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Questions and Answers
What is the equation for universal gravitation according to Newton's law?
What is the equation for universal gravitation according to Newton's law?
- $F = G \frac{m_1}{r^2} - \frac{m_2}{r^2}$
- $F = G (m_1 + m_2) r^2$
- $F = G \frac{m_1 m_2}{r}$
- $F = G \frac{m_1 m_2}{r^2}$ (correct)
What did Newton refer to as the 'first great unification'?
What did Newton refer to as the 'first great unification'?
- The unification of gravity on Earth with known astronomical behaviors (correct)
- The formulation of the Principia
- The empirical observations of gravitational phenomena
- The discovery of the inverse square law
In which work did Newton first publish the law of universal gravitation?
In which work did Newton first publish the law of universal gravitation?
- De Motu Corporum
- Opticks
- Philosophiæ Naturalis Principia Mathematica (correct)
- Arithmetica Universalis
What type of reasoning did Newton use to derive the law of universal gravitation?
What type of reasoning did Newton use to derive the law of universal gravitation?
What did Robert Hooke claim when Newton presented Book 1 of the unpublished text to the Royal Society?
What did Robert Hooke claim when Newton presented Book 1 of the unpublished text to the Royal Society?
What did Newton attribute the derivation of the law of universal gravitation to?
What did Newton attribute the derivation of the law of universal gravitation to?
What significant event marked the publication of Newton's law of universal gravitation?
What significant event marked the publication of Newton's law of universal gravitation?
What is the value of the gravitational force between two particles with masses $m_1$ and $m_2$ separated by a distance $r$ according to Newton's law of universal gravitation?
What is the value of the gravitational force between two particles with masses $m_1$ and $m_2$ separated by a distance $r$ according to Newton's law of universal gravitation?
In what work and when was Newton's law of universal gravitation first published?
In what work and when was Newton's law of universal gravitation first published?
What claim did Robert Hooke make when Newton presented Book 1 of the unpublished text to the Royal Society?
What claim did Robert Hooke make when Newton presented Book 1 of the unpublished text to the Royal Society?
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Study Notes
Newton's Law of Universal Gravitation
- The equation for universal gravitation is F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of two particles, and r is the distance between them.
Newton's Achievements
- Newton referred to his law of universal gravitation as the 'first great unification' because it united the heavens and the Earth under a single force.
- Newton first published the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" in 1687.
Derivation of the Law
- Newton used inductive reasoning to derive the law of universal gravitation, meaning he made observations and experiments to formulate the law.
- Newton attributed the derivation of the law to his own work, rejecting Robert Hooke's claim that he had helped Newton with the concept.
Publication and Reaction
- The significant event that marked the publication of Newton's law of universal gravitation was the publication of "Philosophiæ Naturalis Principia Mathematica" in 1687.
- When Newton presented Book 1 of the unpublished text to the Royal Society, Robert Hooke claimed that he had helped Newton with the concept of universal gravitation.
Key Formula
- The value of the gravitational force between two particles with masses m1 and m2 separated by a distance r is F = G * (m1 * m2) / r^2, according to Newton's law of universal gravitation.
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