# how earth was weighed?

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• Anonymous
6 months ago

It's done mainly by using Kepler's 3 laws of planetary motion. Kepler's laws let you correlate the mass, the orbital distance, and orbital speed of bodies in orbit about each other. So if you know the orbital distance and speed, you can figure out the mass from that. Here's the Kepler's 3rd law equation:

T^2 = (4 π^2 a^3)/(G (m_1 + m_2)) |

T | orbital period

a | semi-major axis

m_1 | primary mass

m_2 | secondary mass

G | Newtonian gravitational constant (≈ 6.674×10^-11 m^3/(kg s^2))

(orbital period and semimajor axis relation)

• goring
Lv 6
6 months ago

If astronauts are weightless in space so is the Earth

• 6 months ago

With a gigantic scale. The scale is about 50,000 miles wide and length. And its thickness is about 5000 miles.

• Clive
Lv 7
6 months ago

What about it? You're supposed to ask a question.

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• Tom
Lv 7
6 months ago

Back in ASTRONOMY 102 lab class we calculated the mass of MARS by the speeds and orbits of its moons. who's masses were negligible.----We likely can do a similar thing with EARTH by using EARTH's moon----But with a slightly more complex formula to account for the mass of the MOON.

• 6 months ago

They dropped it onto a Manx Kitten

• Anonymous
6 months ago

A lever balance since we knew the mass of Jupiter.

• 6 months ago

Weight:

Easy, it's zero, Earth is weightless on its orbit.

Mass:

Moon orbit period has always been well known.

As soon as we could measure Moon distance, Kepler ' 3rd law of planetary motions and Newton's law of gravitation gave the mass of Earth

• RealPro
Lv 7
6 months agoReport

False, the weight of Earth in the gravitational field of the Sun is truly enormous. Or does "weight" only apply with reference to the Earth? Semantics...

• 6 months ago

There are limits as to how big a scale can be to measure weight, a planet is certainly larger than that.

Mass is the term for weight in science.

Because we know some scientific details of earth such as the force of gravity and the volume the earth occupies, by applying some math formulae, we can get a very close measure of its mass.

Because of such large number, we use scientific notation to represent this, and is as follows:

5.96 × 10^24 kg.

Writing this out it looks more like this:

59 600 000 000 000 000 000 000 000 Kg.

We use a similar method to determine the mass of entities to small to weigh on a scale, right down to the mass of an atom.

• 6 months ago

weighed means determine weight, which is meaningless in that context, as the earth is not in a uniform gravitational field, except that of the sun, which is countered by the earth's movement in its orbit.

I think you mean mass. see reference below.

The mass of the Earth may be determined using Newton's law of gravitation. It is given as the force (F), which is equal to the Gravitational constant multiplied by the mass of the planet and the mass of the object, divided by the square of the radius of the planet. We set this equal to the fundamental equation, force (F) equals mass (m) multiplied by acceleration (a). We know that the acceleration due to gravity is equal to 9.8 m/s², the Gravitational constant (G) is 6.673 × 10^−11 Nm²/kg², the radius of the Earth is 6.37 × 10^6 m, and mass cancels out. When we rearrange the equation and plug all the numbers in, we find that the mass of the Earth is 5.96 × 10^24 kg.

F = Gm1m2/r² = ma

Gm/r² = g

m = gr²/G

m = (9.8 m/s²)(6.37 × 10^6 m)2/(6.673 × 10^−11 Nm²/kg²)

m = 5.96 × 10^24 kg