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Physics
The work done can be calculated using the formula W = F × d × cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement.
Gravitational potential energy can be calculated using the formula U = -G(m1m2)/r, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
Newton's third law states that for every action, there is an equal and opposite reaction. In gravitation, this means that the gravitational force exerted by one mass on another is equal in magnitude and opposite in direction to the force exerted by the second mass on the first.
Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without further propulsion. It depends on the mass and radius of the body from which the object is escaping.
Gravitational force decreases with increasing depth below the Earth's surface and also decreases with height above the Earth's surface. The value of gravitational acceleration (g) is maximum at the surface and decreases as one moves away from it.
The formula for gravitational acceleration at a height h above the Earth's surface is g' = g(1 - h/R), where g is the gravitational acceleration at the surface and R is the radius of the Earth.
The formula for gravitational acceleration at a depth d below the Earth's surface is g' = g(1 - d/R), where g is the gravitational acceleration at the surface and R is the radius of the Earth.
In a stable orbit, the kinetic energy of a satellite is equal to the negative of its potential energy. This relationship ensures that the total mechanical energy of the satellite remains constant.
The law of universal gravitation was discovered by Sir Isaac Newton. He formulated this law in the 17th century, describing the gravitational attraction between masses.
A universal constant, such as the gravitational constant (G), has the same value throughout the universe. It is used in the calculation of gravitational forces between masses.
The formula for the period (T) of a satellite in orbit is T = 2π√(r³/GM), where r is the distance from the center of the Earth to the satellite, G is the gravitational constant, and M is the mass of the Earth.
Gravitational force can vary significantly between different celestial bodies due to differences in mass and radius. For example, the gravitational force on Mars is weaker than that on Earth due to its smaller mass.
Gravitational force is independent of temperature and pressure. It remains constant regardless of environmental conditions, as it is solely dependent on mass and distance.
The gravitational constant (G) is a key value in the law of universal gravitation, representing the strength of the gravitational force between two masses. Its value is approximately 6.674 × 10^-11 N(m/kg)².
Gravitational force is directly proportional to the product of the masses of two objects. This means that as the mass of either object increases, the gravitational force between them also increases.
Gravitational force decreases with the square of the distance between two masses. This means that if the distance between the masses doubles, the gravitational force becomes one-fourth as strong.
Gravitational force provides the necessary centripetal force that keeps satellites in orbit around celestial bodies. It balances the satellite's inertia, allowing it to maintain a stable orbit.
If one mass is doubled, the gravitational force between the two objects also doubles, according to Newton's law of universal gravitation, which states that force is proportional to the product of the masses.
The formula for gravitational potential energy (U) is U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above a reference point.
The gravitational force acting on an object is equal to the mass of the object multiplied by the acceleration due to gravity (F = mg). This shows how gravitational force is directly related to the mass of the object and the gravitational field strength.