"Every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the particles."
or
The force by which the Earth attracts objects towards its centre is called gravitational force.
"Every particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them."
"Potential energy is the work done against conservative force (or forces) in achieving a certain position or configuration of a given system."
OR
The energy stored in an object because of its position or state is called potential energy.
"The minimum velocity with which a body should be thrown vertically upwards from the surface of the Earth so that it escapes the Earth’s gravitational field, is called the escape velocity (ve) of the body."
"The minimum energy required by a satellite to escape from Earth’s gravitational influence is the binding energy of the satellite."
Newton’s Universal Law of Gravitation:
F = \[G\frac{m_1m_2}{r^2}\]
where:
Kepler’s Third Law relates the time period T of a planet’s revolution to the semi-major axis a of its elliptical orbit:
T2 ∝ a3
where,
The gravitational force of attraction (F) between two bodies of mass m1 and m2 separated by a distance r is:
F: Gravitational Force of attraction (in Newtons, N).
\[m_1, m_2\]: Masses of the two objects (in kilograms, kg).
r (or d in the first part): Distance between the two objects (in meters, m).
G: The constant of proportionality, called the Universal gravitational constant.
Value in SI units: \[G=6.67\times10^{-11}\mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2\]
Dimensions: \[[G]=[\mathrm{L}^3\mathrm{M}^{-1}\mathrm{T}^{-2}]\]
The area swept by the planet of mass m in a given interval Δt is:
\[\Delta\vec{A}=\frac{1}{2}(\vec{r}\times\vec{v}\Delta t)\]
Based on the relationship between work and energy, the change in potential energy is given by:
\[\vec F\] · d\[\vec x\] = dU
\[v_e=\sqrt{\frac{2GM}{R}}\]
T = \[2\pi\sqrt{\frac{(R+h)^3}{GM}}\]
Where:
Where:
