Kepler's Laws
1. Law of Ellipses- the law that states all planets orbit in the sun in a path called an ellipse. An ellipse is an oval whose shape is determined by two points within the figure. Each of these points is called a focus. The sun is at one focus of the orbit of a planet. The point where an orbit is closest to the sun is the perihelion. The point where an orbit is farthest from the sun is the aphelion.
*Example- the aphelion of the earth's orbit is about 152 million km from the sun. The perihelion is about 147 million km from the sun. The average of 147 million and 152 million is 149.5 million. This average distance between the earth and sun is known as one astronomical unit, or AU
2. Law of Equal Areas- the laws that describes the speed at which planets travel at different points in their orbit. By studying Brahe's data, Kepler found that the orbit of the earth was nearly a perfect circle. He found that the earth moves fastest when it is closest to the sun. He calculated that a line from the center of the sun to the center of the planet sweeps through equal areas and equal periods of time.
*Example- imagine a line connects the center of the sun to the center of a planet. When the planet is near the sun, the imaginary line is relatively short. The planet is moving rapidly and in ten days the imaginary line sweeps through a short, wide triangular sector or part. When the planet is farther from the sun, the imaginary line is longer. However, the planet is moving more slowly and the imaginary line sweeps through a long, thin triangular sector or part.
3. Law of Periods- the law that describes the relationship between the average distance of a planet from the sun and the orbit period (the time required for a planet to make one revolution around the sun) of the planet. According to Kepler's third law, the cube of the average distance of a planet from the sun ( r ) is always proportional to the square of the period ( p ). The mathematical formula that describes this relationship is K x r3 = p2, where K is the mathematical constant. When the distance is measured in AU's and the period is in earth-years, K = 1 and r3 = p2.
*Example- the radius of the earth's orbit, or its distance from the sun, is 1 AU, and its period is 1 year. Putting these numbers into the formula makes 1 x 13 = 12. This simplifies to 1 = 1. Jupiter is 5.2 AU's from the sun, and its period is 11.9 years. The cube of 5.2 is 140.6. The square of 11.9 is 141.6. The two results, 140.6 and 141.6, are approximately equal.
*Example- the aphelion of the earth's orbit is about 152 million km from the sun. The perihelion is about 147 million km from the sun. The average of 147 million and 152 million is 149.5 million. This average distance between the earth and sun is known as one astronomical unit, or AU
2. Law of Equal Areas- the laws that describes the speed at which planets travel at different points in their orbit. By studying Brahe's data, Kepler found that the orbit of the earth was nearly a perfect circle. He found that the earth moves fastest when it is closest to the sun. He calculated that a line from the center of the sun to the center of the planet sweeps through equal areas and equal periods of time.
*Example- imagine a line connects the center of the sun to the center of a planet. When the planet is near the sun, the imaginary line is relatively short. The planet is moving rapidly and in ten days the imaginary line sweeps through a short, wide triangular sector or part. When the planet is farther from the sun, the imaginary line is longer. However, the planet is moving more slowly and the imaginary line sweeps through a long, thin triangular sector or part.
3. Law of Periods- the law that describes the relationship between the average distance of a planet from the sun and the orbit period (the time required for a planet to make one revolution around the sun) of the planet. According to Kepler's third law, the cube of the average distance of a planet from the sun ( r ) is always proportional to the square of the period ( p ). The mathematical formula that describes this relationship is K x r3 = p2, where K is the mathematical constant. When the distance is measured in AU's and the period is in earth-years, K = 1 and r3 = p2.
*Example- the radius of the earth's orbit, or its distance from the sun, is 1 AU, and its period is 1 year. Putting these numbers into the formula makes 1 x 13 = 12. This simplifies to 1 = 1. Jupiter is 5.2 AU's from the sun, and its period is 11.9 years. The cube of 5.2 is 140.6. The square of 11.9 is 141.6. The two results, 140.6 and 141.6, are approximately equal.