How to do mass balance

how to do mass balance

View of Earth from Space

Beth Barbier

Earth's Birth

How was our planet born?

The Earth was born about 4 and a half billion years ago, at the same time the whole solar system (the Sun, Earth, and other planets) formed. An enormous cloud of gas started to get smaller and smaller as the gas particles attracted each other with gravity. Most of the gas went to the center of the solar system and formed the Sun, but several other pieces spinning about the Sun solidified into the planets, including the Earth.

Dr. Eric Christian

Age of the Earth

How old is the Earth?

Current scientific thinking puts the Earth at about 4.5 billion years old.

Distribution of Elements on the Earth

If the Earth formed from elements made in stars, with "dust" forming the Earth via gravity, how did elements settle with like elements? Why is there gold in one spot, silver in another, copper in another, etc.?

Mass of the Earth

AOS vs. AU

Why is Earth Spherical?

How Far to the Center of the Earth?

Earth's Core

The inner core may be hotter, but it is at a much higher pressure. At a fixed temperature (say 5000 degrees), high pressure can make a liquid into a solid. So, even though the temperature increases as you move into the inner core, the pressure increases faster and wins.

Dr. Eric Christian

(March 2001)

Why is Earth's Center So Hot?

Why is the center of the Earth so hot?

It's a combination of radioactivity (the radioactive materials in the Earth generate heat) and the residual heat from the formation of the Earth. When all of the matter that created the Earth fell together, it picked up kinetic energy falling in. When it stopped at the proto-Earth, the kinetic energy was turned into heat. The Earth hasn't cooled yet. The Moon, being much smaller, has had time to cool and probably has a solid core.

Dr. Eric Christian

I'm an astrophysicist, not a geologist. I got my answer from long ago geology courses and research on the web. It's a standard part of geological theory that radioactivity is part of the heating process. See, for example, this Scientific American article .

Why is there not an abundance of fission products observed in materials emitted from either volcanoes or sea-borne vents? Or why are there not more fission products as one penetrates the Earth's crust into deep mines?

There IS increased radioactivity seen in volcanoes (see, for example this news article ).

I don't know about undersea vents, but I wouldn't be surprised if there was increased activity coming from them as well. Your question implies that you think there should be lots and lots of radioactive gas, but you don't need that much radioactivity in the mantle and core.

As for deep mines, local composition is far more important for how much radioactivity there is than depth.

If you want more information, I suggest you contact a real geologist or go to your local college/university library to do some research.

Dr. Eric Christian

(September 2007)

Was the Earth a Star?

Why is the Earth's core so hot? Was the Earth once a star, before it became a planet?

Earth's core temperature is about 6,000° C. By coincidence, this is about the same as the Sun's surface temperature (but much cooler than the Sun's core temperature, which is about 15,600,000° C). The Earth's core is cooling, but at a very slow rate. Over the past three billion years it has probably cooled by a few hundred degrees. Currently, the Earth's core temperature is not changing much because, through radioactive decay (nuclear fission - the breakup of the nuclei of heavy elements, like uranium), it is generating about as much heat as it is losing.

To answer the second part of this question, some definitions are in order. A star is a self-luminous body that shines by generating energy internally through nuclear fusion (the combining of nuclei of light elements like hydrogen and helium). The Sun is a star. A planet shines by reflected light from the Sun. The solar system has nine "major" planets (of which Earth is one) and innumerable "minor" planets (asteroids and comets of various kinds).

Star masses range from about 0.04 times, to 150 times, the mass of the Sun. The mass of the Earth is 0.000003 times that of

the Sun (and the mass of Jupiter, the largest planet in the solar system, is 0.001 times that of the Sun).

Although stars lose mass as they evolve, none lose enough to wind up anywhere near the mass of even the most massive planet. So, the bottom line is: Stars do not evolve into planets.

For a great animated simulation showing the evolution of stars with masses between 0.1 and 120 times that of the Sun see the stellar evolution simulation created by Terry Herter for his Astronomy 101/103 course at Cornell University. You will need a JAVA enabled browser to view this simulation.

Dr. Ed Tedesco

(January 2005)

Weight at Earth's Core

Would your body weigh more or less if standing on the Earth's core? What about above sea level?

As you go further inside the Earth, the force you feel due to gravity lessens, assuming the Earth is has a uniform density all the way throughout. Less force means you weigh less.

The reason is that the mass attracting you is inside a sphere, and is given by M = (4/3) * pi * (radius) 3 * density

The force you feel is given by F = G * M * (your mass) / (radius) 2

This means the net force is F = G * (4/3) * pi * radius * density * (your mass)

(pi=3.14159 and G = Newton's gravitational constant)

So as you go further inside the Earth, the radius is decreasing. so the force you feel is decreasing. The mass above you oddly enough doesn't contribute at all to any net force on your body.

In reality, of course, the Earth is not of uniform density, and there is a slight increase in force as you go down from the surface, before it begins to decrease again. Still, you weigh less standing on the Earth's core.

As far as what happens above sea level - you must realize that what happens outside the Earth is different from what happens inside the Earth. Inside, as you go deeper and deeper, the mass attracting you is less and less (as stated). Above sea level (the surface of the Earth, specifically) as you go further and further away, the mass remains constant (obviously), but the distance gets larger and larger, which makes the force (given by F = G * M(Earth) * M(you) / r 2 ) smaller.

Notice that the formula that applies inside the Earth is different from the one that applies outside.

Dr. Louis Barbier

(October 2003)

Gravity at Earth's Core

Gravity pulls us downward on all sides on the Earth. Does this mean that at the center of the Earth, there is no gravity?

First, the most important thing to know is that gravity exists absolutely everywhere in the universe. Every bit of matter exerts a force on every other bit of matter. This means that you are attracted, and attract, everything in the universe! The force exerted depends on the distance of the object and the mass. The Earth exerts the most force on you because it is close (right here!) and very massive.

Forces add like vectors, so their direction is very important. If you could be at the exact center, the forces that each bit of Earth matter exerted on you would cancel out (up cancelling down, east cancelling west, etc.). This only occurs for a single point, though, and you would still feel a gravitational force on the rest of your body.

Remember, gravity is universal and exists everywhere. This is the fundamental law of physics.

Angela Richard

Earth as a Spherical Shell

Gravitation is attractive, never repulsive, so, in the absence of other forces there, matter will always tend to move to the center of the sphere.

Dr. Eric Christian

How Do We Know About Earth's Layers?

Earth's Gravity Variation

Radius at equator = 6,378,400 meters

omega (angular velocity) = .00007292115 s -1

If you plug these numbers in you find:

Total acceleration at poles = 9.8332 m s -2

gravitational acceleration at equator = 9.7805 m s -2

centrifugal acceleration at equator = -.0002 m s -2

Total acceleration at equator = 9.7803 m s -2

So it is obvious that the oblateness of the Earth is 250 times more important than the centrifugal acceleration.

Why Aren't People on the "Bottom" of the Earth Upside Down?


Category: Forex

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