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Questions and Answers
Which of the following expressions correctly represents the gravitational field intensity (E) at a distance r from a point mass M?
Which of the following expressions correctly represents the gravitational field intensity (E) at a distance r from a point mass M?
- $E = \frac{GM}{r}$
- $E = \frac{GM}{r^2}$ (correct)
- $E = \frac{GM}{r^3}$
- $E = \frac{GMr}{r^2}$
According to Newton's Law of Gravitation, the gravitational force between two objects is inversely proportional to the distance between them.
According to Newton's Law of Gravitation, the gravitational force between two objects is inversely proportional to the distance between them.
False (B)
What is the escape velocity ((v_e)) from a planet with mass (M) and radius (R)? Please provide the formula.
What is the escape velocity ((v_e)) from a planet with mass (M) and radius (R)? Please provide the formula.
$v_e = \sqrt{\frac{2GM}{R}}$
According to Kepler's Third Law, the square of the period of a satellite's orbit is proportional to the cube of the semi-major axis of its orbit, or (T^2 \propto) ______.
According to Kepler's Third Law, the square of the period of a satellite's orbit is proportional to the cube of the semi-major axis of its orbit, or (T^2 \propto) ______.
Match the following scenarios with the appropriate formula for gravitational potential (V):
Match the following scenarios with the appropriate formula for gravitational potential (V):
How does the acceleration due to gravity ((g_h)) vary with height (h) above the Earth's surface (where (h << R))?
How does the acceleration due to gravity ((g_h)) vary with height (h) above the Earth's surface (where (h << R))?
The gravitational field inside a uniform spherical shell of mass M and radius R is given by $E = \frac{GM}{R^2}$.
The gravitational field inside a uniform spherical shell of mass M and radius R is given by $E = \frac{GM}{R^2}$.
What is the formula for the period ((T)) of a satellite orbiting a planet, given the radius of the orbit ((r)) and the gravitational constant (G) and mass of the planet ((M))?
What is the formula for the period ((T)) of a satellite orbiting a planet, given the radius of the orbit ((r)) and the gravitational constant (G) and mass of the planet ((M))?
The variation of the acceleration due to gravity ((g_d)) with depth (d) below the Earth's surface is given by (g_d = g \left(1 - \frac{______}{R}\right)).
The variation of the acceleration due to gravity ((g_d)) with depth (d) below the Earth's surface is given by (g_d = g \left(1 - \frac{______}{R}\right)).
A satellite orbits Earth at a certain radius. If the radius of the orbit is increased by a factor of 4, by what factor does the orbital velocity change?
A satellite orbits Earth at a certain radius. If the radius of the orbit is increased by a factor of 4, by what factor does the orbital velocity change?
Flashcards
Newton's Law of Gravitation
Newton's Law of Gravitation
The force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Acceleration due to Gravity (g)
Acceleration due to Gravity (g)
g is equal to the Gravitational Constant times the Mass of the Earth divided by the Radius of the Earth squared.
Gravitational Potential Energy (U)
Gravitational Potential Energy (U)
The energy required to separate two masses to infinity.
Escape Velocity (v_e)
Escape Velocity (v_e)
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Gravitational Field Intensity (E)
Gravitational Field Intensity (E)
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Gravitational Potential (V)
Gravitational Potential (V)
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Orbital Velocity (v_o)
Orbital Velocity (v_o)
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Time Period of a Satellite (T)
Time Period of a Satellite (T)
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Kepler's Third Law
Kepler's Third Law
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Variation of g with Height (h)
Variation of g with Height (h)
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Study Notes
- Newton's Law of Gravitation: ( F = \frac{G \cdot m_1 \cdot m_2}{r^2} )
- Acceleration due to Gravity, denoted as g: ( g = \frac{GM}{R^2} )
- Gravitational Potential Energy, denoted as U: ( U = -\frac{G \cdot m_1 \cdot m_2}{r} )
- Escape Velocity, denoted as ( v_e ): ( v_e = \sqrt{\frac{2GM}{R}} )
- Gravitational Field Intensity, denoted as E: ( E = \frac{GM}{r^2} )
- Gravitational Potential, denoted as V: ( V = -\frac{GM}{r} )
- Orbital Velocity, denoted as ( v_o ): ( v_o = \sqrt{\frac{GM}{r}} )
- Time Period of a Satellite, denoted as T: ( T = 2\pi \sqrt{\frac{r^3}{GM}} )
- Kepler's Third Law: ( T^2 \propto r^3 ) or ( \frac{T_1^2}{T_2^2} = \frac{r_1^3}{r_2^3} )
- Variation of g with Height (h): ( g_h = g \left(1 - \frac{2h}{R}\right) ) for ( h << R )
- Variation of g with Depth (d): ( g_d = g \left(1 - \frac{d}{R}\right) )
- Gravitational Potential for a Shell (Outside): ( V = -\frac{GM}{r} ) for ( r > R )
- Gravitational Potential for a Shell (Inside): ( V = -\frac{GM}{R} ) for ( r < R )
- Gravitational Field for a Shell (Outside): ( E = \frac{GM}{r^2} ) for ( r > R )
- Gravitational Field for a Shell (Inside): ( E = 0 ) for ( r < R )
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Description
Key formulas and concepts related to gravity. Covers Newton's law of gravitation, gravitational potential energy, escape velocity, and more. Also includes variations in gravitational acceleration with height and depth. Provides a concise overview of gravitational principles.
