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Who discovered Pluto and what was unique about its orbit?
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Clyde Tombaugh discovered Pluto based on Percival Lowell’s predictions; its orbit is highly eccentric, crossing Neptune’s orbit.
What was the role of Pythagorean influence in the historical development of mathematical astronomy?
Pythagorean influence highlighted the importance of mathematical understanding in explaining the universe, shaping early astronomical theories.
What is the mathematical relevance of conic sections in Newton's explanations of orbits?
Conic sections (ellipses, parabolas, hyperbolas) describe the paths of objects in gravitational fields, determined by their energy and eccentricity.
What type of orbit has an eccentricity exactly equal to 1?
Parabolic orbits.
What observation improvements have modern astronomy instruments made possible?
Modern instruments like reflecting telescopes with parabolic mirrors have increased the accuracy of astronomical observations.
How did Newton unify the understanding of planetary orbits?
Newton used his laws of gravity and motion to explain Kepler's laws through conic sections based on energy balance.
What mystery did explaining celestial structures through conic sections resolve?
Using conic sections to explain celestial structures resolved enduring mysteries about planetary motion and orbits.
What are the characteristics of hyperbolic orbits?
Hyperbolic orbits have positive total energy and eccentricity greater than 1.
What historical contributions did Tico Brahe make to astronomy?
Tico Brahe made significant observations using instruments like sextants and quadrants, providing data crucial for Kepler's laws.
What influences the shape of an orbit according to Newton's Laws?
The interplay between energy and eccentricity determines the orbit's shape.
Describe Kepler’s Law of Harmony.
The square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit.
How is Halley's Comet an example of periodic comets?
Halley’s Comet is observed on a predictable cycle, as it returns to the inner solar system approximately every 76 years.
What is the significance of Kepler's Law of Equal Areas?
It states that planets sweep out equal areas in equal times, describing the speed variation in a planet's orbit.
Explain the connection between potential and kinetic energy in the context of orbits.
During an orbit, potential and kinetic energy trade off, but the total energy remains constant.
How do elliptical orbits and circular orbits differ in terms of total energy and eccentricity?
Elliptical orbits have negative total energy and eccentricity less than 1, while circular orbits are a special case with zero eccentricity.
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