Distance to the Moon

Lunar nearside, major maria and craters are labeled. Credit: Peter Freiman, Cmglee, and background photograph by Gregory H. Revera.

This laboratory is an activity for you to determine a distance to the Moon.

Some suggested entities to consider are right ascension, declination, circular orbit, longitude, and latitude.

Evaluation

evaluation activity

Okay, this is an astronomy distance, or displacement, laboratory.

Yes, this laboratory is structured.

I will provide an example of calculations of the distance to the Moon. The rest is up to you.

Questions, if any, are best placed on the discussion page.

Control groups

Main source: Control groups

For measuring a distance to the Moon, what would make an acceptable control group? Think about a control group to compare your experimental results and calculations to.

Sampling

This is a Landsat image of the Barringer Meteor Crater from space. Credit: National Map Seamless Server, NASA Earth Observatory.

One way to calculate an estimate for the distance to the Moon is to use a feature that occurs both on Earth and on the Moon. Subject to size and magnification, the distance should be a function of perceived size. The diameter of the Meteor Crater in the image is 35 mm. For an observer at the level of the crater, it is 1,186 km in diameter. The angle between the observer's path vertically decreases from 90° as the distance of the observer from the crater rim increases from 593 km for an observer starting level with the crater rim at the center.

Landsat 1 has a periapsis of 897 km and an apoapsis of 917 km, for an average of 907 km. If the Barringer Meteor Crater was photographed by Landsat 1 at a magnification of 1 it produced a 35 mm diameter image at 907 km. This suggests a photographic "shrink factor" equal to the actual diameter in mm divided by 35 mm or 3.39 x 107. As the perceived size shrinks with distance from the crater, the "shrink factor" should remain constant until the camera onboard can no longer image the crater (spatial resolutions ranging from 15 to 60 meters).

For the Meteor Crater image:

${\displaystyle 35mm={\frac {1186km}{3.39\times 10^{7}}}\times {\frac {907km}{distance}}.}$

For example, if the size of a crater in the image at the top of the page is 1 mm and the image was taken by the same Landsat 1 camera, then the distance to the crater is approximately 35 times the distance of Landsat 1 above the Meteor Crater or 31,745 km.

If there are 9 pixels/mm, then a comparable crater of one pixel diameter corresponds to a distance of 285,705 km. For a Moon at an average distance of 384,000 km, there would need to be at least 12 pixels per mm.

"A lunar observation by Landsat could provide improved radiometric and geometric calibration of both the Thematic Mapper and the Multispectral Scanner in terms of absolute radiometry, determination of the modulation transfer function, and sensitivity to scattered light. A pitch of the spacecraft would be required."[1]

Therefore, Landsat can take an image of the Moon. If its minimal image size corresponds to a crater comparable to the Meteor Crater, then such a Landsat image would yield a value for the distance to the Moon.

Title

by line

Abstract

Introduction

Experiment

Results

Discussion

Conclusion

Evaluation

To assess your calculations, including your justification, analysis and discussion, I will provide such an assessment of my example for comparison.

Evaluation

Hypotheses

Main source: Hypotheses
1. The width of a feature decreases perceptively the further away vertically the observer travels.