### All The Following Statements Are True. Which One Follows Directly From Kepler’S Third Law?

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• 28 ## Which one follows directly from Kepler’s third law quizlet?

Which one follows directly from Kepler’s third law (p2 = a3)? Venus orbits the Sun at a slower average speed than Mercury.

### Which of the following statements is not true about Kepler’s laws?

Kepler’s first law of planetary motion states that the Sun is at one of the foci of the elliptical orbit. For the ellipse, the center is not generally the same as the foci. Thus the statement ‘Kepler’s first law of planetary motion states that the Sun is at the center of a planet’s elliptical orbit.’ is False.

## Which proportionality does Kepler’s third law describe quizlet?

Kepler’s third law (the law of periods) states that the square of the period of any planet is proportional to the cube of the average radius of its orbit.

### Which one of the following is the correct statement of Kepler’s third law *?

Transcript – The planets orbit the Sun in a counterclockwise direction as viewed from above the Sun’s north pole, and the planets’ orbits all are aligned to what astronomers call the ecliptic plane. The story of our greater understanding of planetary motion could not be told if it were not for the work of a German mathematician named Johannes Kepler.

• Epler lived in Graz, Austria during the tumultuous early 17th century.
• Due to religious and political difficulties common during that era, Kepler was banished from Graz on August 2nd, 1600.
• Fortunately, an opportunity to work as an assistant for the famous astronomer Tycho Brahe presented itself and the young Kepler moved his family from Graz 300 miles across the Danube River to Brahe’s home in Prague.
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Tycho Brahe is credited with the most accurate astronomical observations of his time and was impressed with the studies of Kepler during an earlier meeting. However, Brahe mistrusted Kepler, fearing that his bright young intern might eclipse him as the premier astronomer of his day.

• He, therefore, led Kepler to see only part of his voluminous planetary data.
• He set Kepler, the task of understanding the orbit of the planet Mars, the movement of which fit problematically into the universe as described by Aristotle and Ptolemy.
• It is believed that part of the motivation for giving the Mars problem to Kepler was Brahe’s hope that its difficulty would occupy Kepler while Brahe worked to perfect his own theory of the solar system, which was based on a geocentric model, where the earth is the center of the solar system.

Based on this model, the planets Mercury, Venus, Mars, Jupiter, and Saturn all orbit the Sun, which in turn orbits the earth. As it turned out, Kepler, unlike Brahe, believed firmly in the Copernican model of the solar system known as heliocentric, which correctly placed the Sun at its center.

1. But the reason Mars’ orbit was problematic was because the Copernican system incorrectly assumed the orbits of the planets to be circular.
2. After much struggling, Kepler was forced to an eventual realization that the orbits of the planets are not circles, but were instead the elongated or flattened circles that geometers call ellipses, and the particular difficulties Brahe hand with the movement of Mars were due to the fact that its orbit was the most elliptical of the planets for which Brahe had extensive data.

Thus, in a twist of irony, Brahe unwittingly gave Kepler the very part of his data that would enable Kepler to formulate the correct theory of the solar system, banishing Brahe’s own theory. Since the orbits of the planets are ellipses, let us review three basic properties of ellipses.

The first property of an ellipse: an ellipse is defined by two points, each called a focus, and together called foci. The sum of the distances to the foci from any point on the ellipse is always a constant. The second property of an ellipse: the amount of flattening of the ellipse is called the eccentricity.

The flatter the ellipse, the more eccentric it is. Each ellipse has an eccentricity with a value between zero, a circle, and one, essentially a flat line, technically called a parabola. The third property of an ellipse: the longest axis of the ellipse is called the major axis, while the shortest axis is called the minor axis.

• Half of the major axis is termed a semi-major axis.
• Nowing then that the orbits of the planets are elliptical, johannes Kepler formulated three laws of planetary motion, which accurately described the motion of comets as well.
• Epler’s First Law: each planet’s orbit about the Sun is an ellipse.
• The Sun’s center is always located at one focus of the orbital ellipse.

The Sun is at one focus. The planet follows the ellipse in its orbit, meaning that the planet to Sun distance is constantly changing as the planet goes around its orbit. Kepler’s Second Law: the imaginary line joining a planet and the Sun sweeps equal areas of space during equal time intervals as the planet orbits.

Basically, that planets do not move with constant speed along their orbits. Rather, their speed varies so that the line joining the centers of the Sun and the planet sweeps out equal parts of an area in equal times. The point of nearest approach of the planet to the Sun is termed perihelion. The point of greatest separation is aphelion, hence by Kepler’s Second Law, a planet is moving fastest when it is at perihelion and slowest at aphelion.

Kepler’s Third Law: the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler’s Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.

• Thus we find that Mercury, the innermost planet, takes only 88 days to orbit the Sun.
• The earth takes 365 days, while Saturn requires 10,759 days to do the same.
• Though Kepler hadn’t known about gravitation when he came up with his three laws, they were instrumental in Isaac Newton deriving his theory of universal gravitation, which explains the unknown force behind Kepler’s Third Law.

Kepler and his theories were crucial in the better understanding of our solar system dynamics and as a springboard to newer theories that more accurately approximate our planetary orbits.

## What is true about Kepler’s third law?

A harmonic third law – “The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.” That’s Kepler’s Third Law in a nutshell, and it arises from the third physical property of ellipses, related to its various axis points.

1. The longest axis of the ellipse is called the major axis, while the shortest axis is called the minor axis.
2. Half of the major axis is termed a semi-major axis.
3. The equation for Kepler’s Third Law is P² = a³, so the period of a planet’s orbit (P) squared is equal to the size semi-major axis of the orbit (a) cubed when it is expressed in astronomical units.

What Kepler’s Third Law actually does, is compare the orbital period and radius of orbit of a planet to those of other planets. Thus, unlike Kepler’s first and second laws that describe the motion characteristics of a single planet, the astronomer’s third law compares the motion of different planets and calculates the harmonies of the planets.

This comparison takes the form of the ratio of the squares of the periods (T²) to the cubes of their average distances from the sun (R³), finding it to be the same for every one of the planets. Thanks to this law, if we know a planet’s distance from its star, we can calculate the period of its orbit and vice versa.

Because the distance between Earth and the sun (1 AU) is around 92,960,000 miles (149,600,000 kilometres) and one Earth year is 365 days, the distance and orbital period of other planets can be calculated when only one variable is known. For the solar system, that gives us an accurate picture of every planet’s orbit around the sun.

As a planet’s distances from the sun increase, the time they take to orbit the sun increases rapidly. For example, Mercury – the closest planet to the sun-completes an orbit every 88 days. The third planet from the sun, Earth, takes roughly 365 days to orbit the sun. And Saturn, the solar system’s sixth planet out from its star, takes 10,759.

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Of course, The Harmonic Law doesn’t just tell us about the orbits of planets.

### Which of the following is true about Kepler’s law of planetary motion?

The statements corresponds to Kepler’s laws of planetary motion is : A planet moves around the sun in an elliptical orbit with the sun at the focus. This is called as the Law of Ellipses.

## Which of the following are correct about Kepler’s law?

Which of the following are correct about Kepler’s law? The path of the planets around the sun is elliptical, with the sun being located at one of the two foci. Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses The line joining the planet and the sun sweeps equal areas in equal intervals of time.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses The cube of the average distance of a planet from the sun is directly proportional to the square of the planet’s orbital time period. Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses The path of the planets around the sun is circular, with the sun being located at its centre.

No worries! We‘ve got your back. Try BYJU‘S free classes today! Open in App Suggest Corrections 0 : Which of the following are correct about Kepler’s law?

### Which of the following do not obey Kepler’s law?

Comets do not revolve around the sun in fixed elliptical orbit like other planets and don’t obey Kepler’s law for planetary motion.

## Which concept was not a part of Kepler’s laws of planetary motion quizlet?

Which concept was NOT a part of Kepler’s Laws of Planetary Motion? Epicycles are needed to explain the varying brightness of the planets.

## Which of the following is not one of the inner planets of the solar system?

Detailed Solution. Saturn is an outer planet. The inner planets are closer to the Sun and are smaller and rockier.

## Which of the following suggested that the Earth orbits the Sun and is not the center of the universe?

The Heliocentric System – In a book called On the Revolutions of the Heavenly Bodies (that was published as Copernicus lay on his deathbed), Copernicus proposed that the Sun, not the Earth, was the center of the Solar System. Such a model is called a heliocentric system,

 The Copernican Universe

In this new ordering the Earth is just another planet (the third outward from the Sun), and the Moon is in orbit around the Earth, not the Sun. The stars are distant objects that do not revolve around the Sun. Instead, the Earth is assumed to rotate once in 24 hours, causing the stars to appear to revolve around the Earth in the opposite direction.

#### What does Kepler’s 3rd Law prove?

Kepler’s Third Law – Kepler’s third law states: Definition The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The third law, published by Kepler in 1619, captures the relationship between the distance of planets from the Sun, and their orbital periods. Kepler’s Third Law : Kepler’s third law states that the square of the period of the orbit of a planet about the Sun is proportional to the cube of the semi-major axis of the orbit. The constant of proportionality is \ for a sidereal year (yr), and astronomical unit (AU).

#### What are Kepler’s 3 laws of planetary motion quizlet?

Terms in this set (3) The planets orbits in an elliptical shape. The sun is at one focus. The second focus is not needed because of sun’s mass & gravity. A planet spends equal amount of time perihelion & aphelion.

## Which of the following best describes the third law of motion?

A force is a push or a pull that acts upon an object as a results of its interaction with another object. Forces result from interactions! As discussed in Lesson 2, some forces result from contact interactions (normal, frictional, tensional, and applied forces are examples of contact forces) and other forces are the result of action-at-a-distance interactions (gravitational, electrical, and magnetic forces).

• According to Newton, whenever objects A and B interact with each other, they exert forces upon each other.
• When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.
• There are two forces resulting from this interaction – a force on the chair and a force on your body.

These two forces are called action and reaction forces and are the subject of Newton’s third law of motion. Formally stated, Newton’s third law is: For every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs – equal and opposite action-reaction force pairs.

## What are Kepler’s 3 laws of planetary motion called?

There are actually three, Kepler’s laws that is, of planetary motion: 1) every planet’s orbit is an ellipse with the Sun at a focus; 2) a line joining the Sun and a planet sweeps out equal areas in equal times; and 3) the square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit.

Tycho Brahe’s decades-long, meticulous observations of the stars and planets provided Kepler with what today we’d call a robust, well-controlled dataset to test his hypotheses concerning planetary motion (this way of describing it is, dear reader, a deliberate anachronism).

In particular, Tycho’s observations of the position of Mars in the Uraniborg night sky were the primary source of hard data Kepler used to derive, and test, his three laws. Kepler’s laws have an important place in the history of astronomy, cosmology, and science in general. They marked a key step in the revolution which moved the center of the universe from the Earth (geocentric cosmology) to the Sun (heliocentric), and they laid the foundation for the unification of heaven and earth, by Newton, a century later (before Newton the rules, or laws, which governed celestial phenomena were widely believed to be disconnected with those controlling things which happened on Earth; Newton showed – with his universal law of gravitation – that the same law rules both heaven and earth).

Although Kepler’s laws are only an approximation – they are exact, in classical physics, only for a planetary system of just one planet (and then the focus is the baricenter, not the Sun) – for systems in which one object dominates, mass-wise, they are a good approximation.

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## Which of the following statements best describes Kepler’s third law of planetary motion quizlet?

Planets move faster when they are close to the sun than when they are far away. Which of the following best summarizes Kepler’s third law? The time it takes for a planet to complete one orbit around the sun is related to the distance of that planet from the sun.

## Which statement describes Kepler’s third law of orbital motion quizlet?

Kepler’s third law states that for any planet orbiting the Sun, the orbital period squared (p2 ) is equal to the average orbital distance cubed (a3), or p2=a3.

#### What are Kepler’s 3 laws of planetary motion quizlet?

Terms in this set (3) The planets orbits in an elliptical shape. The sun is at one focus. The second focus is not needed because of sun’s mass & gravity. A planet spends equal amount of time perihelion & aphelion.

#### What does Kepler’s 3rd Law prove?

Kepler’s Third Law – Kepler’s third law states: Definition The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The third law, published by Kepler in 1619, captures the relationship between the distance of planets from the Sun, and their orbital periods. Kepler’s Third Law : Kepler’s third law states that the square of the period of the orbit of a planet about the Sun is proportional to the cube of the semi-major axis of the orbit. The constant of proportionality is \ for a sidereal year (yr), and astronomical unit (AU).

## What does Kepler’s third law depend on?

Just what is that constant, really? – It turns out that the constant in Kepler’s Third Law depends on the total mass of the two bodies involved. Kepler himself, studying the motion of the planets around the Sun, always dealt with the 2-body system of Sun-plus-planet.

The Sun is so much more massive than any of the planets in the Solar System that the mass of Sun-plus-planet is almost the same as the mass of the Sun by itself. Thus, the constant in Kepler’s application of his Third Law was, for practical purposes, always the same. But in the case of the Moon’s orbit around the Earth, the total mass of the two bodies is much, much smaller than the mass of Sun-plus-planet; that means that the value of the constant of proportionality in Kepler’s Third Law will also be different.

On the other hand, if we compared the period and semimajor axis of the orbit of the Moon around the Earth to the orbit of a communications satellite around the Earth, we would once again have (almost) the same total mass in each case; and thus we would end up with the same relationship between period-squared and semimajor-axis-cubed. or The constant k in the equations above is known as the Gaussian gravitational constant, If we set up a system of units with

period P in days semimajor axis a in AU mass Mtot in solar masses

then we can determine k very precisely and very simply: just count the days in a year! Then we can simply turn Kepler’s Third Law around to solve for the value of k : Exercise: What is the value of the Gaussian gravitational constant k ? The key point here is that the only measured quantity we need to find k is time: the period of the Earth’s orbit around the Sun. Now, it’s not quite so easy as it sounds, but it can be done without too much trouble.

Moreover, because we can average over many, many, many years, we can determine the length of the year very accurately – to many significant figures. Therefore, we can also determine the value of k to many significant figures. If all we want to do is calculate the orbits of objects around the Sun, then k is all we need; and with a very accurate value of k, we can calculate very accurate planetary orbits.

For example, it was this constant k that Adams and Leverrier used in their computations of the as-yet-unknown planet VIII, aka Neptune. At this point, you may be thinking, “Hey, wait a minute – isn’t that constant k just another way of writing the Newtonian Constant of Universal Gravitation, G?” Well, the answer is yes, and no:

Yes, the two constants are closely related No, they don’t stand for EXACTLY the same thing

The Gaussian constant, k, is defined in terms of the Earth’s orbit around the Sun. The Newtonian constant, G, is defined in terms of the force between two two masses separated by some fixed distance. In order to measure k, all you need to do is count days; in order to measure G, you need to know very precisely the masses, separation, and forces between test objects in a laboratory.

### What is Kepler’s 3rd motion?

There are actually three, Kepler’s laws that is, of planetary motion: 1) every planet’s orbit is an ellipse with the Sun at a focus; 2) a line joining the Sun and a planet sweeps out equal areas in equal times; and 3) the square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit.

Tycho Brahe’s decades-long, meticulous observations of the stars and planets provided Kepler with what today we’d call a robust, well-controlled dataset to test his hypotheses concerning planetary motion (this way of describing it is, dear reader, a deliberate anachronism).

• In particular, Tycho’s observations of the position of Mars in the Uraniborg night sky were the primary source of hard data Kepler used to derive, and test, his three laws.
• Epler’s laws have an important place in the history of astronomy, cosmology, and science in general.
• They marked a key step in the revolution which moved the center of the universe from the Earth (geocentric cosmology) to the Sun (heliocentric), and they laid the foundation for the unification of heaven and earth, by Newton, a century later (before Newton the rules, or laws, which governed celestial phenomena were widely believed to be disconnected with those controlling things which happened on Earth; Newton showed – with his universal law of gravitation – that the same law rules both heaven and earth).

Although Kepler’s laws are only an approximation – they are exact, in classical physics, only for a planetary system of just one planet (and then the focus is the baricenter, not the Sun) – for systems in which one object dominates, mass-wise, they are a good approximation.