how measure earth mass?

Answer 1

Mass: 5.9742×10^24 kg

Answer 2

In 1798 Henry Cavendish determined the numerical value of the constant "big G" in the gravitational equation.

To measure "big G" Cavendish designed a system which was isolated from air currents and kept at a constant temperature. Since the deflection was expected to be small, Cavendish used a device called an "optical lever".
A mirror was suspended from the cable which supported the small masses .
A beam of light aimed at the mirror was reflected and read on a scale which was as far away as feasible. This allowed the small twist of the supporting cable to be magnified, simply from the geometry of the triangle.
He translated the angle of twist into a force, Cavendish relied upon Hooke's Law.

He determined the value of G.

G =6.673x10^-11 N m^2 / kg^2

Radius of earth R = 6371km.

Force on 1 kg on the earth’s surface = 9.8 N~ 10 N

By Newton’s law,

10 N = G M / R^2

M, the mass of earth

= 10 x (6371)^2 x 10^6 / 6.673x10^-11

= 6 x 10^24 kg.

Thus mass of earth is determined.

Answer 3

We calculate Earth’s mass as follows:

Everything pulls on everything else in a simple way that involves only mass and distance. Newton said every body attracts every other body with a force that, for any two bodies, is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance separating them.

The equation, expressing Newton’s statement, is

(1) F = G (m1) (m2) / d²

where G is the gravitational constant.

Newton also said that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.

The equation, expressing this statement, is

(2) a = F / m.

We substitute Earth’s mass (m) and Earth’s radius (r) in Equation (1) to get the force that Earth attracts a body of mass (M) on the surface of Earth.

(3) F = G (m)(M) / r²

We substitute the acceleration (g) due to gravity in Equation (2) to get the force that the object of mass (m) resists the acceleration due to gravity

(4) F = mg

To calculate Earth’s mass, we equate the forces given by Equations (3) and (4) and solve for (m). We get

(5) m = g r² / G

where the constants are given by G = 6.67300 x 10-11m³/(kg s²),

g = 9.8 m/s²,

and r = 6.378 x 106m.

Plugging the values of the constants in Equation (5) we get the mass of Earth:

m = 5.9742 x 1024 kilograms.

Answer 4

The Earth's mass cannot be measured directly... there is no scale large enough and even if there were, where would you put it? The Earth's mass is calculated by watching its behavior very carefully. By observing the gravitational effects of the Earth-Moon system, Measuring how objects fall in Earth's gravitational field and by measuring the distance between the Earth and Moon carefully, You can calculate what the mass of the Earth must be using the Gravitational Constant G.

Answer 5

Estimating the Earth's Mass

If we want to describe how things in the universe behave, we need to know how much matter they contain. Matter can exert forces on other matter. It is through this interaction that the universe evolves. For example, the amount of matter or MASS of a star governs the intensity of energy it emits during its life cycle. The mass of a planet plays a significant role in its thermal history. The mass of the universe dictates whether it will expand forever or contract at some finite time in the future.

To measure the mass of something accurately and precisely you could count each of its protons, neutrons and electrons. But these parts of atoms are too small to be handled without complex apparatus. Moreover, there are far too many of them in common objects such as pennies to make that method practical. If we want to measure the Earth's mass, we'll have to be content using another, less precise, method.

We can make a good estimate of the number of atoms in a cubic centimeter of water at room temperature and pressure. That value is approximately 6 x10^23 (six hundred thousand billion billion) atoms or the amount of matter in one GRAM , the standard of mass measurement in the metric system. All masses are measured relative to the gram. The amount of matter in three copper pennies is about ten grams. Spring scales measure mass by measuring the amount of gravitational attraction which the Earth exerts on the object suspended on the spring. The more matter the object possesses, the greater the attraction (weight) and the more the spring is stretched or compressed. So, to measure the masses of common objects, you need only observe what they do to a spring.

But how can we measure the mass of the Earth itself? There are no spring scales large enough to hold the Earth! However, there are methods which employ the magnitudes of forces on the Earth which can give us its mass. We will examine them in Lab Two. But for now let's estimate the Earth's mass using a crude method requiring some broad assumptions in order to get an idea of the astronomically large quantities we encounter when we try to describe the universe.

If we know the mass of one sample rock and we know how many sample rocks make up the Earth, then we know the mass of the Earth. Rock masses can be measured using simple spring scales. Rock volumes can be determined by finding how much water they displace. The Earth is nearly spherical and a sphere's volume can be computed readily if we know the sphere's radius. So, if we know the Earth's volume, then all we need do is multiply the rock's mass by the number of rocks in the Earth.

In the applet below, select the value you wish to measure for a sample rock, its mass or volume. Observe the extent to which the blue cursor travels along the graduated scale and find the mass in kilograms. (One kilogram is 1000 grams, the mass of about 333 pennies.) From the difference in water levels, find the volume of fluid which the rock displaces in milliliters. (One milliliter is one thousandth of a liter or a cubic centimeter.)
Approximately 2000 years ago, Eratosthenes is said to have observed the shadow of a gnomon (the pole or object of a sundial that creates a shadow) in Alexandria, Egypt. On the same day that sunlight fell to the bottom of a well in Syene (now Assouan,Egypt), 785 km south of Alexandria, he found that a gnomon in Alexandria cast a shadow. This supported the notion that the Earth is spherical and also enabled Eratosthenes to measure the Earth's circumference. We can use this method to get the Earth's radius and volume.
In the applet below, you can see the gnomon's shadow length and direction (north is up) on the sandy ground. The brown dot below the middle of the frame is the tip of the gnomon which extends 40 cm directly into the screen. The shadow advances one half hour in simulated time. A scale of degrees will appear after the simulation is complete and the shortest shadow length which occurs at noon may be measured.

Compute how many times the angle would fit into the entire Earth, 360 degrees. Then multiply that value by the Alexandria-Syene distance to get the Earth's circumference. The method is analogous to figuring out how the size of a whole pie if you are given the length of the curved edge and the angle of the slice at the pie's center.
Find the Earth's radius by dividing the circumference by 2.0*pi. (pi = 3.14) Convert your radius into centimeters. (We measured our rock volume in cubic centimeters or milliliters.) Find the Earth's volume by cubing the radius and multiplying by 1.33 *pi.

Finally, divide the Earth's volume by the volume of the rock sample. That's how many rocks make up the Earth if we assume that the Earth is made entirely of our sample rock. To get the Earth's mass, multiply the number of rocks in the Earth by the mass of the rock sample.

Answer 6

to measure the mass of the earth use the relation of gravitation by which you can get your answer

Answer 7

To determine the mass of the Earth, ME, using two methods:
(i) by measuring the time taken by a body to fall a specific distance
(ii) by measuring the period of a simple pendulum


visit the following link to get into brief:

http://www.ghiweb.com/cap/Lab107/Mass%20of%20Earth/

Answer 8

The mass comes directly from knowing the acceleration due to gravity at the earth's surface, 9.81. That and the universal gravitational constant are all you need to know. (How you find the universal gravitational constant is up to you.)

Answer 9

earth mass=total weight of eart in kg x9.81

Answer 10

You can use the universal gravitational constant equation. (which you can look up) or just look up the mass.