Physics Chapter on Gravitational Forces

The law of areas states that the rate at which a planet sweeps out area in its orbit is constant. This is a direct consequence of conservation of angular momentum, meaning the planet's angular momentum remains constant throughout its orbit.

A force that acts along the line connecting two objects. An example is the gravitational force between the Sun and a planet.

Angular momentum is a measure of an object's tendency to rotate. In the case of a planet, it depends on its mass, velocity, and distance from the Sun.

Newton's Law of Gravitation states that any two objects in the universe attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The force of attraction between two objects with mass, where the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The force that pulls objects towards the center of the Earth. It is a special case of Newton's Law of Gravitation.

A force that acts towards the center of a spherical object, like a planet or star.

The acceleration towards the center of a circular path. It is caused by the centripetal force acting on the object.

A force that attracts a point mass situated outside a hollow spherical shell of uniform density, as if the entire mass of the shell were concentrated at its center.

The distance between the centers of two objects. In the case of the Earth and Moon, it is the distance between their centers.

The time it takes for an object to complete one full revolution around another object. For example, the moon's orbital period is about 27.3 days.

A force that attracts a point mass situated inside a hollow spherical shell of uniform density. This force is always zero.

The distance between two objects used in calculating gravitational force.

The mass of an object, a key factor determining its gravitational pull.

The force of attraction between a spherical shell and a point mass can be calculated as if the shell’s mass were concentrated at its center. This only applies if the point mass is outside the shell.

There is no gravitational force present between a spherical hollow shell and a point mass situated inside it.

The Universal Gravitational Constant (G) is a fundamental constant in physics that describes the strength of the gravitational force between any two objects.

The acceleration due to gravity (g) is the acceleration experienced by an object due to the gravitational force of the Earth.

The acceleration due to gravity depends on the mass of the Earth and the distance from the Earth's center.

The total energy of a system is the sum of its kinetic energy and potential energy.

The potential energy of a system is the energy it possesses due to its position or configuration.

The kinetic energy of a system is the energy it possesses due to its motion.

A constant that appears in the equation for Newton's Law of Gravitation, representing the strength of the gravitational force.

The total gravitational force on a point mass due to multiple masses is the vector sum of the individual gravitational forces.

A theoretical point within a uniformly dense spherical shell where the gravitational force from the shell is zero. This is because the forces from different parts of the shell cancel each other out.

The process of calculating the total gravitational force between an extended object (like the Earth) and a point mass by adding up the forces from all the individual point masses in the extended object.

An experiment conducted by Henry Cavendish in 1798 to measure the gravitational constant (G) by observing the torsion of a torsion balance caused by the gravitational attraction between lead spheres.

A device used in Cavendish's experiment, consisting of a horizontal rod suspended by a thin wire. The rotation of the rod reveals the gravitational attraction between masses.

The property of a system where the forces acting on it cancel out perfectly, resulting in no net force. This is often achieved by symmetry, where opposing forces balance each other.

The minimum velocity an object needs to escape the gravitational pull of a planet and never return.

A point in space where the gravitational force from a spherical object is balanced, resulting in an apparent weightlessness.

A force that attracts a point mass situated outside a hollow spherical shell of uniform density as if the entire mass of the shell were concentrated at its center.

The force on a point mass inside a hollow spherical shell of uniform density is always zero.

For a particle inside a homogeneous solid sphere, the force acting on it is directed towards the center of the sphere. This force is exerted by the spherical mass interior to the particle.

The gravitational potential energy associated with two particles separated by a distance r, given by V = -Gm1m2/r.

Angular momentum and total mechanical energy are conserved in the motion of an object under the influence of another object's gravity.

The gravitational attraction towards the center of a hemispherical shell at its center is zero. This is because the gravitational forces from all parts of the shell cancel out.

The gravitational intensity at a point outside a hemispherical shell of uniform mass density is directed towards the center of the shell.

The point where the gravitational forces due to Earth and Sun on the rocket cancel each other out. This point lies closer to the Earth because Earth's mass is much smaller than the Sun's.

By observing the orbital period and radius of Earth around the Sun, we can calculate the Sun's mass using Newton's Law of Gravitation. The orbital period is the time it takes for Earth to complete one orbit around the Sun. The orbital radius is the average distance between Earth and the Sun.

Saturn's orbital radius is 29.5 times larger than Earth's orbital radius because Saturn takes 29.5 times longer to complete one orbit around the Sun. This relationship is based on Kepler's Third Law.

The gravitational force on the body is reduced by a factor of four. This is because the gravitational force is inversely proportional to the square of the distance between the object and the center of the Earth.

The body would weigh half its weight on the surface. This assumes constant density, and gravitational force is proportional to distance to the Earth's center.

The escape velocity is the minimum velocity required for an object to escape the gravitational pull of a celestial body. In this case, the rocket's speed is thrice the escape velocity, meaning it will escape Earth's gravity.