SI unit kilogram (kg) | ||
Common symbols M
⊕
{displaystyle M_{oplus }}
,
M
T
{displaystyle M_{mathrm {T} }}
,
M
E
{displaystyle M_{mathrm {E} }}
or
E
{displaystyle E} Other units gram (g) [CGS]
Solar Mass (M⊙) [IAU] In SI base units 7024597220000000000♠(5.9722±0.0006)×10 kg SI dimension [
M
⊕
]
=
M
{displaystyle [M_{oplus }]=mathrm {M} }
(mass) Derivations from
other quantities M⊕ = g · R2
⊕ ∕ G
M⊕ = ρ · V
M⊕ = μ⊕ ∕ G | ||
Earth mass (M⊕, where ⊕ is the standard astronomical symbol for planet Earth) is the unit of mass equal to that of Earth. This value includes the atmosphere but excludes the moon. The current best estimate for Earth mass is M⊕ = 7024597220000000000♠(5.9722±0.0006)×1024 kg Earth mass is a standard unit of mass in astronomy that is used to indicate the masses of other planets, including rocky terrestrial planets and exoplanets.
Contents
Value
The mass of Earth is estimated to be:
which can be expressed in terms of solar mass as:
The ratio of Earth mass to lunar mass has been measured to great accuracy. The current best estimate is:
History of measurement
The mass of Earth is measured indirectly by determining other quantities such as Earth's density, gravity, or gravitational constant.
Using the GM⊕ product
Modern methods of determining the mass of Earth involve calculating the gravitational coefficient of the Earth and dividing by the Newtonian constant of gravitation,
The GM⊕ product is determined using laser ranging data from Earth-orbiting satellites. The GM⊕ product can also be calculated by observing the motion of the Moon or the period of a pendulum at various elevations. These methods are less precise than observations of artificial satellites.
Using the gravitational constant
Earlier efforts (after 1798) to determine Earth's mass involved measuring G directly as in the Cavendish experiment. Earth's mass could be then found by combining two equations; Newton's second law, and Newton's law of universal gravitation:
Substituting earth's gravity, g for the acceleration term, and combining the two equations gives
The equation can then be solved for M⊕
With this method, the values for Earth's surface gravity, Earth's radius, and G were measured empirically.
Using the deflection of a pendulum
Before the Cavendish Experiment, attempts to "weigh" Earth involved estimating the mean density of Earth and its volume. The volume was well understood through surveying techniques, and the density was measured by observing the slight deflection of a pendulum near a mountain, as in the Schiehallion experiment. The Earth mass could then be calculated as:
This technique resulted in a mass estimate that is 20% lower than today's accepted value.
Using the period of a pendulum
An expedition from 1737 to 1740 by French scientist Pierre Bouguer attempted to determine the density of Earth by measuring the period of a pendulum (and therefore the strength of gravity) as a function of elevation. The experiments were carried out in Ecuador and Peru, on Pichincha Volcano and mount Chimborazo. Bouguer's work led to an estimate that is two to three times larger than the true mass of Earth. However, this historical determination showed that the Earth was not hollow nor filled with water, as some had argued at the time. Modern gravitometers are now used for measuring the local gravitational field. They surpass the accuracy limitations of pendulums.
Experiments with pendulums in the nineteenth century
Much later, in 1821, Francesco Carlini determined a density value of ρ = 7000438999999999999♠4.39 g/cm3 through measurements made with pendulums in the Milan area. This value was refined in 1827 by Edward Sabine to 7000476999999999999♠4.77 g/cm3, and then in 1841 by Carlo Ignazio Giulio to 7000495000000000000♠4.95 g/cm3. On the other hand, George Biddell Airy sought to determine ρ by measuring the difference in the period of a pendulum between the surface and the bottom of a mine. The first tests took place in Cornwall between 1826 and 1828. The experiment was a failure due to a fire and a flood. Finally, in 1854, Airy got the value 7000660000000000000♠6.6 g/cm3 by measurements in a coal mine in Harton, Sunderland. Airy's method assumed that the Earth had a spherical stratification. Later, in 1883, the experiments conducted by Robert von Sterneck (1839 to 1910) at different depths in mines of Saxony and Bohemia provided the average density values ρ between 5.0 and 7000630000000000000♠6.3 g/cm3. This led to the concept of isostasy, which limits the ability to accurately measure ρ, by either the deviation from vertical of a plumb line or using pendulums. Despite the little chance of an accurate estimate of the average density of the Earth in this way, Thomas Corwin Mendenhall in 1880 realized a gravimetry experiment in Tokyo and at the top of Mount Fuji. The result was ρ = 7000577000000000000♠5.77 g/cm3.
Variation
Earth's mass is constantly changing due to many contributors. Earth primarily gains mass from micrometeorites and cosmic dust, whereas it loses hydrogen and helium gas. The combined effect is a net loss of material, though the annual mass deficit represents an inconsequential fraction of its total mass, or even the uncertainty in its mass. So its inclusion does not affect total mass calculations. A number of other mechanisms are responsible for mass adjustments, and can be classified into two categories: physical transfer of matter, and mass that is gained or lost through the absorption or release of energy due to the mass–energy equivalence principle. Several examples are provided for completeness, but their relative contribution is negligible.