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What does the gravitational force depend on?
What does the gravitational force depend on?
The universal gravitational constant G is constant regardless of the masses of the objects.
The universal gravitational constant G is constant regardless of the masses of the objects.
True
Who published the Principia Mathematica?
Who published the Principia Mathematica?
Sir Isaac Newton
According to Newton's law of gravitation, the force of attraction F is given by F = G * ____.
According to Newton's law of gravitation, the force of attraction F is given by F = G * ____.
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Match the following terms with their correct descriptions:
Match the following terms with their correct descriptions:
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In vector form, the force exerted on particle m2 by particle m1 is represented as:
In vector form, the force exerted on particle m2 by particle m1 is represented as:
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The distance used in the gravitational force formula is always squared.
The distance used in the gravitational force formula is always squared.
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If two unit masses are placed at a unit distance apart, the gravitational force between them is equal to the value of ____.
If two unit masses are placed at a unit distance apart, the gravitational force between them is equal to the value of ____.
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What is the value of G?
What is the value of G?
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The gravitational force is dependent on the medium between two masses.
The gravitational force is dependent on the medium between two masses.
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State the dimensions of the gravitational constant G.
State the dimensions of the gravitational constant G.
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The gravitational force between two particles acts along the line that connects them and they are part of an action-reaction pair known as Newton's _______ law.
The gravitational force between two particles acts along the line that connects them and they are part of an action-reaction pair known as Newton's _______ law.
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What happens to the acceleration due to gravity g at a height h above the Earth's surface?
What happens to the acceleration due to gravity g at a height h above the Earth's surface?
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The weight of a body at height h can be expressed as mg h = GMm/(R + h)^2.
The weight of a body at height h can be expressed as mg h = GMm/(R + h)^2.
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What is the relationship for g at a very small height h above the Earth's surface?
What is the relationship for g at a very small height h above the Earth's surface?
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Match the values with their corresponding meanings:
Match the values with their corresponding meanings:
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What is the formula for escape velocity (Ve) in terms of gravitational acceleration (g) and the radius of the Earth (R)?
What is the formula for escape velocity (Ve) in terms of gravitational acceleration (g) and the radius of the Earth (R)?
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What height above the Earth's surface do geostationary satellites typically orbit?
What height above the Earth's surface do geostationary satellites typically orbit?
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The escape velocity of a body from the surface of the Earth is equal to its critical velocity when revolving close to the Earth's surface.
The escape velocity of a body from the surface of the Earth is equal to its critical velocity when revolving close to the Earth's surface.
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What is the mean density of a planet represented by?
What is the mean density of a planet represented by?
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Astronauts experience weightlessness because there is no gravitational force acting on them.
Astronauts experience weightlessness because there is no gravitational force acting on them.
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The velocity at which a satellite is in a state of free fall towards Earth without falling is called its __________.
The velocity at which a satellite is in a state of free fall towards Earth without falling is called its __________.
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What is one primary use of communication satellites?
What is one primary use of communication satellites?
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The weight of a body is defined as the gravitational force that pulls it towards the ________.
The weight of a body is defined as the gravitational force that pulls it towards the ________.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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What results from equating centripetal force to gravitational force for a body in circular orbit near Earth's surface?
What results from equating centripetal force to gravitational force for a body in circular orbit near Earth's surface?
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Match the following terms with their descriptions:
Match the following terms with their descriptions:
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The escape velocity from Earth is derived from the formula $v_e = rac{2GM}{R}$.
The escape velocity from Earth is derived from the formula $v_e = rac{2GM}{R}$.
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What phenomenon is experienced by astronauts during the initial hours of weightlessness?
What phenomenon is experienced by astronauts during the initial hours of weightlessness?
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The weight of an object (mg) can be expressed as the product of its mass (m) and the acceleration due to gravity (g), which is derived from the equation __________.
The weight of an object (mg) can be expressed as the product of its mass (m) and the acceleration due to gravity (g), which is derived from the equation __________.
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Kepler's Law states that each planet orbits the sun in a circular path.
Kepler's Law states that each planet orbits the sun in a circular path.
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In an orbiting satellite, the astronaut and the satellite share the same ________ towards the center of the Earth.
In an orbiting satellite, the astronaut and the satellite share the same ________ towards the center of the Earth.
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What is the formula for calculating eccentricity (e) of an ellipse?
What is the formula for calculating eccentricity (e) of an ellipse?
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The distance of the closest approach to the sun is called apogee.
The distance of the closest approach to the sun is called apogee.
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What does the law of areas state regarding the movement of planets?
What does the law of areas state regarding the movement of planets?
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The apogee of a planet can be calculated using the formula ______.
The apogee of a planet can be calculated using the formula ______.
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Match the terms related to orbits with their definitions:
Match the terms related to orbits with their definitions:
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According to the law of periods, which of the following statements is true?
According to the law of periods, which of the following statements is true?
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Gravity is a type of force that always acts outward from the Earth's center.
Gravity is a type of force that always acts outward from the Earth's center.
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What is the relationship between the gravitational pull and weight of a body?
What is the relationship between the gravitational pull and weight of a body?
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What is the mass of the Earth?
What is the mass of the Earth?
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The critical minimum velocity needed for a satellite to maintain a circular orbit around the Earth is 8 km/sec.
The critical minimum velocity needed for a satellite to maintain a circular orbit around the Earth is 8 km/sec.
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What celestial body has a mean radius of $1.74 \times 10^{6}$ m?
What celestial body has a mean radius of $1.74 \times 10^{6}$ m?
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Newton's second law of motion states that F = _____, where F is the external force, mi is the inertial mass, and a is the acceleration.
Newton's second law of motion states that F = _____, where F is the external force, mi is the inertial mass, and a is the acceleration.
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Match the following celestial bodies to their mean densities (10 kg/m^3):
Match the following celestial bodies to their mean densities (10 kg/m^3):
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What happens if the energy of a satellite in orbit is too low?
What happens if the energy of a satellite in orbit is too low?
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Gravitational mass is defined in the same manner as inertial mass.
Gravitational mass is defined in the same manner as inertial mass.
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Which body has the mean radius of $6.37 \times 10^{6}$ m?
Which body has the mean radius of $6.37 \times 10^{6}$ m?
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Study Notes
Introduction to Gravitation
- The universe consists of galaxies, stars, planets, comets, asteroids, and meteoroids.
- Gravitation is a natural force that causes objects to attract each other.
- Sir Isaac Newton described the inverse-square law of gravitation in his Principia Mathematica.
Newton's Law of Gravitation
- Definition: Every particle of matter attracts every other particle of matter with a force that is proportional to the product of their masses and inversely proportional to the square of their separation.
- Mathematical form: F ∝ (m₁m₂)/r² where F is the force of attraction, m₁ and m₂ are the masses of the particles, and r is the distance between them.
- Vector form: The force exerted on particle m₂ by particle m₁ is given by F₂₁ = -G m₁m₂ î₂₁ / r²₁₂, where î₂₁ is a unit vector from m₁ to m₂.
Universal Gravitational Constant (G)
- G = F r²/m₁m₂
- The force of attraction between two unit masses at a unit distance is equal to G numerically.
- G = 6.67 × 10⁻¹¹ Nm²/kg²
- G has dimensions of M⁻¹L³T⁻².
Variation in 'g'
- Acceleration due to gravity at a height (h): g' = g ( R² / (R + h)²), where g is the acceleration due to gravity at the surface of the earth and R is the radius of the earth.
- Acceleration due to gravity at a depth (d): g' = g (1 - d/R), where d is the depth and R is the radius of the earth.
Effect of altitude
- Acceleration due to gravity decreases with altitude.
Effect of depth
- Acceleration due to gravity decreases with depth.
Variation of 'g' with latitude
- g' = g - Rω² cos²λ, where g' is the acceleration due to gravity at a point on the earth's surface, g is the acceleration due to gravity at the equator, λ is the latitude, and ω is the angular velocity of the earth.
- At the poles, g' = g, and at the equator, g' = g - Rω², which results in a difference in g, showing the effect of earth's rotation.
Satellite
- Any smaller body revolving around a larger body due to gravity is known as a satellite.
- Satellites can be natural (like the moon) or artificial.
- Artificial satellites are launched by humans into circular orbits.
- The minimum two-stage rocket is required to launch a satellite in a circular orbit around a planet.
Satellite Projection
- Depending on the horizontal velocity, the satellite can follow an elliptical, parabolic, or hyperbolic path.
- Critical velocity: Projections with critical velocity result in a circular orbit.
- Escape velocity: Projections with an escape velocity result in a hyperbolic path, allowing the satellite to escape the earth's gravitational field.
Orbital Velocity
- Definition: The minimum horizontal velocity required for a satellite to orbit the earth in a circular path is called orbital velocity.
- Expression: v = √(GM/(R + h)), where G is the gravitational constant, M is the mass of the earth, and (R + h) is the radius of the orbit.
Gravitational Potential
- Work done per unit mass to move a mass from infinity to a specific point in a gravitational field defines the gravitational potential at that point.
- The formula for gravitational potential is V = -GM/r.
Gravitational Potential Energy
- The work done in taking a body from infinity to a specific point defines the gravitational potential energy. This energy increases with distance and is negative for the earth-bound bodies.
Escape Velocity
- The minimum velocity required for a body to escape from the gravitational pull of a planet is called the escape velocity. Its value depends on the mass and radius of the planet.
- Formula: vₑ = √(2GM/R).
Communication Satellites
- Artificial satellites, designed for communication purposes, are placed in geostationary or geosynchronous orbits with the same period as the Earth's rotation.
- This ensures that they appear stationary relative to Earth's surface.
Weightlessness
- Weightlessness is a phenomenon where the apparent weight is zero for a reason other than being no weight at all.
- It occurs when the acceleration of a body equals that of the environment, making both forces equal and opposite resulting in no apparent weight.
Kepler's Laws
- Kepler's First Law: Planets orbit the sun in elliptical paths with the sun at one focus.
- Kepler's Second Law: A line joining a planet and the sun sweeps out equal areas during equal intervals of time.
- Kepler's Third Law: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
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Description
Explore the fundamentals of gravitation, including Sir Isaac Newton's laws and the universal gravitational constant. This quiz covers essential concepts such as the inverse-square law and mathematical representations of gravitational force. Test your understanding of how celestial bodies interact through gravitational forces.
