The story of **gravity** is an intriguing one. It starts with Sir Isaac Newton’s ideas and later grows with Albert Einstein’s new theories. We will explore how our view on this key force has changed over time. We’ll look from Newton’s original thoughts to the deeper insights offered by **Einstein**.

Newton’s work was crucial for understanding how things move. His laws helped explain everything from falling objects to the paths of planets. But, by the 19th century, new discoveries in light and **electromagnetism** showed Newton’s ideas had limits. It took **Einstein** to revolutionize our ideas about **gravity** and its connection to the universe’s structure.

### Key Takeaways

**Gravity**is the strongest force on cosmological scales and one of the least understood forces in nature.- Newton’s theory assumed gravity is felt everywhere instantaneously, while Einstein’s theory incorporated the speed of light limit for gravity to travel.
- Einstein’s theory recognizes that the source of gravity is energy, not just mass, and that all forms of energy have gravitational effects.
**General Relativity**explains phenomena like the**anomalous orbit of Mercury**and the**bending of light by gravity**, which were not accounted for by**Newtonian physics**.- Gravity is a form of energy, and the difference between mass and energy in the context of gravity is a key concept in Einstein’s theory.

## Newton’s Groundbreaking Laws of Motion

Isaac **Newton’s laws of motion** changed how we see the world around us. The first law talks about inertia. It says objects at rest stay that way. And things moving keep moving unless something pushes or pulls on them. The law of **acceleration**, or the second law, connects how hard we push or pull (force) with how something speeds up or slows down (**acceleration**). The third law, about action and reaction, tells us every action has an equal and opposite reaction. These ideas help us understand everything from how a ball flies through the air to why planets move in space.

### The Fundamentals of Newtonian Mechanics

Newton’s laws form the heart of **Newtonian mechanics**. They help us explain the motion of all kinds of objects. From how arrows fly to how the moon circles our planet, all obey the **Universal Law of Gravitation**. Newtonian mechanics’ simple yet powerful ideas have guided science for a long time.

### The Principle of Invariance and Absolute Space and Time

Newton’s work also introduced the idea of **absolute space and time**. He thought these were the same for everyone, no matter how fast they might be moving. This idea, called **Invariance**, meant the laws of motion worked the same way for everyone. But, as later discoveries showed, the world isn’t quite that simple.

Newton’s Laws of Motion | Equations | Explanation |
---|---|---|

First Law (Law of Inertia) | v = constant | An object at rest will remain at rest, and an object in motion will remain in motion, unless acted upon by an unbalanced force. |

Second Law (Law of Acceleration) | F = ma | The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. |

Third Law (Law of Action and Reaction) | F₁₂ = -F₂₁ | For every action, there is an equal and opposite reaction. The forces between two interacting objects are equal in magnitude and opposite in direction. |

The ideas in **Newton’s Laws of Motion** and the **Universal Law of Gravitation** deeply impact science. They’re the foundation of **Newtonian Mechanics**. And they’ve helped us move from 17th-century science to the incredible things we achieve today.

## The Puzzles of 19th Century Theoretical Physics

In the 19th century, scientists made big strides in understanding electricity, magnetism, and light. This progress reached a highlight with James Clerk Maxwell’s **electromagnetism** equations. Yet, a puzzling issue surfaced. These equations changed when seen from different moving viewpoints, unlike the fixed rules of **Newtonian physics**. This variation challenged the core idea of **invariance**. This idea was pivotal in **Newtonian mechanics**.

### The Beauty of Invariance in Newtonian Physics

**Newtonian physics** was known for its beauty in the **principle of invariance**. It said the laws of motion didn’t change no matter how you looked at them. This concept was key in explaining everything from a cannonball’s path to the planets’ orbits. Yet, the odd behavior of **electromagnetism** posed a big threat to this principle.

### Problems with Electromagnetism and the Lorentz Transformation

A breakthrough came with the **Lorentz transformation**. This math kept Maxwell’s equations sound in different moving frames. However, it led to a jaw-dropping revelation. Time and space weren’t fixed, as **Newtonian physics** assumed. They seemed to change with the observer’s movement. This made Albert Einstein wonder if **invariance** required rethinking the absolute nature of time and space.

Statistic | Value |
---|---|

General relativity unveiled | A century ago in a series of papers submitted to the Prussian Academy in Berlin |

Einstein’s papers on general relativity | 4 papers, one a week, during November 1915 |

Confirmation of Einstein’s light deflection calculations | During eclipse expeditions in 1919 |

First observation of gravitational lensing | 1979 |

Unexplained shift in Mercury’s orbit | 43 seconds of arc per century, until Einstein’s theory provided a precise explanation |

Einstein’s light bending prediction vs. Soldner’s | Einstein predicted twice as much bending, confirmed by subsequent eclipses |

## Einstein’s Special Theory of Relativity

In 1905, Albert Einstein put forward the **special theory of relativity**. It was based on the idea that all frames of reference moving at constant speed are the same. This means the laws of physics don’t change depending on how fast you’re moving. The discovery that the speed of light is always constant helped shape this theory.

Thanks to this, Einstein concluded **time and space change based on the observer’s view**. It showed that the way we understood the universe was off. **Time dilation and length contraction** became known because of these ideas. They made us question the old belief that time and space were fixed everywhere.

### The Principle of Relativity and the Equivalence of Inertial Frames

The **principle of relativity** said that any frame moving at a steady speed was just as good as another. This means the rules of physics hold no matter how you’re moving. The principle, combined with the fact that light always travels at the same speed, set up Einstein’s **special theory of relativity**.

### The Relativity of Time and Space

Einstein’s work changed the way we see **time and space**. It showed they aren’t fixed but change depending on how you’re moving. This idea went against what we thought before, but it’s been proven right through experiments and how we use technology.

## The Limitations of Special Relativity

**Special relativity** opened new doors, yet it only worked for people moving at a steady speed. Those theories missed the impacts of *gravity* or *acceleration*, big players in our knowledge of the world. Einstein knew this made his work unfinished. He wanted to connect his ideas with how old theories explained *gravity*.

Research on 26,500 far-spread double stars showed strange observations. When these stars moved very slowly together, their speed changes were too high. They were more than what we expected by following old physics rules. This happened specifically when their speeds were very, very low. It pointed to a problem in our usual ideas about how *gravity* works.

In 1983, Mordehai Milgrom suggested Modified Newtonian Dynamics (MOND) might solve this. MOND, with a variant called AQUAL, could account for the weird speed changes seen. This goes against what old theories, including **Special Relativity**, predict at very slow speeds. It implies that maybe our understanding of *gravity* is incomplete.

Yet, MOND, just like older theories that mention dark matter, faces its own issues. It needs more evidence to be widely accepted. MOND could prove to us that we might not know everything about *gravity* yet.

## Einstein’s Thought Experiments and the Equivalence of Gravity and Acceleration

*Albert Einstein* couldn’t do actual tests because of his job. So, he thought about gravity and how it’s tied to space and time. These **thought experiments** showed him something amazing. He found out that gravity isn’t really different from **acceleration**.

An observer on Earth feels similar to someone in a rocket speeding up. This idea was big. It meant gravity isn’t a pull on stuff; it’s more about how space and time curve. Einstein saw that this curved space could even change some big, basic ideas about the universe.

### Geometrical Properties and Physical Conditions

Einstein’s mind experiments were key. They helped him see the link between gravity and acceleration clearer. He dreamed up scenarios, like a person in a speeding-up elevator or rocket. This showed him that gravity doesn’t push. It’s the warping of space and time that makes things fall.

He also saw that this warp can change the universe’s **geometrical properties**. For example, pi might not always be 3.14 like we know it. The curving of space affects how distances and angles relate. These experiments deepened Einstein’s understanding of gravity.

Thought Experiment | Insight |
---|---|

Chasing a beam of light | Led to insights on the principle of relativity |

Magnet and conductor interaction | Highlighted asymmetries in Maxwell’s electrodynamics |

Observer in accelerating elevator or rocket | Demonstrated the equivalence of gravitational and inertial forces |

Curved surfaces and the value of pi | Revealed the impact of spacetime curvature on geometrical properties |

## Gravitation: From Newton to Einstein

### The Curvature of Spacetime and the Nature of Gravity

Einstein’s insight from **thought experiments** led him to the **general theory of relativity**. This theory changed how we see gravity. Einstein showed how the shape of spacetime changes because of mass and energy. This change causes gravity. For example, planets don’t “fall” towards the sun because of a force. They follow curved paths in spacetime, caused by the sun’s mass. These paths are known as **geodesics**.

### Einstein’s General Theory of Relativity

Einstein’s theory brought together **Newtonian physics** and the issues with **electromagnetism**. It improved on our view of the universe. One key difference from **Newton** is the **nature of gravity** itself. In Einstein’s view, all types of energy, even sound and heat, can produce gravity. This concept explains strange orbits like Mercury’s. The precession of Mercury’s orbit proved his theory and added to our cosmic understanding.

Close to the Sun, Einstein’s theory shows gravity as slightly stronger than Newton’s view. This minor difference leads to effects like Mercury’s ever-changing orbit shape. This rosette-like shift was not explainable by **Newton**. As Einstein’s theory correctly predicts Mercury’s movement, it stands as a key proof of his general relativity. It brought a huge leap in our cosmic exploration.

## Triumphs of General Relativity

Einstein’s **general theory of relativity** was a big success. It solved old problems and pointed to new things. For example, it explained why Mercury’s orbit didn’t match what classical physics had predicted.

### Explaining the Anomalous Orbit of Mercury

Much like clockwork, Newton’s physics said Mercury’s orbit should be an ellipse. But this planet’s orbit shifts in a pattern known as a rosette. Einstein’s work, however, foretold this “precession” exactly. It showed that spacetime’s curve, caused by the Sun’s mass, is behind it. This win with Mercury was a key step for his theory and for our view of space.

### Predicting the Bending of Light by Gravity

Relativity also said light should bend around the Sun. This idea checked out during a 1919 eclipse, backing Einstein with solid evidence. It was a major moment for science, giving gravity a new light to shine in.

### Black Holes and the Expanding Universe

Add to that, general relativity pointed towards **black holes** and a growing cosmos. Subsequent efforts have indeed spotted these phenomena. All this firmly brings Einstein’s work into the pantheon of major physics achievements.

## The Cosmic Speed Limit and the Delay in Gravitational Effects

**Newton** and Einstein had different ideas about how gravity works in the universe. Newton thought gravity instantly affected everything no matter the distance. However, Einstein’s **general relativity** showed that nothing could travel faster than light, not even gravity. If the Sun disappeared suddenly, we on Earth wouldn’t feel its gravity disappear for about 8.5 minutes. This is the time it takes for the news of the Sun’s vanishing to travel to Earth. This delay in feeling gravity effects showed a big change from Newton’s ideas to Einstein’s.

Einstein changed our understanding of how the universe’s gravity works. He showed that information like gravity effects couldn’t move faster than light. This key idea showed that the universe works differently than we thought with Newton’s ideas. It made us rethink how gravity, a very important force, truly works.

Einstein’s new way of looking at gravity also explained a mystery about Mercury’s orbit. The way Mercury moves its closest point to the Sun wasn’t understood with Newton’s theories. But, Einstein’s **general relativity** showed that due to gravity not being instant, it explained this movement exactly. This proved that Einstein’s view on gravity is correct and helps us understand our universe better.

## Gravity as a Form of Energy

Albert Einstein’s **general theory of relativity** shook up our understanding of gravity. It taught us that gravity’s source isn’t mass, like we thought with Newton. Rather, it’s energy, including mass as one of its forms. Here’s the kicker: *gravity itself is a form of energy* too. This means gravity creates more gravity, causing interesting things like Mercury’s orbit precession, a mystery for Newton.

### The Difference Between Mass and Energy in Gravity

In Einstein’s **general relativity** theory, grasping the difference between mass and energy is crucial. He showed how **mass and energy** weave together, offering us the iconic E=mc² equation. This concept is at the heart of seeing **gravity as a form of energy**.

Einstein’s work marked a huge shift in how we see the universe. It did away with the narrow view of Newton’s gravity. Instead, we now have a deeper understanding of how **gravity is a form of energy**, part of the very essence of our universe. This change was a critical step toward truly understanding gravity’s role in the cosmos.

## The Rosette Orbit of Mercury and the Precession of the Perihelion

Einstein’s general theory of relativity solved one of science’s big mysteries. It explained why Mercury’s orbit is different from what Newton’s laws predicted. Normally, planets move in ellipses, but Mercury’s path wobbles like a rosette. This change, the “precession of the perihelion,” matches what Einstein’s theory says about space and time bending under the Sun’s pull. So, Einstein showed how gravity makes Mercury’s orbit dance.

The odd shift in Mercury’s perihelion is about 43 arc-seconds every century. Einstein’s General Relativity, from 1915, nailed the reason for this shift. It showed that gravity isn’t just a force from the Sun but is also how space and time can warp. This warping is caused by the Sun and affects things nearby, like Mercury. Without this new theory, there was no good way to explain Mercury’s unusual pattern.

Jump to 1687 when Newton came up with his theory of gravity. It suggested that gravity works instantly across space. Yet, when dealing with Mercury’s extreme orbit, this direct approach didn’t quite fit. People guessed maybe there was a hidden big object near the Sun tugging on Mercury. But no such object was found. Einstein’s successful account for Mercury’s orbit really boosted the idea that gravity is about space and time being bent, not just pulling things together.

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