N E E T H A S U S A N J O S E

P H Y S I C A L S C I E N C E

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CALCULATING THE

MASS OF EARTH

Mass is a measure of how much matter, or

material, an object is made of. Weight is a

measurement of how the gravity of a body pulls on an object. Your mass is the same

everywhere, but your weight would be vastly

different on the Earth compared to on Jupiter or

the Moon.

G, the gravitational constant (also called the

universal gravitation constant), is equal to

G = 6.67 * 10-11N(m / kg)2

Where a Newton, N, is a unit of force and equal

to 1 kg*m/s2. This is used to calculate the force

of gravity between two bodies. It can be used to calculate the mass of either one of the bodies if

the forces are known, or can use used to

calculate speeds or distances of orbits.

Orbits, like that of the moon, have what is called

a calendar period, which is a round number for

simplicity. An example of this would be the

Earth has an orbital period of 365 days around

the sun. The sidereal period is a number used

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by astronomers to give a more accurate

description of time. The sidereal time of one

spin of the Earth is 23 hours and 56 minutes, rather than a round 24 hours. The time period of

an orbit, which you will use in your calculations

in this exercise, will have a great effect on the

outcome of your answers.

Problem: Find Earth's mass using the moon's

orbit.

Materials

Calculator

Calendar

Internet

Procedure

1.Use a calendar to determine how long it

takes for the moon to orbit the Earth. Do

some research on the internet to find the

sidereal period of the moon.

2.Use the following equation to calculate the average velocity of the Moon

v = 2πr / T

Where v is the average velocity of the moon,

r is the average distance between the moon

and the Earth, taken as 3.844 x 108 m,

and T is the orbital period, with units of

seconds.

3.Calculate the mass of the Earth using both

the calendar period of the moon and the

sidereal period of the moon. Why are they

different? Which is a more accurate

calculation and why?

Me = v2r / G

Where Me is the mass of the Earth, in kilograms,

v is the average velocity of the moon,

r is the average distance between the moon

and the Earth

and G is the universal gravitation constant.

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Results

The sidereal period of the moon, which is 27.3

days, will give you a calculation of Earth's mass

that's more accurate than the calendar period of

the moon. The mass of the Earth is 5.97 x 1024

kg.

That is 5,973,600,000,000,000,000,000,000 kg!

Why?

Sir Isaac Newton’s Law of Universal

Gravitation states that all masses in universe

are attracted to each other in a way that is directly proportional to their masses. The

universal gravitation constant gives the relation

between the two masses and the distance

between them. For most things, the masses are

so small that the force of attracted is also very small. This is why you don't get pulled by your

friends' gravity enough to get stuck to them!

These gravitational forces are extremely useful, as they keep the plants in orbit around the Sun,

and the Moon in orbit around the Earth. They

also keep the satellites in orbit that bring us

information from space and allow us to communicate with people across the world

instantaneously.