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Gravitation
The configuration and motion of the Earth, the Sun and the other planets in the Solar System was
debated for ages, till Ptolemy, a Greek scientist, put forward his geocentric theory
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They are the Law of Orbits
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According to Kepler's Second Law, the Sun is the center of the
arcane of the Sun, the planets are under the influence of a central source
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The Law of Periods can be understood by the
fact that the angular momentum of the planet revolving in its orbit remains constant
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The concept can be understood by the concept that the angular momentum of the planet
revolving around the Sun remains constant
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The force of gravity pulls Kepler's Laws revolutionized the field of
astronomy and have helped people understand the configuration and movement of planets better
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The force of attraction between two bodies applies to
all the bodies in the universe
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The Moon revolving around
the Earth has a centripetal force which is due to the Earth's gravitational force which makes it follow a
curved path
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The gravity force between a planet and the Sun is similar as that between the Earth and the
Moon
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Planet towards the Sun
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Newton concluded that the magnitude of the Earth's gravitational force decreases with distance
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The Law can be expressed as shown here:
F = (G * m1 * m2) / r2
Here, m1 and m2 are point masses and r is the distance between the two particles
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Newton concluded that the
gravity of the Earth's gravity force decreased with distance by its time period
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The gravitational force between extended objects can vary depending on the situation
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This is described
by the universal gravitational constant, "g," which is constant throughout the universe
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To calculate the gravitational forces between extended bodies, calculus is used
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" This means that the net force on "m1" is given by adding the
forces of "s21," "f31," "f41," and "s51
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The system of horizontal rods rotates
until the torque due to the gravitational force between the spheres equals the restoring torque on them
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Lamp and Scale Arrangement
The accurate value of "g" is found to be 6
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By knowing this value, along with
the radius of the Earth and the time it takes for a body to descend from a known height, we can measure
the gravity, and subsequently, determine the mass and density of the planet
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Equation 3 represents the gravitational force on a body placed at a given height from the surface of the
Earth
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Equation 4 shows that the weight of a body at a certain height is "mgh,"
where "g" is the acceleration due to gravity at that height
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Acceleration due to gravity at the surface of a sphere of radius r minus d can be expressed as Equation
12: g(d) = g / (re - d)^2 * ms
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By comparing the ratios found in Equations 10 and 13, we can arrive at an
equation for the acceleration due to gravity at a certain depth inside the Earth
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When
considering gravitational force between two particles, the force of attraction between two particles of
masses m1 and m2 separated by distance r acts along d
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The potential energy of a
two-particle system changes as the second particle moves from b to c, with this change being a function
of the distance r
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The gravitational potential energy of a two-particle system can be defined as zero when one particle is
at infinity and the second is at position r
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For a threeparticle system, the total potential energy is given by the sum of the energies of all possible pairs of
constituent particles
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This is a function of the
masses of the objects involved, and is sometimes referred to as the "escape velocity"
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The total energy of a
body on the surface is the sum of its kinetic and potential energies and is the total energy at position a
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The body escapes the gravitational field when it escapes the Earth's gravitational field
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The escape speed of a human body or any other body on a given planet does not depend on the mass of
the body, but rather depends on the acceleration due to gravity on the surface of the planet and the
planet's mass and radius
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The total
energy of a two-body system is determined by the sum of its kinetic energy and potential energy, and so
the total energy is determined
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The Earth's natural satellite is the moon
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In a broader sense, there are two categories of artificial satellites, namely
geosynchronous and sun-synchronous satellites
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Satellites are mainly used for effective communication, and apart from that, they are also used for other
purposes like analyzing weather conditions in a region, exploration of minerals from the Earth, and for
geographical purposes
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Satellites are often used for the transmission of cricket matches through television and for exploration of
minerals of the Earth
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The speed of a satellite in its orbit can be calculated using the formula:
li = √(GMe/re+8)
Where Me is the mass of the earth and G is the universal gravitational constant
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The second type of artificial satellite is called a sunsynchronous satellite, also known as a polar satellite
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This results in a time period of a few hours
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The polar satellite, on the other hand, is primarily used for telecommunications and mass
communications
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This ensures that the satellite moves closely to
the poles of the earth in every revolution
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Similarly, a satellite orbiting the
earth is in freefall due to the gravitational pull of the earth
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The weight of a body is the force it experiences due to the gravitational pull of the earth
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The spring balance reads zero weight of the body in this situation, which is the weightlessness
of the body
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This results in the entire globe being scanned in a single day
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