Assuming I only have a simple telescope, how can I determine the size of the moon, its angular velocity and distance from earth?

  • $\begingroup$ Do you have any of these also: pencil, paper, value of G, the gravitational constant & mass of earth, or just the value of the GMe, standard gravitational parameter of earth of earth? Or even just the fastest speed that you've seen a satellite move relative to the stars? $\endgroup$
    – uhoh
    Mar 13 '16 at 8:38
  • 1
    $\begingroup$ @uhoh pencil, paper, telescope, geometry and not much more. $\endgroup$
    – Sparkler
    Mar 13 '16 at 8:43
  • $\begingroup$ The telescope is redundant, Aristarchus, Hipparcus and Ptolomy did this (and rather more) with essentially naked eye observations, knowledge of elementary geometry and the equivalent of pen and paper. You need the angle between the Sun and Moon at 1/2 Moon (you might need something equivalent to a sextant for this), the angular size of the Moon and the radius of the Earth's shadow on the Moon during a Lunar Eclipse in units of Moon radii, and the actual size of the Earth. $\endgroup$ Mar 13 '16 at 10:01

Finding the distance is tricky. To find the distance you need to carefully note the position of the moon (relative to the stars ) from two different places, *at the same time *. The moon will appear to be in a slightly different position from the two viewpoints (an effect called paralax). That done, finding the distance, and size is a simple exercise in trigonometry, and Khan academy has a page which shows hoebto find the distance to the moon.

Greater accuracy could be obtained by measuring the time that a star is hidden by the moon, from two locations, and using that to determine the position of the moon to greater accuracy than possible by direct measurements. Hipparchus apparently used a solar eclipse to obtain two positions atbthe same time needed for calculation of paralax.

Knowing the distance makes finding the diameter and speed simple to do, by observing the angular size, and using a little trig. Working with photographs takenby the telescope is convenient but not strictly necessary.


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