State Kepler’s three laws in your own words.

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Answer 1

Textbook Question

Chapter 3, Problem 1E

State Kepler’s three laws in your own words.

Expert Solution & Answer

To determine

The Kepler’s three laws.

Explanation of Solution

Introduction:

Copernicus gave the heliocentric model which described the sun to be the center of the solar system where planets, moons and other objects revolve around it in circular orbits. Later, Kepler used the data of Tycho Brahe and wrote three laws describing the planetary motion.

Kepler’s first law states that planets revolve about the sun in elliptical paths instead of circular paths. The sun lies at one of the foci of this elliptical path.

Kepler’s second law states that the line joining the planet and the sun sweeps equal areas in equal interval of time.

Kepler’s third law states that the square of period of orbit is directly proportional to the cube of the semi-major axis.

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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).

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simple diagram to illustrate the setup for each law- coulombs law and biot savart law

Answer 2

Textbook Question

Chapter 3, Problem 1E

State Kepler’s three laws in your own words.

Expert Solution & Answer

To determine

The Kepler’s three laws.

Explanation of Solution

Introduction:

Copernicus gave the heliocentric model which described the sun to be the center of the solar system where planets, moons and other objects revolve around it in circular orbits. Later, Kepler used the data of Tycho Brahe and wrote three laws describing the planetary motion.

Kepler’s first law states that planets revolve about the sun in elliptical paths instead of circular paths. The sun lies at one of the foci of this elliptical path.

Kepler’s second law states that the line joining the planet and the sun sweeps equal areas in equal interval of time.

Kepler’s third law states that the square of period of orbit is directly proportional to the cube of the semi-major axis.

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Answer 3

Textbook Question

Chapter 3, Problem 1E

State Kepler’s three laws in your own words.

Expert Solution & Answer

To determine

The Kepler’s three laws.

Explanation of Solution

Introduction:

Copernicus gave the heliocentric model which described the sun to be the center of the solar system where planets, moons and other objects revolve around it in circular orbits. Later, Kepler used the data of Tycho Brahe and wrote three laws describing the planetary motion.

Kepler’s first law states that planets revolve about the sun in elliptical paths instead of circular paths. The sun lies at one of the foci of this elliptical path.

Kepler’s second law states that the line joining the planet and the sun sweeps equal areas in equal interval of time.

Kepler’s third law states that the square of period of orbit is directly proportional to the cube of the semi-major axis.

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Answer 4

Textbook Question

Chapter 3, Problem 1E

State Kepler’s three laws in your own words.

Expert Solution & Answer

To determine

The Kepler’s three laws.

Explanation of Solution

Introduction:

Copernicus gave the heliocentric model which described the sun to be the center of the solar system where planets, moons and other objects revolve around it in circular orbits. Later, Kepler used the data of Tycho Brahe and wrote three laws describing the planetary motion.

Kepler’s first law states that planets revolve about the sun in elliptical paths instead of circular paths. The sun lies at one of the foci of this elliptical path.

Kepler’s second law states that the line joining the planet and the sun sweeps equal areas in equal interval of time.

Kepler’s third law states that the square of period of orbit is directly proportional to the cube of the semi-major axis.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

The Kepler’s three laws.

Explanation of Solution

Introduction:

Copernicus gave the heliocentric model which described the sun to be the center of the solar system where planets, moons and other objects revolve around it in circular orbits. Later, Kepler used the data of Tycho Brahe and wrote three laws describing the planetary motion.

Kepler’s first law states that planets revolve about the sun in elliptical paths instead of circular paths. The sun lies at one of the foci of this elliptical path.

Kepler’s second law states that the line joining the planet and the sun sweeps equal areas in equal interval of time.

Kepler’s third law states that the square of period of orbit is directly proportional to the cube of the semi-major axis.

Answer 8

Expert Solution & Answer

To determine

The Kepler’s three laws.

Explanation of Solution

Introduction:

Copernicus gave the heliocentric model which described the sun to be the center of the solar system where planets, moons and other objects revolve around it in circular orbits. Later, Kepler used the data of Tycho Brahe and wrote three laws describing the planetary motion.

Kepler’s first law states that planets revolve about the sun in elliptical paths instead of circular paths. The sun lies at one of the foci of this elliptical path.

Kepler’s second law states that the line joining the planet and the sun sweeps equal areas in equal interval of time.

Kepler’s third law states that the square of period of orbit is directly proportional to the cube of the semi-major axis.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

The Kepler’s three laws.

Answer 12

Explanation of Solution

Introduction:

Copernicus gave the heliocentric model which described the sun to be the center of the solar system where planets, moons and other objects revolve around it in circular orbits. Later, Kepler used the data of Tycho Brahe and wrote three laws describing the planetary motion.

Kepler’s first law states that planets revolve about the sun in elliptical paths instead of circular paths. The sun lies at one of the foci of this elliptical path.

Kepler’s second law states that the line joining the planet and the sun sweeps equal areas in equal interval of time.

Kepler’s third law states that the square of period of orbit is directly proportional to the cube of the semi-major axis.