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For an object of mass the energy required to escape the Earth's gravitational field is GMm / r, a function of the object's mass (where r is radius of the Earth, nominally 6,371 kilometres (3,959 mi), G is the gravitational constant, and M is the mass of the Earth, M = 5.9736 × 10 24 kg).
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:
Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s 2, independent of its mass. With air resistance acting on an object that has been dropped, the object will eventually reach a terminal velocity, which is around 53 m/s (190 km/h or 118 mph [ 4 ] ) for a human skydiver.
and are the masses of objects 1 and 2, and is the specific angular momentum of object 2 with respect to object 1. The parameter θ {\displaystyle \theta } is known as the true anomaly , p {\displaystyle p} is the semi-latus rectum , while e {\displaystyle e} is the orbital eccentricity , all obtainable from the various forms of the six ...
The radii of these objects range over three orders of magnitude, from planetary-mass objects like dwarf planets and some moons to the planets and the Sun. This list does not include small Solar System bodies , but it does include a sample of possible planetary-mass objects whose shapes have yet to be determined.
The magnitude of the field at every point is calculated by applying the universal law, and represents the force per unit mass on any object at that point in space. Because the force field is conservative, there is a scalar potential energy per unit mass, Φ, at each point in space associated with the force fields; this is called gravitational ...
The weight of an object on Earth's surface is the downwards force on that object, given by Newton's second law of motion, or F = m a (force = mass × acceleration). Gravitational acceleration contributes to the total gravity acceleration, but other factors, such as the rotation of Earth, also contribute, and, therefore, affect the weight of the ...
Every object in a 2-body ballistic trajectory has a constant specific orbital energy equal to the sum of its specific kinetic and specific potential energy: = = =, where = is the standard gravitational parameter of the massive body with mass , and is the radial distance from its center. As an object in an escape trajectory moves outward, its ...