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7.4 - THE GRAVITATIONAL CONSTANT

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Introduction to the Gravitational Constant

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Teacher
Teacher

Today, we're discussing the gravitational constant, symbolized as G. Can anyone tell me how gravitational attraction is calculated?

Student 1
Student 1

Is it related to the mass of the two objects and the distance between them?

Teacher
Teacher

Exactly! The gravitational force between two objects depends on their masses and the distance that separates them, according to Newton's law of universal gravitation. G is the factor that applies to this relationship.

Student 2
Student 2

Why is G considered a constant?

Teacher
Teacher

G is termed a constant because it does not change regardless of the mass or distance involved in the interaction. Its value remains consistent at approximately 6.67 × 10^(-11) N m²/kg².

Student 3
Student 3

Who first measured this value?

Teacher
Teacher

Good question! The gravitational constant was first experimentally determined by Henry Cavendish in 1798 using a special apparatus. Let's explore how he did that.

Henry Cavendish's Experiment

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Teacher
Teacher

Cavendish used a torsion balance. Can anyone visualize how that apparatus worked?

Student 1
Student 1

Was it a pendulum or something similar?

Teacher
Teacher

Yes! It was a horizontal bar suspended from a wire with lead spheres attached at each end. When larger spheres were placed next to them, they exerted a gravitational force which made the bar twist.

Student 2
Student 2

How did he measure the angle of rotation?

Teacher
Teacher

Cavendish observed the angle at which the bar rotated, and this allowed him to calculate the gravitational force between the spheres, leading him to determine G.

Student 3
Student 3

And from that, he calculated the mass of the Earth too?

Teacher
Teacher

Absolutely! This was a monumental experiment that provided key insights into gravity and mass.

The Value and Importance of G

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Teacher
Teacher

So, to summarize, the gravitational constant is crucial for defining the strength of gravity. How does this affect our calculations in physics?

Student 1
Student 1

It helps us determine the force between any two masses.

Student 2
Student 2

And it’s essential for understanding celestial mechanics too!

Teacher
Teacher

Correct! Applications of G range from calculating orbits of planets to predicting movements of galaxies. It's the cornerstone of gravitational physics.

Introduction & Overview

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Quick Overview

The gravitational constant (G) quantifies the strength of gravitational forces among masses and was first measured by Henry Cavendish in 1798.

Standard

The gravitational constant, denoted as G, is a fundamental constant in physics that describes the strength of gravitational attraction between two masses. It was determined experimentally by Henry Cavendish in the late 18th century using a balance technique and remains a critical value in the field of gravitational physics, helping to form the basis of Newton's law of gravitation.

Detailed

The Gravitational Constant

The gravitational constant (G) is a key figure in the universal law of gravitation, signifying the proportionality factor that relates the gravitational force between two masses to the product of their masses and the inverse of the square of the distance between them. The value of G was first determined through experiments conducted by Henry Cavendish in 1798, making use of a torsion balance to measure the tiny gravitational forces between lead spheres.

Cavendish’s Experiment

Cavendish's apparatus involved a horizontal bar suspended from a wire, with small lead spheres attached at each end. Large lead spheres were then placed near the smaller ones. Due to gravitational attraction, the bar rotated slightly, and the angle of rotation could be measured. This experiment allowed Cavendish to not only measure G accurately but also estimate the mass of the Earth, confirming the efficacy of the gravitational theory.

Current Value

The currently accepted value of the gravitational constant is:

G = 6.67 × 10^(-11) N m²/kg²

This value is fundamental for calculations involving gravitational forces in astrophysics and cosmology.

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Audio Book

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Cavendish's Experiment

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The value of the gravitational constant G entering the Universal law of gravitation can be determined experimentally and this was first done by English scientist Henry Cavendish in 1798. The apparatus used by him is schematically shown in Fig.7.6...

Detailed Explanation

Henry Cavendish conducted a groundbreaking experiment to measure the gravitational constant G in 1798. He designed a device that consisted of a horizontal bar suspended from a wire, with small lead spheres attached to each end of the bar. When larger lead spheres were brought near the smaller spheres, the gravitational attraction caused the bar to rotate, due to the torque generated on it. By measuring the angle of rotation, Cavendish could quantify the gravitational force between the masses, which allowed him to calculate G.

Examples & Analogies

Imagine you have two magnets and you want to measure their pulling force. Instead of just using scales to weigh them, you use a string and a piece of paper to see how much the paper bends when you bring the magnets close. This bending indicates how strong the magnets pull on each other, just like Cavendish observed how the bar rotated to indicate the gravitational force.

Understanding G and its Measurement

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The bar AB has two small lead spheres attached at its ends. The bar is suspended from a rigid support by a fine wire. Two large lead spheres are brought close to the small ones but on opposite sides as shown...

Detailed Explanation

In Cavendish's setup, the gravitational force between the large and small spheres created a torque on the suspended bar. The experiment measured the angle through which the bar twisted, a direct indication of the gravitational force at play. With the known distance between the masses and the measured angle of twist, Cavendish could derive a value for G, leading to a better understanding of gravitational interactions.

Examples & Analogies

Think of spinning a playground swing. If you sit on one side and someone on the other swings their legs to push you, you'd feel the twist. Similar to how Cavendish felt the twist of the bar, he could relate that twist to how strongly the masses attracted each other, telling us how strongly gravity works between those masses.

Value of the Gravitational Constant

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Since Cavendish’s experiment, the measurement of G has been refined and the currently accepted value is G = 6.67×10^-11 N m2/kg2.

Detailed Explanation

The gravitational constant, G, is a crucial parameter in Newton's law of gravitation. The value of G indicates how strong the gravitational force is between two masses. Currently, it stands at 6.67×10^-11 N m²/kg². This low value means that gravity is a relatively weak force compared to other fundamental forces like electromagnetism. Understanding G is vital for calculating the gravitational pull between objects of significant mass, like planets and stars.

Examples & Analogies

If you think about gravity, it's like a soft glue holding things together. Just as you need a lot of glue to hold heavy things, you need masses that are large (like planets) for gravity to be strong enough to feel significant. The small value of G assures us that even a tiny fraction of mass can result in a weak force, which is why we don’t notice gravity from small objects like books or chairs.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Gravitational Constant (G): Measures the strength of gravitational attraction between two masses.

  • Cavendish Experiment: The first experiment that accurately determined the value of G.

  • Newton's Law of Universal Gravitation: Describes how masses interact via gravity.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Cavendish's experiment utilized a torsion balance to measure gravitational forces, allowing for the calculation of G.

  • The gravitational force between two objects can be calculated using the formula F = G * (m1 * m2) / r².

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • G keeps it grand in the gravity land, 6.67, it holds tight, for masses in orbit and in flight.

📖 Fascinating Stories

  • Imagine Cavendish in a dark lab with heavy lead balls, twisting wires, capturing gravity’s calls, he found G, a key to gravity's thrall.

🧠 Other Memory Gems

  • Remember G as 'Great Gravitational Force' – with a value that stays consistent, never off course.

🎯 Super Acronyms

G

  • Gravitational constant; M

Flash Cards

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Glossary of Terms

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  • Term: Gravitational Constant (G)

    Definition:

    A constant that measures the strength of gravitational attraction between two masses, approximately equal to 6.67 × 10^(-11) N m²/kg².

  • Term: Cavendish Experiment

    Definition:

    An experiment conducted by Henry Cavendish to measure the gravitational constant using a torsion balance.

  • Term: Universal Law of Gravitation

    Definition:

    A law stating that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.