Earth mass

Earth Mass
Common symbols	, , or
SI unit	kilogram (kg)
Other units	gram (g) [CGS] Solar Mass (M⊙) [IAU]
In SI base units	7024597220000000000♠(5.9722±0.0006)×1024 kg
SI dimension	(mass)

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^[1][2] 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.

Value

The mass of Earth is estimated to be:

,

or:

.

History of measurement

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.^[5]

Before the space age (and after 1798), efforts to determine Earth's mass involved measuring G directly as in the Cavendish experiment. Earth's mass could be 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.

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.

Variation

Earth's mass is constantly changing due to many contributors. Primarily, Earth is gaining micrometeorites and cosmic dust, and losing Hydrogen and Helium gas. The combined effect is a net loss of material, however the annual mass deficit represents less than a millionth of the mass of our planet. It is much less than the uncertainty in the total mass of the planet and its inclusion or not has no impact on the 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 which 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.

Net gains

<div " style="padding-left: 3em; padding-right:0em; overflow: hidden; ">In-falling material

Cosmic dust, Cosmic Rays, meteors, comets, etc. are the most significant contributor to Earth's increase in mass. The sum of material is estimated to be 7004370000000000000♠37000–78000 tons annually^[6][7]

Global Warming

Nasa has calculated that the Earth is gaining energy due to rising temperatures. It has been estimated that this added energy increases the mass of Earth by a tiny amount - 160 tonnes per year.^[8]

Solar energy conversion (minuscule)

Solar energy is converted to chemical energy by photosynthetic pigments as plants construct carbohydrate molecules. This stored chemical energy represents in increase in mass. Most of the chemical energy is reconverted into heat and then lost (radiated) through chemical processes, but some is sequestered and becomes biomass or fossil fuel.

Artificial photosynthesis (minuscule)

Can also theoretically add mass, assumed to be negligible but added for sake of completeness.

Heat conversion (probably minuscule)

Some outbound radiation is absorbed within the atmosphere by photosynthetic bacteria and archaea, including from chlorophyll f, which bind the energy into matter in the form of chemical bonds.

Net losses

<div " style="padding-left: 3em; padding-right:0em; overflow: hidden; ">Atmospheric escape of gases.

About 3 kg/s of hydrogen or 95,000 tons per year^[9] and 1,600 tons of helium per year^[10] are lost through atmospheric escape.

Spacecraft on escape trajectories (minuscule)

Spacecraft that are on escape trajectories represent an average mass loss at a rate of 7001650000000000000♠65 tons per year.^[11] Earth lost about 3473 tons in the initial 53 years of the space age, but the trend is currently decreasing.

Human energy use (minuscule)

Human activities conversely reduce Earth's mass, by liberation of heat that is later radiated into space; solar photovoltaics generally do not add to the mass of Earth because the energy collected is merely transmitted (as electricity or heat) and subsequently radiated, which is generally not converted into chemical means to be stored on Earth. In 2010, the human world consumed 550 EJ of energy,^[12] or 6 tons of matter converted into heat, then almost entirely lost to space.

Deceleration of Earth's core (minuscule)

As the rotation rate of Earth's inner core decelerates, it loses rotational kinetic energy, which equates to a loss of 16 tons per year. However, this rotation speed has been shown to fluctuate over decades.^[13]

Non photosynthesizing life forms consume energy, and radiate as heat.

Natural processes (probably minuscule)

Events including earthquakes and volcanoes can release energy as well as hydrogen, which may be lost as heat or atmospheric escape.

Radiation Losses(minuscule)

From radioisotopes either naturally or through human induced reactions such as nuclear fusion or nuclear fission amount to 16 tons per year.^[11]

Additional human impact by induced nuclear fission

Nuclear fission, both for civilian and military purposes, greatly speeds up natural process of radiodecay. Some 59,000 tons of uranium was supplied by mines in 2013.^[14] The mass of the uranium is reduced as it is converted to energy during the fission reaction. Also, the growing spent fuel stockpiles and environmental releases continues to produce heat (and therefore mass) largely lost to space.

See also

References