Ch 5Gravitation — Class 11 Physics, concept-first.

All material objects show a natural tendency to move towards the Earth -- a coconut falling from a tree, raindrops falling from clouds, a dropped pencil -- and, remarkably, every falling body accelera…

Kepler's laws of planetary motion describe the actual orbits followed by the planets around the Sun. Kepler published the first two laws in 1609 and the third in 1619, all derived purely from painstak…

Galileo had already shown that all objects, heavy or light, fall towards the Earth with the same acceleration when released from the same height near the surface.

The value of the universal gravitational constant G is determined experimentally, not derived theoretically, by directly measuring the (extremely small) gravitational force of attraction between two k…

Section 5.3 gave the gravitational force between two point masses as . Since the Earth is, to a very good approximation, a uniform sphere, its entire mass M can (by the shell theorem of section 5.3) b…

The value m/s² is often quoted as though it were a fixed universal constant, but it is really only the acceleration due to gravity AT THE EARTH'S SURFACE, at a particular latitude, under an idealised…

Consider a body of mass m at the Earth's surface, where the acceleration due to gravity is . When the same body is raised to height h above the surface (Fig.

The Earth can be modelled as built up from many thin, uniform, concentric spherical shells, one inside another, with the total mass M being the sum of all their individual masses.

So far g has been treated as though the Earth were a perfect, non-rotating sphere. In reality the Earth rotates about its polar axis (west to east) with angular velocity , and every point on its surfa…

In earlier study, potential energy was introduced as the energy an object possesses because of its POSITION or CONFIGURATION within a system -- 'configuration' referring to how the various parts/parti…

To find an explicit formula for gravitational potential energy, consider the work done AGAINST the Earth's gravitational force while displacing an object through a small displacement ; this work appea…

The formula derived in the previous section is the EXACT expression for gravitational potential energy at any distance r from the Earth's centre.

From the gravitational potential energy formula , the factor depends only on the source mass M (the Earth, in this case) and the location r -- it does NOT depend on the particular test mass m being co…

When an object is thrown vertically upward, it rises to some height and then falls back, pulled down by the Earth's continuous gravitational attraction.

Objects that revolve around the Earth are called Earth satellites. The Moon is the Earth's only NATURAL satellite, moving in an almost circular orbit with a period of about 27.3 days.

Launching an artificial satellite into a stable orbit requires giving it a very specific COMBINATION of speed and direction -- something a single-stage rocket cannot achieve, which is why a minimum of…

Newton's second law, , applies to any object with a net force F producing an acceleration a. Consider a passenger standing on a weighing machine inside a lift (an inertial-frame analysis): regardless…

The time period of a satellite is the time it takes to complete exactly one full revolution around the Earth.

A satellite moving in a stable circular orbit possesses BOTH kinetic energy (from its orbital motion) and potential energy (from its position in the Earth's gravitational field), and the sum of the tw…