6.5 Newton’s Universal Law of Gravitation
3 min read•june 18, 2024
Gravity shapes our universe, pulling everything from planets to people together. explains this force, showing how mass and distance affect attraction between objects. It's the reason we stay grounded and planets orbit the sun.
This law helps us understand Earth's tides, caused by the moon's pull, and why astronauts float in space. It's not just about falling apples – gravity governs the motion of celestial bodies and even affects how we launch satellites.
Newton's Universal Law of Gravitation
Newton's Universal Law of Gravitation
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- States every particle attracts every other particle with force proportional to product of masses and inversely proportional to square of distance between them ()
- Mathematically expressed as
- between two objects (N)
- ()
- and masses of two objects (kg)
- distance between centers of two objects (m)
- Explains as result of gravitational force exerted by Earth on nearby objects
- Force of gravity on object near Earth's surface given by
- force of gravity or weight (N)
- mass of object (kg)
- near Earth's surface ()
- Force of gravity on object near Earth's surface given by
Calculation of gravitational forces
- Calculate gravitational force using formula
- Identify masses of two objects and in kg
- Determine distance between centers of objects in m
- Substitute values into formula and calculate gravitational force in N
- Example calculation: gravitational force between Earth (mass kg) and Moon (mass kg) with distance of m
Moon's gravity and Earth's tides
- Moon exerts gravitational force on Earth causing ocean tides
- Tides are rise and fall of sea levels due to combined gravitational forces of Moon and Sun and Earth's rotation
- occur during new moon and full moon when Sun, Earth, and Moon aligned
- Gravitational forces of Moon and Sun combine resulting in higher high tides and lower low tides
- occur during first and third quarter moons when Sun and Moon at right angles relative to Earth
- Gravitational forces of Moon and Sun partially cancel resulting in lower high tides and higher low tides
- difference between high and low tides varies by location (Bay of Fundy up to 16 m, Gulf of Mexico less than 1 m)
Apparent weightlessness in orbit
- Occurs when object in such as orbiting spacecraft
- Spacecraft and contents constantly falling towards Earth due to gravity
- High forward velocity causes spacecraft to continually miss Earth and remain in orbit
- Objects inside spacecraft experience as they fall at same rate as spacecraft
- No normal force acting on objects making them appear to float
- Different from zero gravity as gravity still acts on spacecraft and contents
- Effects not felt due to constant free fall motion
- Experienced by astronauts on International Space Station orbiting Earth at altitude of ~400 km
Celestial Mechanics and Orbital Motion
- studies motion of celestial bodies under influence of gravity
- describes path of objects moving under gravitational influence of another body
- Planets orbiting Sun and satellites orbiting Earth follow elliptical paths
- represents region where object experiences gravitational force
- Strength of field decreases with distance from massive object
- is minimum speed object needs to break free from gravitational pull of a body
- Depends on mass of body and distance from its center
Key Terms to Review (25)
$F = G \frac{m_1 m_2}{r^2}$: $F = G \frac{m_1 m_2}{r^2}$ is the mathematical expression that represents Newton's Universal Law of Gravitation, which describes the gravitational force between two objects. This equation shows that the force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
$F_g = mg$: $F_g = mg$ is the equation that represents the force of gravity, or the gravitational force, acting on an object. This term is fundamental in understanding both projectile motion and Newton's universal law of gravitation, as it describes the force that governs the motion of objects under the influence of gravity.
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. This constant acceleration acts on all objects near the Earth's surface, causing them to experience a downward force and a change in velocity over time.
Apparent Weightlessness: Apparent weightlessness refers to the state of an object or person experiencing the sensation of being weightless, even though they are still under the influence of gravity. This phenomenon is often observed in the context of Newton's Universal Law of Gravitation, which describes the gravitational force between objects.
Celestial Mechanics: Celestial mechanics is the branch of astronomy that deals with the motion of objects in the universe, particularly planets, stars, and other celestial bodies, under the influence of gravity. It provides a mathematical framework for understanding the dynamics and evolution of these systems.
Earth's gravity: Earth's gravity is the force that attracts objects toward the center of the Earth, primarily due to its mass. This gravitational pull keeps everything from people to oceans anchored to the planet and plays a crucial role in the movement of celestial bodies. It is fundamental in understanding how objects interact with one another and influences phenomena like tides, orbits, and weight.
Escape velocity: Escape velocity is the minimum speed an object must reach to break free from a celestial body's gravitational pull without further propulsion. It depends on the mass and radius of the celestial body.
Escape Velocity: Escape velocity is the minimum speed an object must attain to break free of a planet or moon's gravitational pull and leave its orbit. It is a crucial concept in the study of orbital mechanics and the launch of spacecraft.
Free Fall: Free fall is the motion of an object where gravity is the only force acting upon it, leading to uniform acceleration towards the center of a gravitational field. This concept is crucial for understanding how objects behave when they are dropped or thrown, as it allows for the application of motion equations to describe their motion under constant acceleration.
Gravitational Attraction: Gravitational attraction is the fundamental force of nature that attracts objects with mass towards one another. This force, described by Newton's Universal Law of Gravitation, is responsible for the motion of celestial bodies, the weight of objects, and the formation of structures in the universe.
Gravitational constant: The gravitational constant, denoted as $G$, is a fundamental physical constant that quantifies the strength of gravitational attraction between masses. Its value is approximately $6.67430 \times 10^{-11} \, m^3 kg^{-1} s^{-2}$.
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 and plays a significant role in understanding the nature of gravity and its effects on the universe.
Gravitational Field: The gravitational field is a region of space surrounding a massive object, such as a planet or star, where the force of gravity acts upon other objects. It describes the strength and direction of the gravitational force at every point in that region of space.
Gravitational Force: Gravitational force is the attractive force that exists between any two objects with mass. It is the force that causes objects to be pulled towards each other and is responsible for the motion of celestial bodies as well as the acceleration of objects near the Earth's surface.
Inverse Square Law: The inverse square law is a fundamental principle that describes how the strength or intensity of a force or property decreases with the square of the distance from the source. This law applies to various physical phenomena, including gravitational, electrical, and sound fields.
Isaac Newton: Isaac Newton was a renowned physicist and mathematician, credited with formulating the laws of motion and universal gravitation, which laid the foundation for classical mechanics. His work revolutionized our understanding of motion and forces, influencing various fields in science and mathematics, and providing essential insights into the nature of physical interactions.
Microgravity: Microgravity is a condition in which objects appear to be weightless and experience very small forces of gravity. This occurs when an object is in free-fall or orbit, effectively creating a state of continuous free fall towards Earth.
Neap Tides: Neap tides are a type of tide that occurs when the gravitational pull of the sun and moon are at right angles to each other, resulting in a smaller difference between high and low tides. This phenomenon is directly related to Newton's Universal Law of Gravitation, which describes the gravitational forces acting between celestial bodies.
Newton’s universal law of gravitation: Newton’s Universal Law of Gravitation states that every particle 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 mathematically expressed as $F = G \frac{m_1 m_2}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between their centers.
Newton's Universal Law of Gravitation: Newton's Universal Law of Gravitation states that every mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law helps explain the gravitational interaction between objects, such as planets and stars, and is fundamental to understanding orbits and celestial mechanics.
Orbital Motion: Orbital motion refers to the circular or elliptical path that an object, such as a planet or satellite, takes around another object due to the force of gravity. It is a fundamental concept in the study of celestial mechanics and planetary motion.
Proportionality: Proportionality refers to the relationship between two quantities where a change in one quantity results in a corresponding change in another quantity, maintaining a constant ratio. This concept is crucial in understanding how variables relate to each other, and it often helps simplify complex problems by allowing approximations. When two quantities are proportional, they can be expressed mathematically, making it easier to analyze their behavior under various conditions.
Spring Tides: Spring tides are exceptionally high and low tides that occur when the gravitational pull of the Sun and Moon align, resulting in a greater combined gravitational force that causes more extreme tidal ranges. This phenomenon is directly related to Newton's Universal Law of Gravitation, which describes the attractive force between objects with mass.
Tidal Range: Tidal range refers to the vertical difference in height between high tide and low tide in a specific location. This phenomenon is primarily influenced by the gravitational pull of the moon and the sun, which are described by Newton's Universal Law of Gravitation, affecting the movement of water in oceans and seas. The tidal range can vary significantly depending on geographical features, such as coastal shape and water depth, as well as astronomical factors like the positions of the moon and sun.
Universal Gravitation: Universal gravitation is the fundamental principle that describes the attractive force between any two objects with mass, which depends on the masses of the objects and the distance between them. This concept is central to understanding how celestial bodies interact in space, influencing everything from the orbits of planets around the sun to the motion of satellites and the structure of galaxies.