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## PowerPoint Slideshow about 'Weighing the world' - mizell

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The original measurement

- In 1774 Astronomer Royal Maskelyne measured the mass of the Earth for the first time using
- a mountain called Schiehallion
- a plumb line
- a telescope

Gravitation

Universal constant of gravitation

not known to Maskelyne

Mass of the Earth

Mass of the

Pendulum bob

Force due to gravity

Radius of the Earth squared

Density ratios

The method gives the ratio of the Earth’s density to that of Schiehallion

Obtaining the Earth’s mass from its density requires knowledge of its volume

Maskelyne’s result

He found that the mass of the Earth was 4.5 x 1024 kg

The actual value is 5.98 x 1024 kg

Not bad for the technology of that time

It took him 17 weeks and bankrupted the Royal Society

The Pendulum

The period of a pendulum is the time taken for it to move back and forth once.

The period is given by this equation

L is the length of the pendulum

g is the acceleration due to gravity

Going up

- g is slightly different at the top and bottom of a mountain
- This is for two reasons:
- g is decreased by a small amount because you are further away from the Earth
- g is increased by an even smaller amount because of the gravity of the mountain
- If you can measure 2 then you can obtain the ratio of the masses of the Earth and Schiehallion.

Counting Thoughts method

Measure the period of a pendulum at the base of Schiehallion

Repeat at the top (1080 m) with the same pendulum

The difference gives the density ratio

We used equipment found in most schools

Took one day of measurements, didn’t bankrupt us

Period difference

Summit 1.387 971 s ± 0.000 010 s

Car park 1.387 842 s ± 0.000 020 s

Difference 0.000 129 s ± 0.000 022 s

Altitude 0.000 160 s

Schiehallion -0.000 031 s ± 0.000 022 s

The result

Our mass

8.1 x 1024 kg ± 5.7 x 1024 kg

Maskelyne’s mass

4.5 x 1024 kg

Actual mass

5.98 x 1024 kg

www.countingthoughts.com

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