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Weighing the world

Weighing the world. 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. Nice Maskelyne. Nasty Maskelyne. Maskelyne’s method. Gravitation.

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Weighing the world

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  1. Weighing the world

  2. 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

  3. Nice Maskelyne

  4. Nasty Maskelyne

  5. Maskelyne’s method

  6. 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

  7. 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

  8. Eratosthenes

  9. Bouguer

  10. Map

  11. Schiehallion is a ridge

  12. Jeremiah Horrocks

  13. William Crabtree

  14. Edmund Halley

  15. James Gregory

  16. 1761 map

  17. 1761 and 1769 maps

  18. Lunar landscape

  19. 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

  20. 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

  21. 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.

  22. 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

  23. The apparatus Weather shield Pivot Wire Thermometer Pendulum bob Light gate Adjustable feet

  24. At the start

  25. On the way up

  26. Spot the Ptarmigan

  27. At the top

  28. The pendulum

  29. The tent

  30. Analysis (mystery version)

  31. Analysis

  32. The data

  33. 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

  34. 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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