Mass of the earth?

Question

Okay I'm doing my physics homework and I can't get one of the answers to one of the questions which is....
The mass of earth can be calculated using the fact that the weight of an object (in newtons) is equal to the force of gravity between the object and the earth. Given that the radius of Earth is 6.4 x 10^6 m determine its mass.

I don't need people to calculate it out I just need explanation of what to do and what formula to use.....

Answer 1

Consider a mass m on the surface of
Earth. The equation governing this mass
can be written as
mg=G*m*M/R^2
m=mass of the object=kg
g=acceleration due to gravity=9.81m/sec^2
M=mass of Earth kg ?
R=radius of Earth=6.4*10^6m[given]
G=universal constant of Gravitation
=[6.6742+-.0010]*10^-11Nm^2kg^-2
Canceling m we can write
M=g*R^2/G
You have all the values
Substitute and get Mass of Earth.

Answer 2

You will need:

F = G * m1 * m2 / d^2

G is the "constant of gravitation" 6.672 x 10^-11 (N m^2 / kg^2)
m1 mass of Earth
m2 mass of object on Earth's surface
d^2 = distance squared (here d = radius of Earth)
F = force attracting objects to each other.

and
F = m * a

a is the acceleration of an object
m is the mass of that object.


Use the second equation (using m as the mass of an object on Earth's surface, and a as the acceleration due to gravity = approx. 9.8 m/s^2) to find the force F. Then use this value for F in the first equation, where you already have the mass m2 of the object and the distance (Earth's radius). The only missing element is m1 (mass of Earth) for which you can solve.

^means "raised to power" e.g., d^2 means "d squared"
* means multiply
/ means divide

Hint: use a mass of 1 kg for the object on the surface (m2 = m = 1 makes calculations much easier) to find Earth's mass in kg.

Answer 3

First of all weight of a body is not the gravitational force acting on it.
If it is so, than the weight of a freely falling body should not be zero, or the weight of an astronaut inside a satellite shall not be zero.
Weight is the reaction force offered by the ground on the body in vertically upward direction.
Now come to your question.
The gravitational force acting on the body
= G Mm/R^2
Or mg = G Mm/R^2
M= (g R^2)/G
Where, G is the gravitational constant, g is the acceleration due to gravity at that place and R is the radius of earth.

Answer 4

I undergo in suggestions a narrative bearing directly to between the greek philosophers (Aristarchus?), the place they measured the size of a shadow on a stick at different factors on earth at particular cases of the day. From this (i've got faith) they have been waiting to make certain the circumference of the earth, and as a result the diameter. Calculation based suggestion... i'm unsure.

Answer 5

Mass of the sun,M.mass of an object,m.
by using the force of gravity = GMm/R^2
and weight of the object =mg
we get mg = GMm/R^2
==> g=GM/R^2
==>M=gR^2/G

Answer 6

5.974 10^24 kg


attraction force gravity is

F = mg = k m(earth) m / r^2 . you find value with my link

Answer 7

Hello

You must use this:

F = G (M_T *m)/r^2, it is the gravitational force between two bodies, earth )M_T) and other m.

G is a gravitatiional constant.

You must to read about Cavendis experiment