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Questions and Answers
What does Kepler's Third Law express in terms of celestial bodies?
What does Kepler's Third Law express in terms of celestial bodies?
- The relationship between mass and distance
- The relationship between orbital period and average orbital distance (correct)
- The gravitational force between two bodies
- The speed of celestial bodies in orbit
Which equation represents Newton's version of Kepler's Third Law?
Which equation represents Newton's version of Kepler's Third Law?
- p² = 4π²a³/G(M1 + M2) (correct)
- M1 + M2 = Gp²/a³
- p² = a³/(M1 + M2)
- p = G(M1 + M2)/a
What determines the strength of gravitational force?
What determines the strength of gravitational force?
- The product of the masses divided by their distance
- The product of the masses times the square of the distance
- The product of the masses divided by the square of the distance (correct)
- The sum of the masses divided by the square of the distance
What is the significance of Newton's law of gravity in relation to Kepler's laws?
What is the significance of Newton's law of gravity in relation to Kepler's laws?
How does Newton's first law of motion describe the behavior of an object?
How does Newton's first law of motion describe the behavior of an object?
Which of the following expressions is a valid formulation of Newton's second law of motion?
Which of the following expressions is a valid formulation of Newton's second law of motion?
What did Newton's discoveries reveal about the universe?
What did Newton's discoveries reveal about the universe?
What can be deduced from the orbital period and average distance of an object?
What can be deduced from the orbital period and average distance of an object?
Which of the following statements about gravitational attraction is true?
Which of the following statements about gravitational attraction is true?
How did Newton's law of gravity enhance the understanding of Kepler's laws?
How did Newton's law of gravity enhance the understanding of Kepler's laws?
What principle is used to determine the distance of two stars from their center of mass?
What principle is used to determine the distance of two stars from their center of mass?
Which aspect of Newton's discoveries significantly influenced our understanding of the universe?
Which aspect of Newton's discoveries significantly influenced our understanding of the universe?
Which type of orbit is classified as unbound?
Which type of orbit is classified as unbound?
What is the relationship between two orbiting masses and their center of mass?
What is the relationship between two orbiting masses and their center of mass?
What is a key characteristic of elliptical orbits differentiated by their eccentricities?
What is a key characteristic of elliptical orbits differentiated by their eccentricities?
What remains constant in the motion of orbiting objects due to angular momentum conservation?
What remains constant in the motion of orbiting objects due to angular momentum conservation?
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Study Notes
Newton's Version of Kepler’s Third Law
- Equation: p^2 = (4π^2 / G(M1+M2)) * a^3
- p = orbital period
- a = average orbital distance between objects
- (M1+M2) = sum of object masses
Newton and Kepler’s Third Law
- Applies Newton's laws of gravity and motion
- Shows the relationship between orbital period (p) and average orbital distance (a) of a system
- Reveals the total mass of the system
- Can be used to calculate the Sun’s mass, Earth’s mass, and Jupiter’s mass
What Determines the Strength of Gravity?
- Directly proportional to the product of the masses (M x m)
- Inversely proportional to the square of the separation
How Does Newton’s Law of Gravity Allow Us to Extend Kepler’s Laws?
- Applies to other objects, not just planets
- Includes unbound orbit shapes: Parabola, hyperbola
- Can be used to measure mass of orbiting systems
How Did Newton Change Our View of the Universe?
- Realized the same physical laws operating on Earth also operate in the heavens
- Built on the idea of one universe
- Discovered laws of motion and gravity
What Are Newton’s Three Laws of Motion?
- Newton's first law of motion: An object moves at a constant velocity unless a net force acts to change its speed or direction.
- Newton's Second Law of Motion: Force = mass x acceleration or Force = rate of change in momentum
What Determines the Strength of Gravity?
- Every mass attracts every other mass
- Attraction is directly proportional to the product of their masses
- Attraction is inversely proportional to the square of the distance between their centers
How Does Newton’s Law of Gravity Extend Kepler’s Laws?
- Kepler's laws apply to all orbiting objects, not just planets
- Ellipses are not the only orbital paths. Orbits can be bound (ellipses) or unbound (parabola, hyperbola)
Center of Mass
- Because of angular momentum conservation, orbiting objects orbit around their center of mass
- Distance d1 and d2 of stars 1 & 2 from their center of mass are related by d1/d2 = m2/m1
Elliptical Orbits
- The shape of the orbit is determined by the ratio of the masses of the stars and the eccentricity.
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