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An Earth mass (denoted as M 🜨, M ♁ or M E, where 🜨 and ♁ are the astronomical symbols for Earth), is a unit of mass equal to the mass of the planet Earth. The current best estimate for the mass of Earth is M 🜨 = 5.9722 × 10 24 kg , with a relative uncertainty of 10 −4 . [ 2 ]
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 ...
Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than 100 kilograms.
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.
Non-zero coefficients C n m, S n m correspond to a lack of rotational symmetry around the polar axis for the mass distribution of Earth, i.e. to a "tri-axiality" of Earth. For large values of n the coefficients above (that are divided by r ( n + 1) in ( 9 )) take very large values when for example kilometers and seconds are used as units.
The slug is defined as the amount of mass that accelerates at 1 ft/s 2 when one pound-force is exerted on it, and is equivalent to about 32.2 pounds (mass). The kilogram-force is a non-SI unit of force, defined as the force exerted by a one-kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly).
These proportionalities may be expressed by the formula: where g is the surface gravity of an object, expressed as a multiple of the Earth's, m is its mass, expressed as a multiple of the Earth's mass (5.976 × 10 24 kg) and r its radius, expressed as a multiple of the Earth's (mean) radius (6,371 km). [9]
If a first body of mass m A is placed at a distance r (center of mass to center of mass) from a second body of mass m B, each body is subject to an attractive force F g = Gm A m B /r 2, where G = 6.67 × 10 −11 N⋅kg −2 ⋅m 2 is the "universal gravitational constant". This is sometimes referred to as gravitational mass.