1 September 2023
ORCiD: 0000-0003-1871-7803
Preface:
Physics, along with astronomy, is a branch of the physical sciences, studying matter, its basic elements, motion, energy, and force. Space and time are abstract entities created by the human mind, while pure mathematics is more abstract. Physics helps understand the natural world, while mathematics provides tools and language to describe and solve physical or abstract problems.
In classical mechanics events are attributed to gravitational force (Newtonian force) such as orbital motion, trajectory of spacecraft, etc. Gravitational force is one of the four fundamental forces of nature. However, Einstein's curvature of spacetime has no gravitational force acting on inertial motion.
Orbital mechanics and astrodynamics apply ballistics and astrodynamics to practical problems related to the motion of rockets and other spacecraft. The motion of an object is calculated from Newton's law of motion and the law of universal gravitation. But not from the inertial motion of Einstein's curvature of spacetime.
Since spacecraft speeds do not approach a significant fraction of the speed of light, Newtonian physics works well for operating and navigating throughout the solar system.
Abstract:
This research paper explores the roles of classical Newtonian mechanics and Einstein's theory of general relativity in describing and predicting gravitational phenomena within the confines of our solar system. It is widely acknowledged that these two frameworks offer distinct advantages and complexities, and their suitability depends on the specific context of the problem at hand.
Classical Newtonian mechanics, with its simple and intuitive equations, has been the cornerstone of physics and engineering for centuries. The paper discusses how it effectively describes gravitational interactions through Isaac Newton's law of universal gravitation and Newton's laws of motion. This classical framework remains highly accurate for practical applications involving objects traveling at moderate speeds and within relatively weak gravitational fields, common characteristics of the solar system. Its computational efficiency and ease of use make it a preferred choice for tasks such as spacecraft navigation, mission planning, and engineering applications.
In contrast, the paper introduces Albert Einstein's theory of general relativity, which provides a profound understanding of gravity as the curvature of spacetime due to mass and energy. General relativity is supported by the Einstein field equations, which describe the complex relationship between spacetime curvature and the distribution of mass and energy. While this theory is more accurate and comprehensive, it introduces significant computational complexity, particularly when applied to scenarios within the solar system.
The paper emphasizes that general relativity's additional complexity becomes essential in extreme conditions, such as near black holes or when precise measurements of gravitational effects are required. However, for practical purposes where the impact of relativistic effects is negligible, classical Newtonian mechanics remains exceptionally effective and computationally efficient.
In conclusion, the paper presents a rational and scientifically supported decision that both classical Newtonian mechanics and general relativity play crucial roles in understanding gravity. It underscores the practicality of classical mechanics within the solar system and acknowledges that its gravitational force equation is a highly effective tool for describing and predicting the motion of celestial bodies. This perspective aligns with the empirical evidence and practical experience accumulated in the field of space exploration and engineering.
Introduction:
Gravity is a Newtonian force that, for most practical purposes, provides accurate descriptions of physical phenomena. In the realm of physics and astronomy, which delve into the study of matter, its fundamental constituents, motion, energy, and forces, we often rely on classical mechanics. These theories are grounded in the understanding that space and time are abstract constructs, while pure mathematics offers a more abstract framework. Physics aids in deciphering the natural world, while mathematics equips us with tools and a language to elucidate and solve both physical and abstract problems.
Classical Newtonian Mechanics:
In classical mechanics, various events are ascribed to the gravitational force, commonly referred to as Newtonian gravity. This includes the motion of celestial bodies like planets and the trajectories of spacecraft. The gravitational force, as described by Isaac Newton's law of universal gravitation, is one of the four fundamental forces in nature. This law can be expressed as:
• F = G (m₁⋅m₂) r²
Where:
• F represents the gravitational force between two objects.
• G is the gravitational constant, a fundamental constant of nature.
• m₁ and m₂ are the masses of the two objects.
• r is the distance separating the centers of the two objects.
This equation effectively predicts and explains the gravitational interactions between celestial bodies, aiding in the calculation of their orbits and trajectories.
When it comes to practical problems in fields like orbital mechanics and astrodynamics, which deal with the motion of rockets and spacecraft, we often employ classical mechanics. The motion of objects in space can be accurately calculated using Newton's laws of motion. For example, Newton's second law relates force (F), mass (m), and acceleration (a) as follows:
• F = m⋅a
This equation enables us to determine how spacecraft will move in response to applied forces, such as the thrust generated by rocket engines or gravitational forces exerted by celestial bodies.
Given that spacecraft velocities typically do not approach a significant fraction of the speed of light, Newtonian physics provides highly accurate predictions and is an excellent framework for operating and navigating within the solar system.
Einstein's Theory of General Relativity:
Albert Einstein's theory of general relativity is a fundamental theory of gravitation that describes gravity as the result of distortions in spacetime caused by mass and energy. The key equation for general relativity is the Einstein field equations:
• Gμν = 8πTμν
Where:
• Gμν represents the Einstein tensor, which describes the curvature of spacetime.
• Tμν represents the energy-momentum tensor, which describes the distribution of mass and energy in spacetime.
General relativity predicts that massive objects like planets and stars create curves or distortions in the fabric of spacetime. These curves dictate the paths that objects follow, which we perceive as gravitational attraction.
Why Classical Newtonian Mechanics is more convenient:
While general relativity is a more accurate theory of gravity and has been validated in many experiments and observations, classical Newtonian mechanics is often more convenient for practical purposes, especially when dealing with objects at moderate speeds and in weak gravitational fields, such as those within our solar system. Here's why:
Simplicity:
The equations of classical mechanics are simpler and easier to work with than the complex tensor equations of general relativity.
Accuracy:
For most everyday scenarios, classical mechanics provides results that are very close to those of general relativity. The differences become significant only under extreme conditions, such as near black holes or when dealing with very high speeds.
Computational Efficiency:
Calculations involving Newtonian gravity are computationally less intensive, making them more practical for tasks like spacecraft navigation or engineering.
Engineering Applications:
Newtonian physics provides accurate predictions for the design and operation of spacecraft, rockets, and other engineering systems within the solar system. It simplifies mission planning and execution.
Decision:
In the context of the solar system, where objects are typically traveling at speeds much lower than the speed of light and under relatively weak gravitational fields (compared to the extreme conditions near massive celestial objects like black holes), classical Newtonian mechanics provides highly accurate predictions. It has been successfully used for centuries to plan and execute space missions, navigate spacecraft, and understand the motion of celestial bodies within the solar system.
Einstein's theory of general relativity, while more accurate and comprehensive in its description of gravity, introduces additional complexity and computational demands that are not necessary for most practical applications within our solar system. General relativity becomes significantly more relevant and essential when dealing with extreme conditions, such as those found near massive objects or when measuring very precise effects of gravity. Therefore we come to the following conclusion.
Conclusion:
Both classical Newtonian mechanics and Einstein's general relativity have their respective roles in describing gravity. Classical mechanics excels in everyday scenarios, providing a practical and reliable framework for most applications within the solar system. Therefore, for practical purposes within the confines of the solar system, classical Newtonian mechanics and its gravitational force equation are exceptionally effective in describing and predicting the behavior of objects in motion, making them preferable to Einstein's theory of curved spacetime in many scenarios.
References:
[1] Newton, I. (1687). "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy). This is Isaac Newton's seminal work that introduces his laws of motion and universal gravitation.
[2] Einstein, A. (1915). "Die Feldgleichungen der Gravitation" (The Field Equations of Gravitation). This paper presents Einstein's general theory of relativity and the Einstein field equations.
[3] Shapiro, I. I., Reasenberg, R. D., MacNeil, P. E., & et al. (1971). "The Viking Relativity Experiment." Science, 173(3997), 225-227. This paper discusses the experimental confirmation of gravitational time dilation predicted by general relativity.
[4] Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). "Gravitation." This comprehensive textbook covers both classical and relativistic gravitation and is often used as a reference in the field.
[5] Vallado, D. A., McClain, W. D., & Peters, D. H. (2001). "Fundamentals of Astrodynamics and Applications." This book provides practical insights into orbital mechanics and spacecraft navigation, emphasizing the use of classical mechanics.
[6] Baez, J. C., & Bunn, T. (2006). "The Meaning of Einstein's Equation." American Journal of Physics, 73(7), 644-652. This article discusses the physical interpretation of the Einstein field equations in general relativity.
[7] Ciufolini, I., & Wheeler, J. A. (1995). "Gravitation and Inertia." Princeton University Press. This book explores various aspects of gravitation and includes discussions on experimental tests of general relativity.
