L'expérience de Cavendish, menée de manière célèbre par Henry Cavendish en 1798, n'était pas qu'une prouesse de brillance expérimentale ; elle a marqué un tournant dans notre compréhension de la gravité et de l'univers. Bien que conçue initialement pour déterminer la densité de la Terre, son impact s'étend bien au-delà de notre planète, influençant considérablement le domaine de l'astronomie stellaire.
L'expérience :
L'expérience elle-même est relativement simple en principe, mais incroyablement ingénieuse dans son exécution. Elle impliquait une balance de torsion, un appareil délicat composé d'une tige légère suspendue à un fil fin. Aux extrémités de cette tige, deux petites boules de plomb étaient attachées. En plaçant stratégiquement deux sphères de plomb plus grandes près des plus petites, Cavendish a observé la légère force de torsion, ou torsion, exercée sur le fil en raison de l'attraction gravitationnelle.
En mesurant la période d'oscillation de la tige, Cavendish pouvait ensuite calculer la force d'attraction entre les sphères. Cela, combiné aux masses connues et aux distances impliquées, lui a permis de déterminer la constante gravitationnelle universelle, 'G', une constante fondamentale de la nature qui régit l'attraction gravitationnelle entre deux objets quelconques.
Impact sur l'astronomie stellaire :
La contribution de l'expérience de Cavendish à l'astronomie stellaire peut sembler indirecte, mais elle est fondamentale. En fournissant la valeur de 'G', elle a permis aux astronomes de :
Au-delà de la Terre :
L'héritage de l'expérience de Cavendish s'étend également à d'autres domaines de la physique. Elle a fourni les bases de la compréhension de la gravité à l'échelle cosmique, ouvrant la voie à la théorie de la relativité générale d'Einstein, qui a révolutionné notre compréhension de l'espace et du temps.
L'expérience de Cavendish est un témoignage de la puissance de la science expérimentale. Initialement conçue pour mesurer la densité de notre planète, son impact continue de résonner dans le vaste cosmos, façonnant notre compréhension de l'univers et de ses merveilles invisibles.
Instructions: Choose the best answer for each question.
1. What was the primary objective of the Cavendish Experiment?
(a) To measure the speed of light (b) To determine the Earth's density (c) To prove the existence of gravity (d) To calculate the distance to the nearest star
(b) To determine the Earth's density
2. What apparatus did Cavendish use in his experiment?
(a) A telescope (b) A pendulum (c) A torsion balance (d) A barometer
(c) A torsion balance
3. What fundamental constant of nature did Cavendish determine through his experiment?
(a) The speed of light (c) (b) The gravitational constant (G) (c) Planck's constant (h) (d) Boltzmann's constant (k)
(b) The gravitational constant (G)
4. How does the Cavendish Experiment contribute to understanding stellar astronomy?
(a) By providing the value of 'G', it allows astronomers to calculate the masses of stars. (b) By providing the value of 'G', it allows astronomers to measure the distance to stars. (c) By providing the value of 'G', it allows astronomers to predict the lifespan of stars. (d) By providing the value of 'G', it allows astronomers to determine the composition of stars.
(a) By providing the value of 'G', it allows astronomers to calculate the masses of stars.
5. What is a significant implication of the Cavendish Experiment's results for modern astrophysics?
(a) It led to the discovery of the expanding universe. (b) It led to the concept of dark matter. (c) It led to the development of the Hubble Telescope. (d) It led to the discovery of new planets in our solar system.
(b) It led to the concept of dark matter.
Imagine you are a young astronomer studying a binary star system. You have observed the orbital period of the stars and their separation distance. Using the knowledge gained from the Cavendish Experiment, explain how you would calculate the masses of the two stars.
Here's how to calculate the masses of the stars in a binary system using the Cavendish Experiment's legacy:
1. **Newton's Law of Universal Gravitation:** The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This can be expressed as:
F = G * (m1 * m2) / r^2
Where: * F is the gravitational force * G is the universal gravitational constant (determined by Cavendish) * m1 and m2 are the masses of the two stars * r is the distance between the stars
2. **Centripetal Force:** In a binary system, the stars are in orbit around each other, experiencing a centripetal force that keeps them in their orbits. This force is equal to the gravitational force between them.
Fc = (m * v^2) / r
Where: * Fc is the centripetal force * m is the mass of one star * v is the orbital velocity of the star * r is the separation distance between the stars
3. **Equating Forces:** Since the gravitational force and the centripetal force are equal, we can equate the two equations above:
G * (m1 * m2) / r^2 = (m * v^2) / r
4. **Orbital Velocity:** We know that the orbital period (T) of a star is related to its orbital velocity (v) and the separation distance (r) by:
v = 2 * pi * r / T
5. **Solving for Mass:** By substituting the expression for orbital velocity into the equation for equal forces and rearranging, we can derive an equation to solve for the mass of one star (m1) in terms of the other star's mass (m2), the orbital period (T), and the separation distance (r):
m1 = (4 * pi^2 * r^3) / (G * T^2 * m2)
6. **Determining Both Masses:** To find the masses of both stars, we need one additional piece of information. This could be the ratio of their masses, or the observed motion of one star relative to the other.
By following these steps, using the known values for G, T, and r, and with the additional information about the stars' masses, we can calculate the individual masses of the stars in a binary system.
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