Law #3: The period (in Earth years) of a planet squared is equal to the semi-major...

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Law #3: The period (in Earth years) of a planet squared is equal to the semi-major axis (in Astronomical Units or AU) of the planet's orbit cubed. Let's look at an example. The Earth takes one year to complete its orbit and 10 AU the semi-major axis of its orbit is 1 AU. squared is 1 x 1 = 1 and a cubed is 1 x 1x1 = 1. The third law works for these values. 8 AU Astronomers can determine the period of a planet or any other celestial object in orbit around the Sun by observing it carefully. Kepler's third law allows them to compute the semi-major axis from the periods they observe. Nothing else is needed. The third law established the scale of the solar system before astronomers had an independent way of determining the true 16 AU dimensions of the orbits of the planets. (P) = 12 AU+ = a (AU) For the planets and asteroid in the table below, compute the semi-major axes 18 AUT using Kepler's third law. You will need to find the cube root of the period squared. Then plot and label the objects on the figure at right. This will illustrate their approximate relative distances from the Sun. 3 spread P (yr) p2 Select Object sp Mercury 0.24 Venus 0.62 Earth 1.0 Mars 1.88 Asteroid Ceres 4.6 Jupiter 11.86 Saturn 29.5 Uranus 84 Neptune 165 Did you know that you can use Google to find the cube root of a number? In the search box, type cube root(number). Then press the Enter key. For example, to find the cube root of 64, you would type cube root(64). 14 AU 20 AU 22 AU+ 24 AU 26 AL 28 A 30 Law #3: The period (in Earth years) of a planet squared is equal to the semi-major axis (in Astronomical Units or AU) of the planet's orbit cubed. Let's look at an example. The Earth takes one year to complete its orbit and 10 AU the semi-major axis of its orbit is 1 AU. squared is 1 x 1 = 1 and a cubed is 1 x 1x1 = 1. The third law works for these values. 8 AU Astronomers can determine the period of a planet or any other celestial object in orbit around the Sun by observing it carefully. Kepler's third law allows them to compute the semi-major axis from the periods they observe. Nothing else is needed. The third law established the scale of the solar system before astronomers had an independent way of determining the true 16 AU dimensions of the orbits of the planets. (P) = 12 AU+ = a (AU) For the planets and asteroid in the table below, compute the semi-major axes 18 AUT using Kepler's third law. You will need to find the cube root of the period squared. Then plot and label the objects on the figure at right. This will illustrate their approximate relative distances from the Sun. 3 spread P (yr) p2 Select Object sp Mercury 0.24 Venus 0.62 Earth 1.0 Mars 1.88 Asteroid Ceres 4.6 Jupiter 11.86 Saturn 29.5 Uranus 84 Neptune 165 Did you know that you can use Google to find the cube root of a number? In the search box, type cube root(number). Then press the Enter key. For example, to find the cube root of 64, you would type cube root(64). 14 AU 20 AU 22 AU+ 24 AU 26 AL 28 A 30

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