Identify the common names given to Kepler's three laws of planetary motion. List the three letters ...

Kepler's Three Laws:

Johannes Kepler proposed three laws of planetary motion in the early 1600s. The three laws are:

• The Law of Ellipses: The path of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus.
• The Law of Equal Areas: An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time.
• The Law of Harmonies: The ratio of the square of the periods of any two planets is equal to the ratio of the cube of their average distances from the sun.

What are the common names given to each of Kepler's three laws of planetary motion?

Which one of the following statements would NOT be consistent with Kepler's three laws of planetary motion?

Kepler's Three Laws:

Johannes Kepler proposed three laws of planetary motion in the early 1600s. The three laws are:

• The Law of Ellipses: The path of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus.
• The Law of Equal Areas: An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time.
• The Law of Harmonies: The ratio of the square of the periods of any two planets is equal to the ratio of the cube of their average distances from the sun.

Kepler's Law of Equal Areas:

Kepler's law of equal areas proposed that if an imaginary line connected a planet and the sun, then the line would move as the planet moved along its elliptical path. As the imaginary line moved, it would sweep out an area. The line would sweep out equal areas in equal amounts of time. Since the planet's orbit is elliptical, it is not always the same distance from the sun at all times during its orbit. For the area to be the same amount during all time periods, the planet must move faster along its orbital path when it is closest to the sun.

The Law of Harmonies:

Kepler's law of harmonies proposed that the ratio of the square of the periods of any two planets is equal to the ratio of the cube of their average distances from the sun. This magical T²/R³ ratio shows very little variation from planet to planet. An extension of this law would be that the period of orbit must be greater for any planet which is a greater distance from the sun. More distant planets require greater periods of time to orbit than closer planets.

What are the common names given to each of Kepler's three laws of planetary motion?

What is the meaning of Kepler's second law?

What is the meaning of Kepler's third law?

Kepler's second law of planetary motion is the law of equal areas. Which one of the following statements would be an extension of this law?

Kepler's Law of Equal Areas:

Kepler's law of equal areas proposed that if an imaginary line connected a planet and the sun, then the line would move as the planet moved along its elliptical path. As the imaginary line moved, it would sweep out an area. The line would sweep out equal areas in equal amounts of time. Since the planet's orbit is elliptical, it is not always the same distance from the sun at all times during its orbit. For the area to be the same amount during all time periods, the planet must move faster along its orbital path when it is closest to the sun.

What is the meaning of Kepler's second law?

Kepler's second law of planetary motion states that a line connecting a planet to the Sun ____. Choose one.

Kepler's Law of Equal Areas:

Kepler's law of equal areas proposed that if an imaginary line connected a planet and the sun, then the line would move as the planet moved along its elliptical path. As the imaginary line moved, it would sweep out an area. The line would sweep out equal areas in equal amounts of time. Since the planet's orbit is elliptical, it is not always the same distance from the sun at all times during its orbit. For the area to be the same amount during all time periods, the planet must move faster along its orbital path when it is closest to the sun.

What is the meaning of Kepler's second law?

Kepler's third law of planetary motion states that the ratio of ____.

The Law of Harmonies:

Kepler's law of harmonies proposed that the ratio of the square of the periods of any two planets is equal to the ratio of the cube of their average distances from the sun. This magical T²/R³ ratio shows very little variation from planet to planet. An extension of this law would be that the period of orbit must be greater for any planet which is a greater distance from the sun. More distant planets require greater periods of time to orbit than closer planets.

What is the meaning of Kepler's third law?

Two planets - planet A and planet B - are orbiting a star. If Planet A has an orbital radius which is two times (or three times) as large as Planet B, then the period of Planet A's orbit is ____ times larger than the period of Planet B's orbit.

The Law of Harmonies:

Kepler's law of harmonies proposed that the ratio of the square of the periods of any two planets is equal to the ratio of the cube of their average distances from the sun. This magical T²/R³ ratio shows very little variation from planet to planet. An extension of this law would be that the period of orbit must be greater for any planet which is a greater distance from the sun. More distant planets require greater periods of time to orbit than closer planets.

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Applying Kepler's law of harmonies to this situation would result in:

This equation can be algebraically rearranged to

The ratio of the period squared of planet A to planet B will be equal to the ratio of the radius cubed of planet A to planet B. The ratio of the radii of the two planets is given - planet A's radius is two (or three) times larger than planet B's radius. The cube of this ratio is equal to the square of the ratio of the period. Taking the square root of the period squared ratio will yield the ratio of the periods of the planets. Mathematically, this could be written as

How can Kepler's third law be applied to analyze the period-radius ratios of two planets around the Sun?

Two planets - planet A and planet B - are orbiting a star. If Planet A has an orbital radius which is four times (or five times) as large as Planet B, then the period of Planet A's orbit is ____ times larger than the period of Planet B's orbit.

The Law of Harmonies:

Kepler's law of harmonies proposed that the ratio of the square of the periods of any two planets is equal to the ratio of the cube of their average distances from the sun. This magical T²/R³ ratio shows very little variation from planet to planet. An extension of this law would be that the period of orbit must be greater for any planet which is a greater distance from the sun. More distant planets require greater periods of time to orbit than closer planets.

Click the button below to play an audio file in a separate window.

Applying Kepler's law of harmonies to this situation would result in:

This equation can be algebraically rearranged to

The ratio of the period squared of planet A to planet B will be equal to the ratio of the radius cubed of planet A to planet B. The ratio of the radii of the two planets is given - planet A's radius is four (or five) times larger than planet B's radius. The cube of this ratio is equal to the square of the ratio of the period. Taking the square root of the period squared ratio will yield the ratio of the periods of the planets. Mathematically, this could be written as

How can Kepler's third law be applied to analyze the period-radius ratios of two planets around the Sun?