3.3 Newton’s Universal Law of Gravitation
3 min read•june 12, 2024
Newton's_Law_of_Gravitation_0### explains how gravity works between objects. It shows that the force depends on mass and distance, with bigger objects and closer distances creating stronger attraction. This fundamental principle helps us understand everything from falling apples to orbiting planets.
The law's power lies in its ability to predict orbits and calculate masses of celestial bodies. By observing how objects move in space, we can figure out the masses of planets, , and even entire . It's like cosmic detective work using math and motion.
Newton's Universal Law of Gravitation
Gravity's dependence on mass and distance
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- strengthens with increasing mass of objects
- More massive objects (planets, stars) exert stronger gravitational pull on each other
- Less massive objects (, ) experience weaker gravitational attraction
- Gravitational force weakens with increasing distance between objects
- Objects in close proximity ( and ) have stronger gravitational interaction
- Objects far apart (Earth and distant galaxies) have negligible gravitational effect on each other
- Newton's law of gravitation: quantifies the relationship
- Gravitational force () directly proportional to product of masses (, )
- Gravitational force inversely proportional to square of distance () between objects
- () scales the magnitude of the force as a
- Gravity is a , having both magnitude and direction
- Newton's law describes gravity as an force
Newton's law for orbital predictions
- Orbits result from balance of gravitational force and object's
- Gravitational force pulls objects together (Earth pulling on Moon)
- Inertia causes objects to resist changes in motion and move in straight lines (Moon's tendency to move away from Earth)
- Stable orbits occur when gravitational force equals needed for circular motion
- describe orbital behavior
- Orbits are with central object at one focus (planets orbiting in elliptical paths)
- Orbiting object sweeps out equal areas in equal time intervals (planet moves faster when closer to Sun)
- squared proportional to cubed ()
- () depends on mass of central object () and orbital radius ():
- in low Earth orbit move faster than those in higher orbits
- Planets closer to Sun () orbit faster than those farther away ()
- is the minimum speed needed for an object to break free from a planet's gravitational pull
Mass calculations from orbital data
- Kepler's third law relates (), semi-major axis (), and mass of central object ():
- Rearranging equation allows calculation of central object's mass:
- Requires knowledge of orbital period and semi-major axis of orbiting object
- Method used to determine masses of celestial bodies from satellite or companion object orbits
- Masses of planets calculated from orbits of or artificial satellites
- Masses of stars determined from orbits of companions
- Masses of galaxies estimated from orbits of stars within them
Gravitational effects and energy
- varies with distance from the center of mass
- Gravitational represents the stored energy in a system due to the relative positions of objects
Key Terms to Review (47)
$F = G \frac{m_1 m_2}{r^2}$: $F = G \frac{m_1 m_2}{r^2}$ is the mathematical expression of Newton's Universal Law of Gravitation, which describes the gravitational force between two objects with masses $m_1$ and $m_2$ that are separated by a distance $r$. This fundamental equation governs the attraction between all objects with mass in the universe.
Acceleration Due to Gravity: Acceleration due to gravity, often denoted as 'g', is the acceleration experienced by an object due to the Earth's gravitational pull. It is a fundamental concept in the study of mechanics and plays a crucial role in understanding the motion of objects near the Earth's surface.
Action at a Distance: Action at a distance refers to the ability of an object to exert a force on another object without any physical contact or intermediary medium between them. This concept is central to Newton's Universal Law of Gravitation, which describes how gravitational forces can act across vast distances in space.
Active galaxies: Active galaxies are galaxies that emit an exceptionally high amount of energy from their cores, often due to the presence of a supermassive black hole. They are characterized by their strong and variable emissions across the electromagnetic spectrum.
Asteroids: Asteroids are irregularly shaped rocky objects that orbit the Sun, typically found in the asteroid belt between the orbits of Mars and Jupiter. They are remnants of the formation of the solar system and provide valuable insights into the early history and composition of our planetary system.
Binary Star: A binary star is a system of two stars that orbit a common center of mass. These stars are gravitationally bound and revolve around each other, forming a single astronomical object that can be observed and studied as a unit.
Binary star system: A binary star system consists of two stars that orbit around a common center of mass. These systems can significantly influence the evolution and eventual death of both stars involved.
Centripetal Force: Centripetal force is the force that causes an object to move in a curved path, directing the object towards the center of the curved trajectory. It is the force that provides the necessary acceleration to maintain a circular or curved motion.
Coronal mass ejection: A Coronal Mass Ejection (CME) is a significant release of plasma and magnetic field from the Sun's corona into space. CMEs can impact space weather, potentially affecting satellites, astronauts, and power grids on Earth.
Distance: Distance is a fundamental concept in physics that refers to the measure of the separation between two points or objects in space. It is a scalar quantity, meaning it has a magnitude but no direction. Distance is a critical component in understanding various physical phenomena, including Newton's Universal Law of Gravitation.
Earth: Earth is the third planet from the Sun and the only known planet in the universe to harbor life. It is the largest and densest of the inner planets, with a diverse range of geological features, a dynamic atmosphere, and a unique position in the Solar System that has enabled the development of complex life forms.
Elliptical: An elliptical is a type of celestial object with an elongated, oval-shaped appearance. In the context of Newton's Universal Law of Gravitation, elliptical objects play a crucial role in understanding the motion and behavior of celestial bodies within a gravitational field.
Escape velocity: Escape velocity is the minimum speed an object must reach to break free from the gravitational pull of a massive body without further propulsion. In astronomy, it's crucial for understanding phenomena like black holes where gravitational forces are extreme.
Escape Velocity: Escape velocity is the minimum speed an object must attain to break free of a planet or moon's gravitational pull and enter outer space without being pulled back down. It is a fundamental concept in the study of orbital mechanics and the motion of satellites and spacecraft.
G: G, or the gravitational constant, is a fundamental physical constant that describes the strength of the gravitational force between two objects. It is a crucial parameter in Newton's Universal Law of Gravitation, which governs the motion and interactions of celestial bodies in the universe.
Galaxies: Galaxies are vast, gravitationally bound systems of stars, stellar remnants, interstellar gas, dust, and dark matter. They range in size from dwarfs with just a few hundred million stars to giants with one trillion stars, each orbiting its galaxy's center of mass. Galaxies are categorized according to their visual morphology as elliptical, spiral, or irregular. Many galaxies are thought to have supermassive black holes at their centers. The Milky Way is the galaxy that contains our Solar System, and is just one of the hundreds of billions of galaxies in the observable universe.
Gravitational Constant: The gravitational constant, denoted as 'G', is a fundamental physical constant that describes the strength of the gravitational force between two objects. It is a crucial parameter in Newton's Universal Law of Gravitation, as well as in the study of the mass and center of the Milky Way galaxy.
Gravitational Force: Gravitational force is the attractive force that exists between any two objects with mass. It is the fundamental force responsible for the motion of celestial bodies and the formation of structures in the universe, from planets to galaxies.
Inertia: Inertia is the tendency of an object to resist changes in its state of motion. It is a fundamental property of matter that describes an object's resistance to acceleration or deceleration, and it is a key concept in understanding the laws of motion and the behavior of objects in the universe.
Inverse square law: The inverse square law states that the intensity of light or radiation from a point source decreases proportionally to the square of the distance from the source. This means if you double the distance, the intensity becomes one-fourth.
Inverse Square Law: The inverse square law is a fundamental principle that describes how the strength or intensity of a force or quantity decreases with the distance from the source. It states that the intensity or effect of a force or quantity is inversely proportional to the square of the distance from the source.
Kepler's Laws: Kepler's laws are a set of three fundamental principles that describe the motion of planets around the Sun. Formulated by the 17th-century astronomer Johannes Kepler, these laws provide a mathematical framework for understanding the dynamics of the solar system and laid the groundwork for Newton's universal law of gravitation.
Mass: Mass is a fundamental property of matter that quantifies the amount of material in an object. It is a measure of the object's resistance to changes in its motion, and it is a key concept in Newton's laws of motion and his universal law of gravitation.
Mass Calculations: Mass calculations refer to the quantitative determination of the amount of matter present in an object or system. This concept is fundamental in the context of Newton's Universal Law of Gravitation, as the masses of interacting objects directly influence the gravitational force between them.
Mercury: Mercury is the closest planet to the Sun and the smallest of the eight planets in the Solar System. It is a terrestrial planet, meaning it has a solid surface, and is known for its dense composition, slow rotation, and extreme temperature variations.
Moon: The Moon is Earth's only natural satellite, a celestial body that orbits the planet and plays a crucial role in various astronomical and geological phenomena. It is a prominent feature in the night sky and has captivated humanity for millennia.
Moons: A moon is a natural satellite that orbits a planet. Moons can vary in size, composition, and geological activity.
Moons: Moons are natural satellites that orbit around planets in the Solar System. They are celestial bodies that revolve around their host planets, influenced by the planets' gravitational pull. Moons are an integral part of the planetary systems and play a crucial role in understanding the formation and evolution of planets, as well as the dynamics of the Solar System.
Neptune: Neptune is the eighth and farthest known planet from the Sun in the Solar System. It is a gas giant with a dense, blue atmosphere primarily composed of hydrogen and helium, and it is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the most distant major planet from the Sun.
Newton: Newton is the unit of force in the International System of Units (SI), named after the renowned English physicist and mathematician, Sir Isaac Newton. It is the fundamental unit used to quantify the amount of force acting on an object, and is central to understanding Newton's Universal Law of Gravitation, a key concept in classical mechanics and astrophysics.
Newton's Law of Gravitation: Newton's Law of Gravitation is a fundamental principle in physics that describes the universal attractive force between any two objects with mass. It establishes a mathematical relationship between the masses of the objects and the distance between them, allowing for the prediction and explanation of a wide range of gravitational phenomena in the universe.
Newtons: Newtons are the standard unit of force in the International System of Units (SI). They are named after the renowned physicist Sir Isaac Newton, who formulated the laws of motion and the universal law of gravitation. Newtons are a fundamental measure used to quantify the amount of force acting on an object, which is crucial in understanding the dynamics of celestial bodies and their interactions.
Orbital period: The orbital period is the time it takes for a celestial object to complete one full orbit around another object. It is commonly measured in Earth days, months, or years depending on the context of the objects involved.
Orbital Period: The orbital period is the time it takes for a celestial body, such as a planet or a moon, to complete one full revolution around its parent body or another celestial object. This term is crucial in understanding the motion and dynamics of objects within a gravitational system.
Orbital Predictions: Orbital predictions refer to the ability to forecast the future positions and movements of celestial bodies, such as planets, moons, and comets, based on the principles of gravitational dynamics. This is a fundamental aspect of astronomy and is closely tied to Newton's Universal Law of Gravitation, which governs the motion of objects in the universe.
Orbital Velocity: Orbital velocity is the speed at which an object, such as a planet or satellite, travels in its orbit around another object, typically a larger body like a star or planet. This velocity is a critical factor in determining the stability and characteristics of an object's orbit.
Planets: Planets are large, spherical celestial bodies that orbit around stars, such as the Sun, and have cleared their orbits of other objects. They are the dominant gravitational bodies in their respective solar systems and exhibit a wide range of physical characteristics, including size, composition, and atmospheric properties.
Potential Energy: Potential energy is the stored energy that an object possesses due to its position or state, which can be converted into kinetic energy or other forms of energy when the object is moved or changes its state. It is a fundamental concept in the study of physics, particularly in the context of Newton's Universal Law of Gravitation.
Satellites: Satellites are objects that orbit a larger body, such as a planet or a star, due to the force of gravity. They can be natural, like moons, or artificial, like the ones humans have launched into space to study the Earth, communicate, and explore the universe.
Semi-major Axis: The semi-major axis is a fundamental parameter that defines the size and shape of an elliptical orbit, such as the orbit of a planet around the Sun or a star around another star. It represents the average distance between the two objects in an elliptical system.
Spacecraft: A spacecraft is a vehicle or machine designed to travel and operate in outer space. It is a critical component in the exploration and utilization of space, enabling humans and robotic missions to study celestial bodies, conduct scientific experiments, and expand our understanding of the universe.
Stars: Stars are massive, luminous celestial bodies composed primarily of hot plasma and held together by their own gravity. They are the most prominent objects in the night sky and play a crucial role in the structure and evolution of the universe.
Sun: The Sun is the star at the center of the solar system, providing light, heat, and energy that sustains life on Earth. As the closest star to our planet, the Sun's gravitational influence shapes the orbits of the planets and other objects in the solar system, and its nuclear fusion powers the processes that drive the evolution of the universe.
Universal Constant: A universal constant is a fundamental physical quantity that has the same value throughout the universe, regardless of location or time. These constants are essential in describing the underlying laws and principles that govern the behavior of the physical world.
Universal law of gravitation: Newton's Universal Law of Gravitation states that every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law is fundamental in understanding the behavior of objects in orbit.
Universal Law of Gravitation: The Universal Law of Gravitation, formulated by Sir Isaac Newton, describes the fundamental force of attraction that exists between all objects with mass in the universe. It states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Vector Quantity: A vector quantity is a physical quantity that has both magnitude (size) and direction. It is used to describe quantities that require more than just a single numerical value to be fully specified, such as displacement, velocity, acceleration, and force.