How do you calculate the mass of the Earth? How is the mass of the earth calculated

The mass of the earth is m=, and the radius of the earth is r=From Newton's second law f=mg and the law of gravitational force g=fm r2, it can be concluded that the mass of the earth should be m=mgr2 f. where m is the mass of an object on the surface of the earth that is subject to gravity, and g is the acceleration due to gravity. Therefore, to calculate the mass of the earth, we only need to know the radius r and the gravitational constant f of the earth.

The former uses a simple geometric principle, while the latter requires a well-designed experiment.

Make use of the gravitational force formula.

gmm/r^2=f

m is the mass of the earth and r is the radius of the earth.

This force can be approximated as the gravitational force exerted on an object.

Namely. f=mg

mg=gmm/r^2

m=gr^2/g

Replace g = g =

r=6400km

Substituting the above equation can be obtained. m=

Earth's mass. kg

Average density: 5, kg m 3

Gravitational acceleration at the equatorial surface.

1 m/s^2（ 32 g）

There are three ways to do it in high school physics:

1. **Substitution: ignore the rotation of the earth, mg=gmm r 2, get m=gr 2 g;

2. Earth-Moon system: GMM R 2=4 2mr T 2, which can be solved by knowing the distance between the lunar period t and the Earth-Moon center, m=4 2r 3 gt 2;

3. Earth-satellite system: gmm r 2=mv 2 r 2, the satellite linear velocity and orbiting radius can be solved.

In short, according to the motion of celestial bodies, the law of gravitation provides centripetal force, and the centripetal force formula can be expressed by physical quantities such as linear velocity, angular velocity, period, etc., and the mass of the central celestial body can be found as long as the two physical quantities surrounding the celestial body.

Launch a near-Earth satellite, measure the period, you can get the density of the earth, and then use sunlight to measure the radius of the earth, and finally you can calculate the mass of the earth.

f=gmm/r^2=1/2mv^2(1)

v=wr(2)

w=2pi/30*24*3600

f is the gravitational force between the Earth and the Moon.

g is the gravitational constant.

m is the mass of the earth.

m is the mass of the moon.

v is the linear velocity of the Moon.

w is the angular velocity of the moon.

r is the average distance from the center of the earth to the center of the moon.

Pi is pi.

Combining the above three formulas, you can deduce the mass of the earth.

Need to wait for a lunar eclipse.

The radius of the Earth can be calculated based on the radian of the moon in the middle of the crescent.

The time difference between the moon and the shadow calculates the distance between the Earth and the Sun.

Erect a rod on the ground and calculate the time it takes for the earth to spare the sun for one week, perihelion, aphelion, and the g's of the sun to get the mass of the earth.

The mass of the Earth is 10 times 24 kilograms, which is determined according to the law of gravitation. The mass of the Earth does provide a basis for determining the mass of other celestial bodies, from which the average density of the Earth is 5,52 grams per cubic centimeter. The first person to measure the mass of the earth was the British scientist Henry Cavendis, who indirectly measured the huge mass of the earth through ingenious experiments, and was hailed as the first person to call the earth.

Calculation method: Using a hanging weight similar to a dumbbell that is attracted by the gravitational attraction of another object, it magnifies a small offset value by reflecting a very long ray of light, and a more accurate g value is measured. In the end, the mass of the Earth was measured to be about 60 trillion tons.

There are many ways to calculate the mass of the Earth, but if we think of the Earth as homogeneous and ignore the influence of other celestial bodies, then we can calculate the mass of the Earth by:

Method. 1. At the equator, the gravitational pull of the Earth on an object of mass m is equal to the sum of the gravitational force of the object and the centripetal force of rotation with the Earth.

Method. Second, in the Arctic, if the rotation of the earth is not taken into account, the result is:

Method. 3. Treat the earth as a sphere with uniform mass, ignore the influence of rotation, take the average of the radius, and take the standard value of gravitational acceleration. then is.

Take advantage of gravitational acceleration and orbit.

In the motion of celestial bodies, it is approximately believed that the motion of celestial bodies is uniform circular motion, and the decisive factor in the process of its motion is gravitational force, that is, gravitational force provides the centripetal force required for the celestial body to do uniform circular motion, and there is g(mm r )=m 2 t) r where the period can be obtained by astronomical observation, so that the mass of the celestial body is: m = [(2 t) r ] g.

However, since the orbit of the celestial body is actually elliptical, and the earth has a super-large moon called the moon, and the sun itself as the focal point is also moving, the calculation formula is much more complicated than this.

However, with approximate estimates, it should not be a big problem.

In order to know the mass of the earth, Newton conceived a very strange experiment, but this experiment was so strange that even Newton himself did not bother to try it. Let's take a look at how humans know the mass of the Earth.

How much does the earth really weigh? In 1522, Magellan's fleet successfully sailed around the globe and confirmed the conjecture of the sphere, and people began to wonder how much the earth weighed.

Let the mass of the earth be m, the radius of the earth r, the gravitational constant g, the mass of the object m, and the acceleration of gravity g

then gmm (r*r)=mg, m=grr g

Cavendish believed that the mass of the Earth was about 6 10 24 kg.

The equatorial radius of the earth ra=6378137m, the polar radius rb=6356752m, the flattening rate e=1, ignoring the non-spherical symmetry of the earth, the average radius r=. The value of gravitational acceleration at a certain sea level at the equator is ga=, the value of gravitational acceleration at a certain sea level in the North Pole is gb=, the global standard value of gravitational acceleration is g=, and the earth's rotation period is 23 hours, 56 minutes and 4 seconds (sidereal days), that is, t=.

Weigh the mass of an object on a scale and denote it as y (unit: kilograms).

On the earth, the number of Ox measured by a spring dynamometer is the number of Ox, which is denoted as x (unit: Ox) x y, that is, the gravitational acceleration of the Earth g =

Let the mass of the earth be m, the radius of the earth r, and the gravitational acceleration of the earth's surface g, then mg=gmm (r*r), if it is a satellite on the earth's surface, gmm(r*r)=mrw*w, so as to find the mass of the earth m

Do you know? How is the mass of the earth calculated, let me tell you.

Let the masses of the sun and the earth be m and m respectively, the speed of light is c, the distance between the sun and the earth is r, the time of light from the sun to the earth is t, the time for the earth to revolve around the sun is t (that is, one year), the angular velocity of the earth is w, the gravitational constant is g, the gravitational force of the sun on the earth is f, and the centripetal force required for the earth to move around the sun is f.

f=gmm/rr，r=ct，f=mwwr，w=2π/t，f=f。

Joining the above five equations can be obtained: m=[(2 t) 2][(ct) 3] g, where g and c are fundamental physical constants and should be known; t and t are also known, so m can be found.

The mass of the Earth is grams, which is determined according to the law of gravitation. The determination of the mass of the Earth provides a basis for determining the mass of other celestial bodies. From the mass of the Earth, the average density of the Earth is 5 52 g cm3

From the law of gravitation gmmr 2=m 4 2 r t 2, taking the moon as an example g = , the distance between the moon and the earth r m, the lunar revolution period is 27 days, 7 hours, 43 minutes and 11 seconds (sidereal days), that is, t s, the mass of the earth m = kg.

The law of gravitation ---

gmm/(r+h)^2=m*(2pai/t)^2...1) r is the radius of the earth, h is the height of the satellite, c is the speed of light, t is the rotation period of the earth, and m, m are the masses of the earth and the satellite, respectively.

The result can be obtained by substituting the relevant data into the above two formulas.