Question

1. who was the english scientist that began the scientific understanding of gravity?
2. what observation led newton to think about gravity extending beyond earth?
3. in what year did newton publish his law of universal gravitation?
4. does gravity push objects apart or pull them together?
5. what do you need to know to calculate the gravitational force between two objects?
6. if you double the mass of an object, what happens to the gravitational force?
7. if you double the distance between two objects, what happens to the gravitational force?

Explanation:

1. Isaac Newton is widely recognized as the English scientist who began the scientific understanding of gravity. His work on universal gravitation was a cornerstone in physics.
2. Newton observed the moon's orbit around the Earth. He realized that the force keeping the moon in orbit (centripetal force) could be the same gravitational force that causes objects to fall on Earth, thus extending the concept of gravity beyond Earth.
3. Newton published his law of universal gravitation in 1687 in his work Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy).
4. Gravity is an attractive force. According to Newton's law of universal gravitation \(F = G\frac{m_1m_2}{r^{2}}\), where \(G> 0\), \(m_1\) and \(m_2\) are masses of two objects, and \(r\) is the distance between them. The positive value of \(G\) implies that the force is attractive, so gravity pulls objects together.
5. To calculate the gravitational force between two objects using the formula \(F = G\frac{m_1m_2}{r^{2}}\), you need to know the masses of the two objects (\(m_1\) and \(m_2\)) and the distance (\(r\)) between their centers of mass. Also, the gravitational constant \(G\approx6.67\times 10^{- 11}\space N\cdot m^{2}/kg^{2}\) is a known constant.
6. From the formula \(F = G\frac{m_1m_2}{r^{2}}\), if we double the mass of one object (say \(m_1\) becomes \(2m_1\)) while keeping \(m_2\) and \(r\) constant, then \(F'=G\frac{(2m_1)m_2}{r^{2}} = 2G\frac{m_1m_2}{r^{2}}=2F\). So the gravitational force doubles.
7. Using the formula \(F = G\frac{m_1m_2}{r^{2}}\), if the distance \(r\) is doubled (\(r' = 2r\)), then \(F'=G\frac{m_1m_2}{(2r)^{2}}=G\frac{m_1m_2}{4r^{2}}=\frac{1}{4}F\). So the gravitational force is reduced to one - fourth of its original value.

Answer:

1. Isaac Newton
2. The moon's orbit around the Earth
3. 1687
4. Pull them together
5. The masses of the two objects and the distance between their centers of mass (and the gravitational constant \(G\))
6. The gravitational force doubles
7. The gravitational force is reduced to one - fourth of its original value