"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."
Answer the following question in detail.
What is a critical velocity?
The exact horizontal velocity of projection that must be given to a satellite at a certain height so that it can revolve in a circular orbit round the Earth is called the critical velocity or orbital velocity (vc).
The objects that revolve around the Earth are called Earth satellites.
A man-made object that orbits a planet or other celestial body is called an artificial satellite.
A satellite that orbits the Earth at a height of approximately 36,000 km above the equator with a period of revolution of 24 hours is called a geosynchronous satellite.
A satellite that travels over Earth's poles, passing close to the Earth's surface, with a period of revolution of nearly 85 minutes is called a polar satellite.
Answer the following question.
Define the binding energy of a satellite.
The minimum energy required by a satellite to escape from Earth’s gravitational influence is the binding energy of the satellite.
"The minimum energy required by a satellite to escape from Earth’s gravitational influence is the binding energy of the satellite."
"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."
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 formulas for acceleration due to gravity (g) are provided below:
Definition of Terms:
U(r) = -\[\frac {GMm}{r}\]
Where:
Where:
\[v_e=\sqrt{\frac{2GM}{R}}\]
Statement:
The law which states that every particle of matter attracts every other particle in the universe with a force whose magnitude is directly proportional to the product of masses and inversely proportional to the square of distance between them is called Newton's Law of Gravitation.
Derivation:
Newton's Universal Law of Gravitation states that every particle of matter attracts every other particle of matter with a force which is:
Combining both, the gravitational force is expressed as:
F = G\[\frac{m_1m_2}{r^2}\]
where G is the Universal Gravitational Constant, measured by Henry Cavendish using the Cavendish balance, with the value:
G = 6.67 × 10−11Nm2/kg2
