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Questions and Answers
What happens to the acceleration of an object when it is attracted to a more massive object?
Why do all objects, regardless of mass, accelerate towards the Earth at the same rate?
Where is the center of mass for a system like the Earth and the moon located?
What did Newton's work on gravity fail to explain?
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What is the rate of acceleration towards the Earth for all objects, disregarding air resistance?
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What did later scientists develop to explain gravity?
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What is the force that causes planets to move in their orbits?
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What is the constant of universal gravitation approximately equal to?
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According to Newton, what is the force that causes objects to fall towards the Earth?
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What is the equation that describes the gravitational force between two objects?
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What is the distance used when discussing the radius between two objects?
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What does the gravitational force exerted by an object depend on?
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Study Notes
Newton's Law of Universal Gravitation
- Newton's law states that every object with mass attracts every other object with mass through a force called gravity.
- The centripetal force causing the motion of planets in their orbits is the same force that causes objects to fall towards the Earth.
- Newton proposed that planets are in a kind of free fall towards the Sun, just like an apple is in free fall towards the Earth.
Thought Experiment and Orbit
- A cannonball can be fired with great force, producing a speed great enough to fall at the same rate as the Earth's curvature, thus orbiting the Earth.
- This concept applies to satellites and space stations, which are in orbit around the Earth at a fixed speed and radius.
Gravitational Force
- Every object with mass exerts gravity on every other massive object.
- The gravitational force can be described using the equation: F = G * (m1 * m2) / r^2, where F is the force, G is the constant of universal gravitation, m1 and m2 are the masses, and r is the distance between them.
- The constant G is approximately 6.67 x 10^-11 N m^2 kg^-2.
Mass and Radius
- When discussing the radius between two objects, the distance between their centers is used, not their surfaces.
- Newton showed that the gravitational force exerted by an object depends only on its mass, not its volume.
Center of Mass and Acceleration
- When examining a system like the Earth and the moon, both objects exert gravitational force on each other, and the forces are equal in magnitude.
- The center of mass for the system lies within the more massive object (in this case, the Earth).
- The acceleration of an object towards a more massive object is greater due to the difference in masses.
Falling Objects and Inertia
- All objects, regardless of mass, accelerate towards the Earth at the same rate (9.8 m/s^2) if air resistance is disregarded.
- This is because the force of gravity imparts greater acceleration on a more massive object, but the object also has greater inertia or resistance to being accelerated.
Impact and Legacy
- Newton's work on gravity correlated an incredible amount of data, from terrestrial motion to celestial motion.
- However, Newton could not explain how objects exert gravitational force on each other from a distance.
- Later scientists developed the concept of gravity as a field force, and Einstein's general theory of relativity provided a more sophisticated understanding of gravity.
Newton's Law of Universal Gravitation
- Every object with mass attracts every other object with mass through a force called gravity.
- The centripetal force causing the motion of planets in their orbits is the same force that causes objects to fall towards the Earth.
- Planets are in a kind of free fall towards the Sun, just like an apple is in free fall towards the Earth.
Thought Experiment and Orbit
- A cannonball can be fired with great force, producing a speed great enough to fall at the same rate as the Earth's curvature, thus orbiting the Earth.
- Satellites and space stations are in orbit around the Earth at a fixed speed and radius, applying the same concept.
Gravitational Force
- Every object with mass exerts gravity on every other massive object.
- The gravitational force can be described using the equation: F = G * (m1 * m2) / r^2.
- The constant G is approximately 6.67 x 10^-11 N m^2 kg^-2.
Mass and Radius
- The distance between the centers of two objects is used when discussing radius, not their surfaces.
- The gravitational force exerted by an object depends only on its mass, not its volume.
Center of Mass and Acceleration
- Both objects in a system, like the Earth and the moon, exert gravitational force on each other, with equal magnitude.
- The center of mass for the system lies within the more massive object.
- The acceleration of an object towards a more massive object is greater due to the difference in masses.
Falling Objects and Inertia
- All objects, regardless of mass, accelerate towards the Earth at the same rate (9.8 m/s^2) if air resistance is disregarded.
- The force of gravity imparts greater acceleration on a more massive object, but the object also has greater inertia or resistance to being accelerated.
Impact and Legacy
- Newton's work correlated an incredible amount of data, from terrestrial motion to celestial motion.
- Newton could not explain how objects exert gravitational force on each other from a distance.
- Later scientists developed the concept of gravity as a field force, and Einstein's general theory of relativity provided a more sophisticated understanding of gravity.
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Description
Learn about Newton's law, which states that every object with mass attracts every other object with mass, and its application to planetary motion and free fall.
