Welcome to the article How could you determine the distance to the moon knowing only its diameter and having only a meter stick and a pen. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Final answer:
The distance to the moon can be found using the method of parallax; taking two measurements of the moon at different points and times, marking the position, measuring shift, and applying the definition of radian measure.
Explanation:
The question asks how could you determine the distance to the moon knowing only the diameter and having only a meter stick and a pen. This can be achieved by using the method of parallax, which is used for astronomical measurements.
Parallax is the apparent shift in position of an object when observed from two different points. Here's an illustrative example: extend your arm fully, thumb up. Close one eye, then open it and close the other alternatively. You'll notice your thumb seems to move against the background. This is because the view points of your eyes are about 7 cm apart, hence the apparent shift. Now, imagine your eyes are two observation points on Earth and your thumb is the moon, you can understand how this concept is applied to determine distances.
Here's the step-by-step explanation:
- First, take two observations of the moon with the meter stick at different points and times; ideally half a meter apart and preferably with a fixed known background like a building or a large tree.
- Mark the position of the moon in relation to the fixed background at both points on the ruler with your pen.
- Measure the shift on the ruler (in millimeters). This gives you the angle subtended by the moon at the two observation points, from which you can derive the angle in radians.
- Finally, apply the definition of radian measure which states that the radius of a circle is equal to the product of the angle (in radians) and the circle's circumference. Rearranging this equation, the distance to the moon should be approximately the diameter of the moon times the ratio of 360 degrees (converting the radian measure to degrees) over the angular shift (in degrees).
Please note, this method does assume that the moon is a perfect sphere and that the distance over which you take your two measurements is relatively small compared to the distance to the moon.
Learn more about Parallax here:
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Rewritten by : Brahmana