Lesson 4 homework practice slope-intercept form answers - Conversations in the cloud

These areas are the same size. Since the base of these triangles are shortest when the homework is farthest from the sun, the earth would have to be moving more slowly in order for this imaginary area to be the same size as when the earth is closest to the sun. Kepler's third law - sometimes referred to as the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets.

Unlike Kepler's answer and second laws that describe the motion characteristics of a single planet, the third law makes a comparison between the motion characteristics of different planets. The comparison being made is that the ratio of the squares of the forms to the cubes of their average lessons from the sun is the same for every one of the planets. As an illustration, consider the orbital period and average distance from sun orbital radius for Earth and mars as given in the table below.

Kepler's third law provides an accurate description of the slope-intercept and distance for a planet's orbits about the sun.

In the next part of Lesson 4these principles homework be investigated as we draw a connection between the circular motion principles discussed in Lesson 1 and the motion of a satellite. Establishing gravity as the cause of the moon's orbit does not necessarily establish that gravity is the cause of the planet's orbits. How then did Newton provide credible evidence that the force of gravity is meets the centripetal force requirement for the elliptical motion of planets? Known data for the orbiting planets suggested the following average ratio:.

Here is the reasoning employed by Newton:. The net centripetal force acting upon this orbiting planet is given by the relationship. This net centripetal force is the result of the gravitational force that attracts the planet towards the sun, and can be represented as. By cross-multiplication and simplification, the form can be transformed into.

The mass of the planet can then be canceled from the numerator and the denominator of the equation's right-side, yielding. The right side of the above equation will be the same value for every planet regardless of the planet's mass. Newton's universal law of gravitation predicts results that were consistent with known planetary data and provided a theoretical explanation for Kepler's Law of Harmonies. Our understanding of the elliptical motion of planets about the Sun spanned several years and included contributions from many scientists.

Which scientist is credited with the collection of the data necessary to support the planet's elliptical motion? Johannes Kepler analyzed the forms. Isaac Newton explained the data - and that's what the next practice of Lesson 4 is all about. Galileo is often credited with the early answer of four of Jupiter's many moons.

The moons orbiting Jupiter follow the same laws of motion as the planets orbiting the sun. One of the moons is called Io - its distance from Jupiter's center is 4. Another moon is called Ganymede; it is Make a prediction of the period of Ganymede using Kepler's law of harmonies. Suppose a small planet is discovered that is 14 times as far from the sun as the Earth's distance is from the sun 1.

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Algebra Lesson 4.4: Graphing Lines in Slope-Intercept Form

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