immemorial. The orbits of planets, asteroids, meteors, and comets around the sun are no less interesting. If we look farther, we see almost unimaginable numbers of stars, galaxies, and other celestial objects orbiting one another and interacting through gravity.

All these motions are governed by gravitational force. The orbital motions of objects in our own solar system are simple enough to describe with a few fairly simple laws. The orbits of planets and moons satisfy the following two conditions:

The mass of the orbiting object, m, is small compared to the mass of the object it orbits, M.

The system is isolated from other massive objects.

Teacher Support

Teacher Support

[OL] Ask the students to explain the criteria to see if they understand relative mass and isolated systems.

Based on the motion of the planets about the sun, Kepler devised a set of three classical laws, called Kepler's laws of planetary motion, that describe the orbits of all bodies satisfying these two conditions:

1. The orbit of each planet around the sun is an ellipse with the sun at one focus.

2. Each planet moves so that an imaginary line drawn from the sun to the planet sweeps out equal areas in equal times.

3. The ratio of the squares of the periods of any two planets about the sun is equal to the ratio of the cubes of their average distances from the sun.

These descriptive laws are named for the German astronomer Johannes Kepler (1571-1630). He devised them after careful study (over some 20 years) of a large amount of meticulously recorded observations of planetary motion done by Tycho Brahe (1546-1601). Such careful collection and detailed recording of methods and data are hallmarks of good science. Data constitute the evidence from which new interpretations and meanings can be constructed. Let's look closer at each of these laws.

Teacher Support

Teacher Support

[BL] Relate orbit to year and rotation to day. Be sure that students know that an object rotates on its axis and revolves around a parent body as it follows its orbit.

[OL] See how many levels of orbital motion the students know and fill in the ones they don't. For example, moons orbit around planets; planets around stars; stars around the center of the galaxy, etc.

[AL] From the point of view of Earth, which objects appear (incorrectly) to be orbiting Earth (stars, the sun, galaxies) and which can be seen to be orbiting parent bodies (the moon, moons of other planets, stars in other galaxies)?

Kepler's First Law

The orbit of each planet about the sun is an ellipse with the sun at one focus, as shown in Figure 7.2. The planet's closest approach to the sun is called perihelion and its farthest distance from the sun is called aphelion.

Teacher Support

Teacher Support

[AL] Ask for a definition of planet. Prepare to discuss Pluto's demotion if it comes up. Discuss the first criterion in terms of center of rotation of a moon-planet system. Explain that for all planet-moon systems in the solar system, the center of rotation is within the planet. This is not true for Pluto and its largest moon, Charon, because their masses are similar enough that they rotate around a point in space between them.

If you know the aphelion ( r a) and perihelion ( r p) distances, then you can calculate the semi-major axis ( a) and semi-minor axis ( b).

a= ( r a+ r p)2 b= r a r p a= ( r a+ r p)2 b= r a r p

Teacher Support

Teacher Support

[AL] If any students are interested and proficient in algebra and geometry, ask them to derive a formula that relates the length of the string and the distance between pins to the major and minor axes of an ellipse. Explain that this is a real world problem for workers who design elliptical tabletops and mirrors.

[BL] [OL] Impress upon the students that Kepler had to crunch an enormous amount of data and that all his calculations had to be done by hand. Ask students to think of similar projects where scientists found order in a daunting amount of data (the periodic table, DNA structure, climate models, etc.).

Teacher Demonstration

Demonstrate the pins and string method of drawing an ellipse, as shown in Figure 7.3, or have the students try it at home or in class.

Ask students: Why does the string and pin method create a shape that conforms to Kepler's second law? That is, why is the shape an ellipse?

Kepler's Second Law

Each planet moves so that an imaginary line drawn from the sun to the planet sweeps out equal areas in equal times, as shown in Figure 7.4.

Teacher Support

Teacher Support

Ask the students to imagine how complicated it would be to describe the motion of the planets mathematically, if it is assumed that Earth is stationary. And yet, people tried to do this for hundreds of years, while overlooking the simple explanation that all planets circle the sun.

[OL] Ask students to use this figure to understand why planets and comets travel faster when they are closer to the sun. Explain that time intervals and areas are constant, but both velocity and distance from the sun vary.

Tips For Success

Note that while, for historical reasons, Kepler's laws are stated for planets orbiting the sun, they are actually valid for all bodies satisfying the two previously stated conditions.

Kepler's Third Law

The ratio of the periods squared of any two planets around the sun is equal to the ratio of their average distances from the sun cubed. In equation form, this is

where T is the period (time for one orbit) and r is the average distance (also called orbital radius). This equation is valid only for comparing two small masses orbiting a single large mass. Most importantly, this is only a descriptive equation; it gives no information about the cause of the equality.

Teacher Support

Teacher Support

[BL] See if students can rearrange this equation to solve for any one of the variables when the other three are known.

[AL] Show a solution for one of the periods T or radii r and ask students to interpret the fractional powers on the right hand side of the equation.

[OL] Emphasize that this approach only works for two satellites orbiting the same parent body. The parent body must be the same because r 2/ T 2= G M/ (4 π 2) r 2/ T 2= G M/ (4 π 2) and M is the mass of the parent body. If M changes, the ratio r ³/ T ² also changes.

Virtual Physics

Acceleration

This simulation allows you to create your own solar system so that you can see how changing distances and masses determines the orbits of planets. Click Help for instructions.

Grasp Check

When the central object is off center, how does the speed of the orbiting object vary?

1. The orbiting object moves fastest when it is closest to the central object and slowest when it is farthest away.

2. The orbiting object moves slowest when it is closest to the central object and fastest when it is farthest away.

3. The orbiting object moves with the same speed at every point on the circumference of the elliptical orbit.

4. There is no relationship between the speed of the object and the location of the planet on the circumference of the orbit.

Calculations Related to Kepler's Laws of Planetary Motion

Kepler's First Law

Refer back to Figure 7.2 (a). Notice which distances are constant. The foci are fixed, so distance f 1 f 2¯ f 1 f 2¯ is a constant. The definition of an ellipse states that the sum of the distances f 1 m¯+ m f 2¯ f 1 m¯+ m f 2¯ is also constant. These two facts taken together mean that the perimeter of triangle Δ f 1 m f 2 Δ f 1 m f 2 must also be constant. Knowledge of these constants will help you determine positions and distances of objects in a system that includes one object orbiting another.

Kepler's Second Law

Refer back to Figure 7.4. The second law says that the segments have equal area and that it takes equal time to sweep through each segment. That is, the time it takes to travel from A to B equals the time it takes to travel from C to D, and so forth. Velocity v equals distance d divided by time t: v =d/t v =d/t . Then, t=d/v t=d/v , so distance divided by velocity is also a constant. For example, if we know the average velocity of Earth on June 21 and December 21, we can compare the distance Earth travels on those days.

The degree of elongation of an elliptical orbit is called its eccentricity ( e). Eccentricity is calculated by dividing the distance f from the center of an ellipse to one of the foci by half the long axis a.

When e=0 e=0 , the ellipse is a circle.

The area of an ellipse is given by A=π a b A=π a b , where b is half the short axis. If you know the axes of Earth's orbit and the area Earth sweeps out in a given period of time, you can calculate the fraction of the year that has elapsed.

Teacher Support

Teacher Support

[OL] Review the definitions of major and minor axes, semi-major and semi-minor axes, and distance f. The major axis is the length of the ellipse and passes through both foci. The minor axis is the width of the ellipse and is perpendicular to the major axis. The semi-major and semi-minor axes are half of the major and minor axes, respectively.

Worked Example

Kepler's First Law

At its closest approach, a moon comes within 200,000 km of the planet it orbits. At that point, the moon is 300,000 km from the other focus of its orbit, f ₂. The planet is focus f ₁ of the moon's elliptical orbit. How far is the moon from the planet when it is 260,000 km from f ₂?

Strategy

Show and label the ellipse that is the orbit in your solution. Picture the triangle f ₁m f ₂ collapsed along the major axis and add up the lengths of the three sides. Find the length of the unknown side of the triangle when the moon is 260,000 km from f ₂.

Perimeter of f 1 m f 2=200,000 km+100,000 km+300,000 km=600,000 km. f 1 m f 2=200,000 km+100,000 km+300,000 km=600,000 km.

m f 1=600,000 km−(100,000 km+260,000 km)=240,000 km. m f 1=600,000 km−(100,000 km+260,000 km)=240,000 km.

The perimeter of triangle f ₁ mf ₂ must be constant because the distance between the foci does not change and Kepler's first law says the orbit is an ellipse. For any ellipse, the sum of the two sides of the triangle, which are f ₁ m and mf ₂, is constant.

Teacher Support

Teacher Support

Walk the students through the process of mentally collapsing the f ₁ mf ₂ at the end of the major axis to reveal what the three sides of the triangle f ₁ mf ₂ are equal to. Picture the sections of the string as the pencil approaches the major axis. This distance f ₁ f ₂ remains constant, f ₁ m is the distance from f ₁ to the end of the major axis, and mf ₂ is f ₁ m + f ₁ f ₂.

[OL] Have students relate eccentricity, distance between foci, and shape of orbit.

[AL] Ask for examples of orbits with high eccentricity (comets, Pluto) and low eccentricity (moon, Earth).

Worked Example

Kepler's Second Law

Figure 7.6 shows the major and minor axes of an ellipse. The semi-major and semi-minor axes are half of these, respectively.

Earth's orbit is slightly elliptical, with a semi-major axis of 152 million km and a semi-minor axis of 147 million km. If Earth's period is 365.26 days, what area does an Earth-to-sun line sweep past in one day?

Strategy

Each day, Earth sweeps past an equal-sized area, so we divide the total area by the number of days in a year to find the area swept past in one day. For total area use A=π a b A=π a b . Calculate A, the area inside Earth's orbit and divide by the number of days in a year (i.e., its period).

area per day = total area total number of days = π a b 365 d = π 365 d = 1.92× 10 14 km 2/d area per day = total area total number of days = π a b 365 d = π 365 d = 1.92× 10 14 km 2/d

The area swept out in one day is thus 1.92× 10 14 km 2 1.92× 10 14 km 2 .

The answer is based on Kepler's law, which states that a line from a planet to the sun sweeps out equal areas in equal times.

Teacher Support

Teacher Support

Explain that this formula is easy to remember because it is similar to A=π r 2. A=π r 2. Discuss Earth's eccentricity. Compare it with that of other planets, asteroids, or comets to further emphasize what defines a planet. Note that Earth has one of the least eccentric orbits and Mercury has the most eccentric orbit of the planets.

[BL]Have the students memorized the value of π? π?

[OL] [AL]What is the formula when a = b? Is the formula familiar?

[OL]Can the student verify this statement by rearranging the equation?

Kepler's Third Law

Kepler's third law states that the ratio of the squares of the periods of any two planets ( T ₁, T ₂) is equal to the ratio of the cubes of their average orbital distance from the sun ( r ₁, r ₂). Mathematically, this is represented by

From this equation, it follows that the ratio r ³/T ² is the same for all planets in the solar system. Later we will see how the work of Newton leads to a value for this constant.

Worked Example

Kepler's Third Law

Given that the moon orbits Earth each 27.3 days and that it is an average distance of 3.84× 10 8 m 3.84× 10 8 m from the center of Earth, calculate the period of an artificial satellite orbiting at an average altitude of 1,500 km above Earth's surface.

Strategy

The period, or time for one orbit, is related to the radius of the orbit by Kepler's third law, given in mathematical form by = = . Let us use the subscript 1 for the moon and the subscript 2 for the satellite. We are asked to find T ₂. The given information tells us that the orbital radius of the moon is r 1=3.84× 10 8 m r 1=3.84× 10 8 m , and that the period of the moon is T 1=27.3 days T 1=27.3 days . The height of the artificial satellite above Earth's surface is given, so to get the distance r ₂ from the center of Earth we must add the height to the radius of Earth (6380 km). This gives r 2=1500 km+6380 km=7880 km r 2=1500 km+6380 km=7880 km . Now all quantities are known, so T ₂ can be found.

To solve for T ₂, we cross-multiply and take the square root, yielding

T 2 2= T 1 2 ( r 2 r 1)3; T 2= T 1 ( r 2 r 1) 3 2 T 2=(27.3 d)( 24.0 h d) ( 7880 km 3.84× 10 5 km) 3 2=1.93 h. T 2 2= T 1 2 ( r 2 r 1)3; T 2= T 1 ( r 2 r 1) 3 2 T 2=(27.3 d)( 24.0 h d) ( 7880 km 3.84× 10 5 km) 3 2=1.93 h.

This is a reasonable period for a satellite in a fairly low orbit. It is interesting that any satellite at this altitude will complete one orbit in the same amount of time.

Practice Problems

1 .

A planet with no axial tilt is located in another solar system. It circles its sun in a very elliptical orbit so that the temperature varies greatly throughout the year. If the year there has 612 days and the inhabitants celebrate the coldest day on day 1 of their calendar, when is the warmest day?

1. Day 1

2. Day 153

3. Day 306

4. Day 459

2 .

A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth's rotation). The ratio \frac{r^3}{T^2} for the moon is 1.01\times10^{18}\,\frac{\text{km}^3}{y^2}. Calculate the radius of the orbit of such a satellite.

1. 2.75\times10^3\,\text{km}

2. 1.96\times10^4\,\text{km}

3. 1.40\times10^5\,\text{km}

4. 1.00\times10^6\,\text{km}

Check Your Understanding

3 .

Are Kepler's laws purely descriptive, or do they contain causal information?

1. Kepler's laws are purely descriptive.

2. Kepler's laws are purely causal.

3. Kepler's laws are descriptive as well as causal.

4. Kepler's laws are neither descriptive nor causal.

4 .

True or false-According to Kepler's laws of planetary motion, a satellite increases its speed as it approaches its parent body and decreases its speed as it moves away from the parent body.

1. True

2. False

5 .

Identify the locations of the foci of an elliptical orbit.

1. One focus is the parent body, and the other is located at the opposite end of the ellipse, at the same distance from the center as the parent body.

2. One focus is the parent body, and the other is located at the opposite end of the ellipse, at half the distance from the center as the parent body.

3. One focus is the parent body and the other is located outside of the elliptical orbit, on the line on which is the semi-major axis of the ellipse.

4. One focus is on the line containing the semi-major axis of the ellipse, and the other is located anywhere on the elliptical orbit of the satellite.

Teacher Support

Use the Check Your Answers questions to assess whether students master the learning objectives for this section. If students are struggling with a specific objective, the Check Your Answers will help identify which objective is causing the problem and direct students to the relevant content.

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7.1 Kepler's Laws of Planetary Motion - Physics | OpenStax

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Section Learning Objectives By the end of this section, you will be able to do the following: Explain Kepler's three laws of planetary motion Apply Kepler's laws to calculate characteristics of orbits Teacher Support The learning objectives in this section will help your students master the following standards: (4) Science concepts.

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Johannes Kepler is known as the Father of Planetary Motion because of the three laws.  He was helped by his assistant Tycho Brahe, an astronomer who helped him define the orbits of Mars

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Aristotle was able to construct a model that depicted the planets' orderly motion around the Earth. He created a Geocentric model in which the Earth is orbited by the Sun, Moon, planets, and stars, all of which are included inside Eudoxus' sphere. Another was the heliocentric model of the cosmos, in which the Sun, rather than the Earth, is at the center.

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Isaac Newton described that a body in motion keeps the same motion unless acted upon by an outside force - first law of motion. He also developed other two laws of motion. The planets would be travelling in straight lines if not for the sun's gravitational attraction.

https://education.seattlepi.com/newton-explain-planetary-motion-6264.html

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Isaac Newton's three laws of motion explain how forces and solid bodies interact, including planets floating in the vacuum of space. His law of gravity describes how the masses of two objects creates an attraction between them that weakens with distance. Together, these scientific principles help explain the movements of the planets around the sun in our solar system.

First Law of Motion

Newton's First Law of Motion states that a body in motion keeps the same motion unless acted upon by an outside force. Likewise, if it is not moving, it remains that way unless a force acts on it. Any moving object in space will travel in a straight line at the same speed forever, planets included. The planets would be moving in straight lines, but the sun's gravity pulls them toward it. The force of gravity causes the moving planets to travel in roughly circular orbits around the sun. They have been circling the sun for billions of years because other forces have been too weak to change the orbits in any significant way.

Second Law of Motion

In Newton's Second Law of Motion, an object accelerates in proportion to the amount of force acting on it. If no force acts on the object, its velocity remains constant. The motion of the planets around the sun involves a constant acceleration. Here, however, acceleration means "changing direction" instead of "changing speed;" both are valid under the Second Law. The gravitational force exerted by the sun continually alters a planet's path, bending it towards the sun although never directly at it.

Third Law of Motion

The Third Law of Motion states that for every force acting on an object, another, equal force also acts in the opposite direction. For example, a cat sitting on a chair exerts a downward force on the chair from her weight; the chair also exerts a force on the cat, holding her up. In the same manner, the force exerted on a planet by the sun is also "felt" by the sun; however, because the sun is hundreds of times more massive than the planets, the force has barely any effect on the sun's motion, although it affects the planet in a major way.

Law of Universal Gravity

Newton's Law of Gravity takes into consideration the masses of two objects and the distance between them. The strength of the gravitational force attracting the two objects together goes up as their masses increase and decreases as the distance increases. Gravity acts across even the enormous distances between the sun and outer planets. The mass of the sun and a planet create a force, pulling the planet's orbit into a circle.

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How Does Newton Explain Planetary Motion?

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How Does Newton Explain Planetary Motion?. Isaac Newton's three laws of motion explain how forces and solid bodies interact, including planets floating in the vacuum of space. His law of gravity describes how the masses of two objects creates an attraction between them that weakens with distance. Together, these ...

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Newton's three laws of motion and the Law of Universal Gravity are the contributions of Isaac Newton to the Planetary movement/attraction.

Papiewski, J., (n.d.). How Does Newton Explain Planetary Motion? seattlepi. https://education.seattlepi.com/newton-explain-planetary-motion-6264.html

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By applying the concept of the laws of motion and the force of gravitation between two bodies, he provided explanations as to why do planets travel and move the way they move.

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Galileo supported Copernicus’ heliocentric theory when he observed that four moons orbit around Jupiter. He also observed different phases of Venus, that proved that the planet orbits around the sun.

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Galileo Galilei claims that heavenly bodies do not require a cause to continue its movement.

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Newton published a formula that explained the motion of an apple and that of the planets. He shoed the direct relationship of gravitational force to the product of two masses and inversely related to square of the distance between them.

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Galileo Galilei proved that Aristotle's idea that the Earth is the center of the universe is not true by developing a telescope. He believed that the idea of Copernicus is more accurate that the Sun is the center of the universe.

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Tycho Brahe recorded the positions of the Sun. Moon, and planets for over 20 years. This made him note the positions of the planets is different from of that of Ptolemy's. His work was later on assisted Johannes Kepler.

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Tycho's data was stolen by Johannes Kepler. Kepler then was able to create the three laws of planetary motion with Tycho's data.

Fowler, M., (n.d.). Tycho Brahe and Johannes Kepler. https://galileoandeinstein.phys.virginia.edu/lectures/tycho.htm

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Galileo's claim that force causes acceleration is inseparable from his claim that bodies do not require a cause to continue their movement.He came to believe that the idea that the Sun and other planets orbited around the Earth was not correct.

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Through the use of telescope, he discovered that moons orbited Jupiter and studied the phases of Venus which later on proved that planets orbit the Sun. He also supported Copernicus' heliocentric theory upon observing the 4 moons orbiting around Jupiter.

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Aristotle believed that other planets and the sun revolve around the earth - Geocentric belief. The Moon, the planets, the Sun, and the stars all rotate around the Earth (which stays still), with uniform circular motion.

http://astronomy.nmsu.edu/geas/lectures/lecture11/slide01.html#:~:text=In%20the%20geocentric%20system%2C%20the,to%20be%20ethereal%20and%20unchanging.

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The Ptolmeic (Geocentric, or Earth-centered) Model of the Solar System

Cladius Ptolemy
Greek astronomer and mathematician
Modeled the movements of the Sun, the Moon, and the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) in the skies to great accuracy, with a geocentric system of orbits and epicycles.
Born: 85 in Egypt
Died: 165 in Alexandria, Egypt

Quotation: When I trace at my pleasure the windings to and fro of the heavenly bodies, I no longer touch the earth with my feet: I stand in the presence of Zeus himself and take my fill of ambrosia, food of the gods.
C B Boyer, A History of Mathematics (New York 1968)

In the geocentric system, the Earth is considered to be the center of the solar system. The Moon, the planets, the Sun, and the stars all rotate around the Earth (which stays still), with uniform circular motion. They compose the heavens, which are considered to be ethereal and unchanging.

An Icelandic manuscript from roughly 1750, depicting the geocentric model of the solar system.

Aristotle argued strongly in favor of this system, on the grounds that if the Earth itself were to be moving:

We would be aware of the movement of the ground or the air.

The apparent position of nearby stars would change in the sky (parallax).

But why did the planets display retrograde motion, moving both forwards and backwards on the sky?

And why did the planets appear brighter at certain times than others?

To explain the orbits of the Moon and planets in this system, it was not enough to have them travel on circular paths (deferents) about the Earth. Each one traveled on a small circular orbit (an epicycle) which in turn traveled on a larger deferent about the Earth. This combination, rather like the interlocked gears of a mechanical clock or watch, produced a path which matched the observed non-circular elements of the planetary orbits.

The next figure shows how a deferent (large circle) and an epicycle (small circle) could produce both the overall prograde (counterclockwise) and the occasional retrograde (clockwise) motion of the planet Jupiter under the geocentric system. The red dot shows the location of Jupiter, and the blue line shows how it would shift forward and backward against background stars.

Consider two interesting links about celestial navigation in the past: (1) Is the Pleiades star cluster depicted in prehistoric cave paintings in Lascaux? (2) Is the biblical story of Samson and the Philistines a clever navigational map of the sky, built from the legends of Gilgamesh?

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The Ptolmeic (Geocentric, or Earth-centered) Model of the Solar System Cladius Ptolemy Greek astronomer and mathematicianModeled the movements of the Sun, the Moon, and the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) in the skies to great accuracy, with a geocentric system of orbits and epicycles.Born: 85 in EgyptDied: 165 in Alexandria, Egypt Quotation: When I trace at my pleasure the windings to and fro of the heavenly bodies, I no longer touch the earth with my feet: I stand in the presence of Zeus himself and take my fill of ambrosia, food of the gods.

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Tycho determined that the planets orbit the Sun in elliptical orbits and proposed some simple laws that govern the motion of the planets and other objects. He developed a model of the solar system in which the Sun was at the center.

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Tycho Brahe's viewpoint on planetary motion has a mixture of the viewpoints of Galileo and Aristotle, in which all the planets except the Earth, orbit the Sun. Meanwhile, the Sun and the stars are orbiting the Earth.

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Galileo was aware of Copernicus' heliocentric (Sun-centered) hypothesis and had accepted it. Galileo's observations of Venus were the ones that proved the theory.

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Brahe contributed a new model for the cosmos. In his model concerning the cosmos, all of the planets orbited the sun, while the sun and the moon orbited the Earth.

https://www.loc.gov/collections/finding-our-place-in-the-cosmos-with-carl-sagan/articles-and-essays/modeling-the-cosmos/whose-revolution-copernicus-brahe-and-kepler#:~:text=Brahe's%20Model%20of%20the%20Cosmos&text=In%20Brahe's%20model%2C%20all%20of,the%20path%20of%20the%20sun.

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Tycho accurately discussed and described the planetary positions. He believed that the sun orbited the earth and the other planets orbit the sun.
He developed three laws:
I The planets move in elliptical orbits with the sun at a focus. II In their orbits around the sun, the planets sweep out equal areas in equal times.
III The squares of the times to complete one orbit are proportional to the cubes of the average distances from the sun.

https://galileoandeinstein.phys.virginia.edu/lectures/tycho.htm

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Michael Fowler, University of Virginia
These two colorful characters made crucial contributions to our understanding of the universe: Tycho's observations were accurate enough for Kepler to discover that the planets moved in elliptic orbits, and his other laws, which gave Newton the clues he needed to establish universal inverse-square gravitation.
What you should know:
Tycho Brahe (1546-1601), from a rich Danish noble family, was fascinated by astronomy, but disappointed with the accuracy of tables of planetary motion at the time. He decided to dedicate his life and considerable resources to recording planetary positions ten times more accurately than the best previous work. After some early successes, and in gratitude for having his life saved by Tycho's uncle, the king of Denmark gave Tycho tremendous resources: an island with many families on it, and money to build an observatory. (One estimate is that this was 10% of the gross national product at the time!) Tycho built vast instruments to set accurate sights on the stars, and used multiple clocks and timekeepers.

He achieved his goal of measuring to one minute of arc. This was a tremendous feat before the invention of the telescope. His aim was to confirm his own picture of the universe, which was that the Earth was at rest, the sun went around the Earth and the planets all went around the sun - an intermediate picture between Ptolemy and Copernicus.

Johannes Kepler (1571-1630) believed in Copernicus' picture. Having been raised in the Greek geometric tradition, he believed God must have had some geometric reason for placing the six planets at the particular distances from the sun that they occupied. He thought of their orbits as being on spheres, one inside the other. One day, he suddenly remembered that there were just five perfect Platonic solids, and this gave a reason for there being six planets - the orbit spheres were maybe just such that between two successive ones a perfect solid would just fit. He convinced himself that, given the uncertainties of observation at the time, this picture might be the right one. However, that was before Tycho's results were used. Kepler realized that Tycho's work could settle the question one way or the other, so he went to work with Tycho in 1600. Tycho died the next year, Kepler stole the data, and worked with it for nine years.

He reluctantly concluded that his geometric scheme was wrong. In its place, he found his three laws of planetary motion:

I The planets move in elliptical orbits with the sun at a focus.

II In their orbits around the sun, the planets sweep out equal areas in equal times .

III The squares of the times to complete one orbit are proportional to the cubes of the average distances from the sun .

These are the laws that Newton was able to use to establish universal gravitation.

Kepler was the first to state clearly that the way to understand the motion of the planets was in terms of some kind of force from the sun. However, in contrast to Galileo, Kepler thought that a continuous force was necessary to maintain motion, so he visualized the force from the sun like a rotating spoke pushing the planet around its orbit.

On the other hand, Kepler did get right that the tides were caused by the Moon's gravity. Galileo mocked him for this suggestion.

A much fuller treatment of Tycho Brahe and Johannes Kepler can be found in my 1995 notes:

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Michael Fowler, University of Virginia These two colorful characters made crucial contributions to our understanding of the universe: Tycho's observations were accurate enough for Kepler to discover that the planets moved in elliptic orbits, and his other laws, which gave Newton the clues he needed to establish universal inverse-square gravitation.

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Tycho Brahe made significant contributions by developing the most precise devices for studying the planets prior to the invention of the telescope. Brahe's devices enabled him to determine the detailed movements of the planets with more precision than had previously been achievable. Brahe, in particular, gathered substantial data on the planet Mars, which would later be vital to Kepler in his development of the laws of planetary motion.

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Johannes Kepler believed that planets orbit the sun. He developed 3 laws:
(1) the planets move in elliptical orbits with the Sun at one focus
(2) the time necessary to traverse any arc of a planetary orbit is proportional to the area of the sector between the central body and that arc (the “area law”)
(3) there is an exact relationship between the squares of the planets’ periodic times and the cubes of the radii of their orbits (the “harmonic law”).

https://www.britannica.com/biography/Johannes-Kepler

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What was Johannes Kepler's profession? When and how did it begin?

What was Johannes Kepler known for?

Who did Johannes Kepler influence?

Where was Johannes Kepler born?

How and where did Johannes Kepler die?

Johannes Kepler, (born December 27, 1571, Weil der Stadt, Württemberg [Germany]-died November 15, 1630, Regensburg), German astronomer who discovered three major laws of planetary motion, conventionally designated as follows: (1) the planets move in elliptical orbits with the Sun at one focus; (2) the time necessary to traverse any arc of a planetary orbit is proportional to the area of the sector between the central body and that arc (the "area law"); and (3) there is an exact relationship between the squares of the planets' periodic times and the cubes of their mean distances from the Sun (the "harmonic law"). Kepler himself did not call these discoveries "laws," as would become customary after Isaac Newton derived them from a new and quite different set of general physical principles. He regarded them as celestial harmonies that reflected God's design for the universe. Kepler's discoveries turned Nicolaus Copernicus's Sun-centred system into a dynamic universe, with the Sun actively pushing the planets around in noncircular orbits. And it was Kepler's notion of a physical astronomy that fixed a new problematic for other important 17th-century world-system builders, the most famous of whom was Newton.

Among Kepler's many other achievements, he provided a new and correct account of how vision occurs; he developed a novel explanation for the behaviour of light in the newly invented telescope; he discovered several new, semiregular polyhedrons; and he offered a new theoretical foundation for astrology while at the same time restricting the domain in which its predictions could be considered reliable. A list of his discoveries, however, fails to convey the fact that they constituted for Kepler part of a common edifice of knowledge. The matrix of theological, astrological, and physical ideas from which Kepler's scientific achievements emerged is unusual and fascinating in its own right. Yet, because of the highly original nature of Kepler's discoveries, it requires an act of intellectual empathy for moderns to understand how such lasting results could have evolved from such an apparently unlikely complex of ideas. Although Kepler's scientific work was centred first and foremost on astronomy, that subject as then understood-the study of the motions of the heavenly bodies-was classified as part of a wider subject of investigation called "the science of the stars." The science of the stars was regarded as a mixed science consisting of a mathematical and a physical component and bearing a kinship to other like disciplines, such as music (the study of ratios of tones) and optics (the study of light). It also was subdivided into theoretical and practical categories. Besides the theory of heavenly motions, one had the practical construction of planetary tables and instruments; similarly, the theoretical principles of astrology had a corresponding practical part that dealt with the making of annual astrological forecasts about individuals, cities, the human body, and the weather. Within this framework, Kepler made astronomy an integral part of natural philosophy, but he did so in an unprecedented way-in the process, making unique contributions to astronomy as well as to all its auxiliary disciplines.

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Johannes Kepler | Biography, Discoveries, & Facts

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Johannes Kepler, German astronomer who discovered three major laws of planetary motion. His discoveries turned Nicolaus Copernicus's Sun-centered system into a dynamic universe, with the Sun actively pushing the planets around in noncircular orbits. Learn more about Kepler's life and discoveries in this article.

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Newton deduced that if gravity could draw the apple off the tree, then gravity could also pull on objects that were much, much further away. Newton's theory contributed to the discovery that all things, from as tiny as an apple to as huge as a planet, are subject to gravity.

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Johannes Kepler presented three laws of planetary motion in the early 1600s. These three laws are the Law of  Ellipses, The Law of Equal Areas, and The Law of Harmonies.

https://www.physicsclassroom.com/class/circles/Lesson-4/Kepler-s-Three-Laws

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Aristotle believes that the Sun and the other planets revolve around the Earth.

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Aristotle presented an opposing view with Copernicus' heliocentric theory which is he geocentric theory stating that the Earth is in a fixed position and that the planets, Sun and other bodies orbit around the Earth.

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Tycho Brahe proposed a theory that the universe with the sun orbits the Earth, but other planets orbit the sun. Brahe's astronomical records were used by Kepler to prove his own theory heliocentrism and calculate orbital laws.

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He discovered the three major laws of planetary motion.
1.) The planets move in elliptical orbits with the sun at one focus
2.) The area law
3.) The harmonic law