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It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r 12 and m instead of m 2 and define the gravitational field g(r) as:
For example, the Schwarzschild radius r s of the Earth is roughly 9 mm (3 ⁄ 8 inch); at the surface of the Earth, the corrections to Newtonian gravity are only one part in a billion. The Schwarzschild radius of the Sun is much larger, roughly 2953 meters, but at its surface, the ratio r s / r is roughly 4 parts in a million.
Gravitation, also known as gravitational attraction, is the mutual attraction between all masses in the universe.Gravity is the gravitational attraction at the surface of a planet or other celestial body; [6] gravity may also include, in addition to gravitation, the centrifugal force resulting from the planet's rotation (see § Earth's gravity).
According to the IAU's explicit count, there are eight planets in the Solar System; four terrestrial planets (Mercury, Venus, Earth, and Mars) and four giant planets, which can be divided further into two gas giants (Jupiter and Saturn) and two ice giants (Uranus and Neptune). When excluding the Sun, the four giant planets account for more than ...
Newton defined the force acting on a planet to be the product of its mass and the acceleration (see Newton's laws of motion). So: Every planet is attracted towards the Sun. The force acting on a planet is directly proportional to the mass of the planet and is inversely proportional to the square of its distance from the Sun.
If, for example, two bodies are initially at rest relative to each other, but are then dropped in the Earth's gravitational field, they will move towards each other as they fall towards the Earth's center. [17] Compared with planets and other astronomical bodies, the objects of everyday life (people, cars, houses, even mountains) have little mass.
The actual Hill radius for the Earth-Moon pair is on the order of 60,000 km (i.e., extending less than one-sixth the distance of the 378,000 km between the Moon and the Earth). [9] In the Earth-Sun example, the Earth (5.97 × 10 24 kg) orbits the Sun (1.99 × 10 30 kg) at a distance of 149.6 million km, or one astronomical unit (AU). The Hill ...
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [2] [3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2), [4] depending on altitude, latitude, and longitude.