Timelines of Events

1609
- Johannes Kepler demonstrated that Mars has an elliptical orbit.
1798
- For the first time, Henry Cavendish measures the gravitational constant.
1846
- Urbain Le Verrier, a French mathematician, uses Newton's laws to calculate the position of the planet Neptune.
1915
- General relativity is first presented by Albert Einstein, who explains how the gravitational force depends on the curvature of spacetime.
2014
- Atomic behavior is used to calculate the gravitational constant.

Gravity

Gravity: The force of attraction between any two masses.
- It is the force that draws all objects to Earth and gives them mass.
- It pulls objects downward, toward the Earth's core.
If the object were on the moon, which has a much lower mass than Earth, the force would be six times lower and the weight would be one-sixth of what it is on Earth.
Isaac Newton, an English physicist, astronomer, and mathematician, was the first to recognize gravity as a universal force acting on all objects and explaining the movement of planets.

Describing orbits

Based on the three laws of planetary motion established by Johannes Kepler, the shapes of the planets' orbits were already well known by the time of Isaac Newton.
- First Law of Planetary Motion: Demonstrated that the orbits were ellipses as sun as their center.
- Second Law of Planetary Motion: Stated that planets moved faster along their orbits when they were close to the sun than when they were farther away.
- Third Law of Planetary Motion: Described the relationship between the time required to complete one orbit and the distance from the sun: the time required to complete one orbit, squared, was equal to the cube of the average distance between the planet and the sun.
Kepler correctly discovered the shapes and speeds of planetary orbits, but he had no idea why the planets moved the way they did.
- In his book Astronomia Nova (1609), he suggested that an angel driving a chariot was guiding Mars around its orbit.
- He changed his mind a year later, claiming that the planets were magnets being pushed around by magnetic "arms" extending from the spinning sun.

Newton’s Insight

Robert Hooke of England and Giovanni Alfonso Borelli of Italy, proposed the existence of a force of attraction between the sun and the various planets.
- They also claimed that as distance increased, the force diminished.
On December 9, 1679, Hooke expressed his opinion in a letter to Newton that the force might decrease with the inverse square of distance.
- Hooke did not publish the concept, and he lacked the mathematical knowledge necessary to fully support his claim.
- Newton, on the other hand, was able to rigorously demonstrate that an inverse square law of attractive force would result in an elliptical planetary orbit.
The planetary orbits and their adherence to Kepler's three laws were fully explained by Newton's mathematical proof that the force of attraction (F) between the sun and the planets varied exactly as an inverse square of the distance (r) between those.
- This is written mathematically as F ⧜ 1/r^2 .
- By doubling the distance between the objects, the attractive force is reduced to a quarter of its initial strength.

The Great Comet

The Great Comet of 1680 was the brightest comet of the 17th century, shining so brilliantly that it was briefly visible during the day.
Two comets were seen:
- one that was en route to the sun between November and December 1680; and
- another that was moving away from the sun between the end of December 1680 and the beginning of March 1681.
John Flamsteed, an astronomer, hypothesized that the two sightings might be of the same comet, which had come from the edge of the solar system, revolved around the sun, and then moved out again.
The mysterious form of cometary orbits piqued Halley's interest, and he traveled to Cambridge to discuss the issue with his friend Newton.
- Newton calculated the parameters of the comet's orbit as it passed through the inner solar system using his law that related force to acceleration and his insistence that the strength of the force ranged as the inverse square of the distance.
This discovery piqued Halley's interest, and he went on to calculate the orbits of 24 other comets and prove that one comet (Halley's comet) returned to the sun every 76 years.
Philosophiae Naturalis Principia Mathematica by Isaac Newton.
- Published in Latin on July 5, 1687.
- He explains his laws of motion, his theory of gravitation, how he proved Kepler's three laws, and how he calculated a comet's orbit.
- He emphasized that his law was universal—gravity affects everything in the universe, no matter how far away it is.
- It explained how an apple fell on his head in Woolsthorpe's orchard, the tides in the seas, the moon orbiting Earth, Jupiter orbiting the sun, and even a comet's elliptical orbit.
- The exact same physical law that created the solar system and caused the apple to fall in his yard also caused stars and far-off galaxies to form, as would later be revealed.
- There was evidence all around that Newton's law of gravitation worked.
- It enabled future planet predictions in addition to illuminating where planets had gone and were going.

Constant of proportionality

Gravitational Law: It states that the size of the gravitational force is proportional to the masses of the two bodies multiplied together and divided by the square of the distance between them
It consistently gathers masses and moves in a straight line between them. If the object in question is spherically symmetrical, like Earth, then its gravitational pull can be thought of as emanating from a point at its center.
Gravitational Constant (G): The constant of proportionality, a number that gives the strength of the force.

Measuring Gravitational Constant

Gravity is a weak force, so measuring the gravitational constant accurately is difficult.
In 1798, 71 years after Newton's death, Henry Cavendish performed the first laboratory test of Newton's theory.
- He replicated an experimental system proposed by geophysicist John Michell and successfully measured the gravitational force between two lead balls with diameters of 2 and 12 in.
This has resulted in a slow improvement in G's accuracy, with some scientists suggesting that G changed over time.

Shaping the planets

Understanding how gravity works is essential to comprehending why the universe appears as it does.
Gravity is responsible for planets' spherical shapes.
Gravity also influences life on Earth by regulating animal size.
Gravity is also responsible for the tides,
- Tides: These are formed as a result of water bulging in both directions: away from the sun and moon on one side of Earth where their gravitational pull is stronger, and toward them on the other.
- High Spring Tide: Occurs when the sun and moon are aligned.
- Low Neap Tide: Occurs when the sun and moon are at right angles.

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Gravitational Theory

Timelines of Events

1609
- Johannes Kepler demonstrated that Mars has an elliptical orbit.
1798
- For the first time, Henry Cavendish measures the gravitational constant.
1846
- Urbain Le Verrier, a French mathematician, uses Newton's laws to calculate the position of the planet Neptune.
1915
- General relativity is first presented by Albert Einstein, who explains how the gravitational force depends on the curvature of spacetime.
2014
- Atomic behavior is used to calculate the gravitational constant.

Gravity

Gravity: The force of attraction between any two masses.
- It is the force that draws all objects to Earth and gives them mass.
- It pulls objects downward, toward the Earth's core.
If the object were on the moon, which has a much lower mass than Earth, the force would be six times lower and the weight would be one-sixth of what it is on Earth.
Isaac Newton, an English physicist, astronomer, and mathematician, was the first to recognize gravity as a universal force acting on all objects and explaining the movement of planets.

Describing orbits

Based on the three laws of planetary motion established by Johannes Kepler, the shapes of the planets' orbits were already well known by the time of Isaac Newton.
- First Law of Planetary Motion: Demonstrated that the orbits were ellipses as sun as their center.
- Second Law of Planetary Motion: Stated that planets moved faster along their orbits when they were close to the sun than when they were farther away.
- Third Law of Planetary Motion: Described the relationship between the time required to complete one orbit and the distance from the sun: the time required to complete one orbit, squared, was equal to the cube of the average distance between the planet and the sun.
Kepler correctly discovered the shapes and speeds of planetary orbits, but he had no idea why the planets moved the way they did.
- In his book Astronomia Nova (1609), he suggested that an angel driving a chariot was guiding Mars around its orbit.
- He changed his mind a year later, claiming that the planets were magnets being pushed around by magnetic "arms" extending from the spinning sun.

Newton’s Insight

Robert Hooke of England and Giovanni Alfonso Borelli of Italy, proposed the existence of a force of attraction between the sun and the various planets.
- They also claimed that as distance increased, the force diminished.
On December 9, 1679, Hooke expressed his opinion in a letter to Newton that the force might decrease with the inverse square of distance.
- Hooke did not publish the concept, and he lacked the mathematical knowledge necessary to fully support his claim.
- Newton, on the other hand, was able to rigorously demonstrate that an inverse square law of attractive force would result in an elliptical planetary orbit.
The planetary orbits and their adherence to Kepler's three laws were fully explained by Newton's mathematical proof that the force of attraction (F) between the sun and the planets varied exactly as an inverse square of the distance (r) between those.
- This is written mathematically as F ⧜ 1/r^2 .
- By doubling the distance between the objects, the attractive force is reduced to a quarter of its initial strength.

The Great Comet

The Great Comet of 1680 was the brightest comet of the 17th century, shining so brilliantly that it was briefly visible during the day.
Two comets were seen:
- one that was en route to the sun between November and December 1680; and
- another that was moving away from the sun between the end of December 1680 and the beginning of March 1681.
John Flamsteed, an astronomer, hypothesized that the two sightings might be of the same comet, which had come from the edge of the solar system, revolved around the sun, and then moved out again.
The mysterious form of cometary orbits piqued Halley's interest, and he traveled to Cambridge to discuss the issue with his friend Newton.
- Newton calculated the parameters of the comet's orbit as it passed through the inner solar system using his law that related force to acceleration and his insistence that the strength of the force ranged as the inverse square of the distance.
This discovery piqued Halley's interest, and he went on to calculate the orbits of 24 other comets and prove that one comet (Halley's comet) returned to the sun every 76 years.
Philosophiae Naturalis Principia Mathematica by Isaac Newton.
- Published in Latin on July 5, 1687.
- He explains his laws of motion, his theory of gravitation, how he proved Kepler's three laws, and how he calculated a comet's orbit.
- He emphasized that his law was universal—gravity affects everything in the universe, no matter how far away it is.
- It explained how an apple fell on his head in Woolsthorpe's orchard, the tides in the seas, the moon orbiting Earth, Jupiter orbiting the sun, and even a comet's elliptical orbit.
- The exact same physical law that created the solar system and caused the apple to fall in his yard also caused stars and far-off galaxies to form, as would later be revealed.
- There was evidence all around that Newton's law of gravitation worked.
- It enabled future planet predictions in addition to illuminating where planets had gone and were going.

Constant of proportionality

Gravitational Law: It states that the size of the gravitational force is proportional to the masses of the two bodies multiplied together and divided by the square of the distance between them
It consistently gathers masses and moves in a straight line between them. If the object in question is spherically symmetrical, like Earth, then its gravitational pull can be thought of as emanating from a point at its center.
Gravitational Constant (G): The constant of proportionality, a number that gives the strength of the force.

Measuring Gravitational Constant

Gravity is a weak force, so measuring the gravitational constant accurately is difficult.
In 1798, 71 years after Newton's death, Henry Cavendish performed the first laboratory test of Newton's theory.
- He replicated an experimental system proposed by geophysicist John Michell and successfully measured the gravitational force between two lead balls with diameters of 2 and 12 in.
This has resulted in a slow improvement in G's accuracy, with some scientists suggesting that G changed over time.

Shaping the planets

Understanding how gravity works is essential to comprehending why the universe appears as it does.
Gravity is responsible for planets' spherical shapes.
Gravity also influences life on Earth by regulating animal size.
Gravity is also responsible for the tides,
- Tides: These are formed as a result of water bulging in both directions: away from the sun and moon on one side of Earth where their gravitational pull is stronger, and toward them on the other.
- High Spring Tide: Occurs when the sun and moon are aligned.
- Low Neap Tide: Occurs when the sun and moon are at right angles.