How to measure the distance to the Moon?

Question

Is it possible to measure this distance using only the knowledge about the Earth, such as time, equator length, etc?

Answer 1

Hi. Yes, the size of the earth was determined with pretty good accuracy in ancient times using nothing more than two sticks. One was in a city where the sun was directly overhead on a particular day and one was in a more southern city where the stick cast a shadow (you can research which ones). They estimated the earth to be about 25,000 miles in diameter based on the angle of the shadow. During a lunar eclipse the earth casts a shadow on the moon with a radius equal to earth's. They determined the relative size of the moon relative to the earth. Two sticks and observing. Clever. Based on the diameters they estimated the distance.

Answer 2

Yes. The Moon isn't all that far away as astronomical objects go. You could get an accurate measure of the Moon's distance by parallax measurement. You and I are a known distance apart, preferably for accuracy a large distance. We each point our telescopes at the same feature on the Moon's surface at the same time, and measure our azimuth and elevation angles. The rest is just trigonometry. These days, since the speed of light in a vacuum is known very accurately, and time can be measured more accurately than any other quantity, the most accurate measurements of the Moon's distance are made by bouncing a light or radio signal off its surface and measuring the travel time.

Answer 3

http://homepage.mac.com/dtrapp/ePhysics.f/labII_4.html

Measuring the Distance to Moon
Method of Parallax


Observation suggests that the objects in the sky revolve daily about the earth, with the Sun and stars slowly falling behind over a year, and the Moon and other planets doing so each at their own rate. But Aristarchos suggested that most of the appearances could alternatively be due to motions of the Earth. The Earth could rotate daily to the East making everything in the sky appear to rotate Westward. And if the Earth revolved around the Sun annually, part of the slower motions would be explained. This was an early recognition of relativity: Motions can be viewed from different perspectives, but the observations differ relative to the position of the observer.

Humans had always assumed that they were in the center of the universe. But Aristarchos suggested that since the Sun was larger than the Earth, perhaps the Sun was in the center of heavenly motions rather than the Earth. This is different from relativity so would cause observable differences. The most fundamental would be parallax. The lack of any observable parallax led to the Greek's rejecting Aristarchos' proposal that the heavenly objects orbit the sun.

If parallax is observed, careful measurements of it can be used to measure the distance to the to the observed object. In this experiment we shall measure the distance to the Moon, but the procedure could be used in a great many situations. When the location of the Moon simultaneously viewed from two different locations, the Moon seems to be in a different position compared to the much more distant stars, That angle is then used with the law of sines: The lengths of sides of a triangle are proportional to the sines of the opposite angles.

Experiment
Below are two photographs taken about 1200 miles apart by amateur astronomers when Jupiter, Venus, and the Moon were unusually close together in the sky. Because of this conjunction the photographs were accidentally taken at the same time. The crescent lit by the Sun was over exposed by both photographers resulting in the swollen blur. The remainder of the Moon was illuminated by earthshine. At first glance the photographs appear to be identical but just rotated a few degrees. But if one photograph is superimposed on the other, the stars (indicated by purple markers) and planets are aligned, but the Moon appears to be in a different position.

Procedure

1. Print the Farley photograph and the negative of Polley photograph provided below on paper thin enough to be semitransparent.


2. Align the planets and stars on the Polley negative with those on the Farley photograph.


3. Mark the apparent difference in the Moon's location and used the angular scale provided to determine the amount of parallax.


4. Use a calculator to determine the sine of this angle and that of 90°.


5. Use the ratios of the distances to the sines of these two angles to determine the distance to the Moon

6. After finding the distance to the Moon, measure the angular size of the Moon and again use the law of sines to determine the diameter of the Moon.

7. Finally, record your procedures, measurements, and findings in your journal

Answer 4

RADAR and LIDAR ! Both use electromagnetic radiation and simple kinematics to calculate the return time for the echo. The return time multiplied by the speed of light divided by 2 is the approximate distance to the moon. The moon therefore is about 245,000 miles from earth.

Aristarchus of Samos was the first to measure this distance using simple geometry of the earth as opposed to radio waves.

Answer 5

Sure. The "classical" method used by the astronomer Aristarchos (3rd century BC) was to observe the curvature of the earth's shadow on the face of the moon during a lunar eclipse. This gives you the relative size of the moon compared to the earth. Then knowing the earth's size (in miles), you compute the moon's size (in miles). And knowing the moon's size in miles and its apparent size (in degrees), you can compute the distance.

Aristarchos came up with the result that the Moon is 60 earth radii from the earth, which is essentially correct.

Answer 6

The ancient Greeks came pretty close, using geometry/trigonometry. Nowadays, you just bounce a laser beam off the moon and us a very accurate atomic clock to time how long it takes the beam to bounce back.

Answer 7

...and mass and rotational dynamics - speed, orbit...and other variables.......I believe we know the answer because we have shot the distance with a laser of known wavelength such as used by surveyors...I believe we put a reflector on the moon..

Answer 8

yes it is just using basic knowledge of trig