Lunar Observations - Part 2

Summary: In this section, you will measure the diameter of the moon, "prove" that the moon is spherical, and look at other interesting features on the near side of the moon.

Grading (25 points): After all students on your lab night have had enough time to completed this lab, the TA may give a quiz at the beginning of the next lab period or may ask you to turn in a write-up, including your observing notes and sketches and your answers to the questions.

Note: Much of what you should do during lab time is to make observations and sketches and to discuss what you are doing with your lab partner and classmates. Any calculations can be done outside of lab time, based on the data you collect during lab. Similarly, you should discuss during lab time how to answer questions posed in this lab, but you should write down your answers outside of lab time.

1. How big is the moon? For a quick and dirty estimate of the diameter of the moon, use the fist and finger rules (Appendix A) to estimate the angular diameter (theta) of the moon.

theta [degrees] =

Convert this angular diameter from units of degrees to units of radians (remember there are 360 degrees in a circle, or 2 x pi radians in a circle):

Theta [degrees] x ( 2 x pi [radians])/360 [degrees] =

The small triangle formula enables us to determine the diameter of the moon (d_moon) if we know the angular size (which we just measured) in units of radians (and we just did that units conversion) and the distance to the moon (D_moon), according to the formula:

d_moon = D_moon x Theta

Using radio signals, we know that the average distance beteen the center of the earth and the center of the moon is 384,000 km. Provided that the diameter of the moon is much, much smaller than 384,000 km, our formula above will be a valid method for determining d_moon.

Question: What is d_moon?

Question: Is the small triangle approximation we just used reasonable?

A better way to measure the diameter of the moon is by the method of transit times described in Appendix B. With the telescope drive on, this can be accomplished by first aligning the westen edge of the moon with the eastern edge of the field. Switch the drive off and measure the time T it takes for the entire moon to drift across this edge. Also, note the current declination of the moon. You can do the final calculation of d_moon outside of class.

T [seconds] =

declination [degrees] =

d_moon [km] =

In principal, we could use the transit time method to measure the size of any feature on the moon. You could measure the diameters of individual craters, for instance. You might want to try this on a lunar feature of interest to you, later during this lab.

Question: How does the diameter of the moon compare with the diameter of the earth? To do this, compute the ratio d_earth / d_moon.

Question: Calculate the volume of the moon and compare your answer to the volume of the earth? To do this, compute the ratio Volume_earth / Volume_moon. Assume both objects are spheres (V = 4/3 x pi x (D/2)^3.

Question: The mass of the moon is about 1/80 the mass of the earth. Calculate the average density of the moon (density = mass/volume) and compare this to the average density of the earth? What can we learn about the composition of the moon and earth from this result?

Question: Calculate the surface gravity on the moon relative to that of the earth using Newton's Law of Gravitation (F = G x M_1 x M_2 / (D/2)x(D/2). To do this, you can calculate the surface gravity for the moon and also for the earth and then take the ratio, or you can take the ratio, algebraically, and only calculate the ratio.

2.What shapes are craters? Select craters that you think are similar in angular size that lie at a constant latitude on the moon. For the craters at your selected latitude, draw a sketch of a few craters, some near the middle of the moon, some part way to the lunar limb (the curved edge of the moon), some as close to the limb as you can find.

Question: Do the craters appear to change shape, moving from the lunar center outwards toward the limbs? If so how does the shape change?

Question: Why should or shouldn't the shapes of craters change or be the same at different lunar longitudes?

Question:What can you deduce about the shape of the moon based on these observations of apparent shapes of lunar craters?

3. More Observing. Find as many of the lunar features from the following tables as you can.

Sketch in reasonable detail examples of at least three different types of features.

Measure the linear size, using the method of Transit times, for a surface feature that interests you. Include your measurements and size calculations on the page with your sketch.

Question: Having extensively observed the near side of the moon, compare what you know and have seen with pictures of the far side of the moon (included in ClassPak). What differences do you notice between the near and far sides? Can you offer an explanation as to why these difference exist?

Lunar Observing List 1: Craters, Rays, Mountains

Notes: Selenographic longitude and latitude are measured from sub-Earth point on the lunar surface (i.e. the sub-Earth point is at position (0E, 0N). East and West are defined for an observer standing on the Moon (cartographic convention) and are reversed from the astronomical directions in the sky.

Name Sel. Long. Sel. Lat. Comments

Langrenus 62E -9 Large crater near the lunar limb

Petavius 60E -26 Rima Petavius, running from the central peak to the rim is an unusual feature. Best seen when the Moon is young.

Messier & Messier A 47E -2 This pair of craters probably formed simultaneously by a broken/binary impactor. Note the comet-like double ray extending from Messier A. Were these two craters caused by a grazing impact?

Proclus 47E +16 Small crater with a very bright ray system on the edge of Mare Crisium.

Fracastorius 33E -23 Flooded crater with collapsed N wall

Theophilus 26E -11 Relatively young crater overlapping Cyrillus

Altai Mtns 25E -25 Battered mountain range with sinuous scarp

Ariadaeus Rille 13E +6 Long, straight ``canyon''

Cassini 5E +40 Two smaller craters inside give it an unusual appearance.

Hyginus Rille 6E +8 Long, narrow rille (``canyon'') with a bend and a superimposed crater (Hyginus). Terrain to the North has many smaller grooves.

Alpine Valley 2E +49 Long, flat valley in the lunar Alps Mountains

Apennines Mtns 0 +18 Beautiful and complex chain of mountains

Mt. Piton 1W +41 Isolated mountain peak in Mare Imbrium

Ptolemaeus 2W -9 Large, round crater with dark floor. How many small craters can you see on its floor? Ptolemaeus is so wide (90km) that if you were standing at the center, you wouldn't see the crater rim as it would be below your horizon!

Archimedes 4W +30 Large crater with flat floor

Rupes Recta 8W -22 The ''Straight wall'' is a cliff that is 80 km long and 300 m high.

Mt. Pico 9W +46 Isolated mountain peak in Mare Imbrium

Plato 10W +52 Flat lava-flooded crater with dark floor. Can you see very small craters on its floor?

Tycho 11W -43 Young crater with the most extensive ray system on the Moon.

Eratosthenes 12W +14 Young crater at the S end of the Apennines Mtns. Compare to the larger Copernicus.

Stadius 14W +11 ``Ghost of a crater'', flooded by lava during the formation of Sinus Aestuum. Only the upper part of the rim is visible.

Clavius 14W -58 Very large, very old crater with many smaller craters superimposed (Seething Bay).

Montes Recti 20W +48 Small chain of mountains at the edge of Mare Imbrium

Copernicus 20W +10 Young crater. Note: central peaks, terraces inside wall, structure of outer slopes, chain of craterlets to the NE. About 60 km across, roughly the size of Davidson county.

Kepler 38W +8 Very bright ray system, visible to the naked eye!

Gassendi 40W -18 Floor criss-crossed by cracks

Schroter's Valley 50W +55 Deep ``canyon'' near crater Aristarchus

Grimaldi 68W -6 Large crater with flat, dark floor. Best seen near full Moon

High mountains -- near South pole This region shows the largest vertical relief on the Moon. These mountains and crater rims are seen sideways and reveal their true elevation. Compare with your perception of relief along the terminator.

Name	Sel. Long.	Sel. Lat.	Comments
Langrenus	62E	-9	Large crater near the lunar limb
Petavius	60E	-26	Rima Petavius, running from the central peak to the rim is an unusual feature. Best seen when the Moon is young.
Messier & Messier A	47E	-2	This pair of craters probably formed simultaneously by a broken/binary impactor. Note the comet-like double ray extending from Messier A. Were these two craters caused by a grazing impact?
Proclus	47E	+16	Small crater with a very bright ray system on the edge of Mare Crisium.
Fracastorius	33E	-23	Flooded crater with collapsed N wall
Theophilus	26E	-11	Relatively young crater overlapping Cyrillus
Altai Mtns	25E	-25	Battered mountain range with sinuous scarp
Ariadaeus Rille	13E	+6	Long, straight ``canyon''
Cassini	5E	+40	Two smaller craters inside give it an unusual appearance.
Hyginus Rille	6E	+8	Long, narrow rille (``canyon'') with a bend and a superimposed crater (Hyginus). Terrain to the North has many smaller grooves.
Alpine Valley	2E	+49	Long, flat valley in the lunar Alps Mountains
Apennines Mtns	0	+18	Beautiful and complex chain of mountains
Mt. Piton	1W	+41	Isolated mountain peak in Mare Imbrium
Ptolemaeus	2W	-9	Large, round crater with dark floor. How many small craters can you see on its floor? Ptolemaeus is so wide (90km) that if you were standing at the center, you wouldn't see the crater rim as it would be below your horizon!
Archimedes	4W	+30	Large crater with flat floor
Rupes Recta	8W	-22	The ''Straight wall'' is a cliff that is 80 km long and 300 m high.
Mt. Pico	9W	+46	Isolated mountain peak in Mare Imbrium
Plato	10W	+52	Flat lava-flooded crater with dark floor. Can you see very small craters on its floor?
Tycho	11W	-43	Young crater with the most extensive ray system on the Moon.
Eratosthenes	12W	+14	Young crater at the S end of the Apennines Mtns. Compare to the larger Copernicus.
Stadius	14W	+11	``Ghost of a crater'', flooded by lava during the formation of Sinus Aestuum. Only the upper part of the rim is visible.
Clavius	14W	-58	Very large, very old crater with many smaller craters superimposed (Seething Bay).
Montes Recti	20W	+48	Small chain of mountains at the edge of Mare Imbrium
Copernicus	20W	+10	Young crater. Note: central peaks, terraces inside wall, structure of outer slopes, chain of craterlets to the NE. About 60 km across, roughly the size of Davidson county.
Kepler	38W	+8	Very bright ray system, visible to the naked eye!
Gassendi	40W	-18	Floor criss-crossed by cracks
Schroter's Valley	50W	+55	Deep ``canyon'' near crater Aristarchus
Grimaldi	68W	-6	Large crater with flat, dark floor. Best seen near full Moon
High mountains	--	near South pole	This region shows the largest vertical relief on the Moon. These mountains and crater rims are seen sideways and reveal their true elevation. Compare with your perception of relief along the terminator.

Lunar Observing List 2: Apollo Landing Sites

Name	Sel. Long.	Sel. Lat.	Comments
Apollo 11 (7/20/69)	23.5E	+0.7	Between craters Sabine and Moltke
Apollo 12 (11/19/69)	23.5W	-3.0	Between craters Fra Mauro and Lansberg
Apollo 14 (2/5/71)	17.5W	-3.7	Just North of Fra Mauro
Apollo 15 (7/30/71)	3.6E	+26.1	At the North end of the Apennines Mtns
Apollo 16 (4/21/72)	16.0E	-9.0	In the lunar highlands, W of crater Theophilus, just north of crater Descartes
Apollo 17 (12/11/72)	30.8E	+20.2	In the Taurus Mtns, near crater Littrow

After you have completed this lab and attempted to answer the questions, based on your observations, on your discussions with your lab partner and classmates, and after consulting your textbood for help, compare your analysis of your moon observations with the discussion found in More About the Moon