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The publication of the law has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors. [1] [2] [3] This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. [4]
Gravitational potential energy from Newtonian mechanics is defined as: [3] U = − G m 1 m 2 r , {\displaystyle U=-{\frac {Gm_{1}m_{2}}{r}},} where G is the gravitational constant , and the two masses in this case are that of the thin shells of width dr , and the contained mass within radius r as one integrates between zero and the radius of ...
For two pairwise interacting point particles, the gravitational potential energy is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): = = where is the displacement vector of the mass, is gravitational force acting on it and denotes scalar product.
Entering a Hohmann transfer orbit from Earth to Jupiter from low Earth orbit requires a delta-v of 6.3 km/s, [170] which is comparable to the 9.7 km/s delta-v needed to reach low Earth orbit. [171] Gravity assists through planetary flybys can be used to reduce the energy required to reach Jupiter. [172]
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 ...
The absolute value of gravitational potential at a number of locations with regards to the gravitation from [clarification needed] the Earth, the Sun, and the Milky Way is given in the following table; i.e. an object at Earth's surface would need 60 MJ/kg to "leave" Earth's gravity field, another 900 MJ/kg to also leave the Sun's gravity field ...
For example, the fact that Earth is a gravitationally-bound sphere of its current size costs 2.494 21 × 10 15 kg of mass (roughly one fourth the mass of Phobos – see above for the same value in Joules), and if its atoms were sparse over an arbitrarily large volume the Earth would weigh its current mass plus 2.494 21 × 10 15 kg kilograms ...
Gravity well (or funnel) is a metaphorical concept for a gravitational field of a mass, with the field being curved in a funnel-shaped well around the mass, illustrating the resulting gravitational potential and the gravitational potential energy needed to be accounted for to escape or stay in the immediate sphere of influence of the gravity ...
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