Tag Archives: Lunar Eclipse

NASA Space Place – Measure The Moon’s Size And Distance During The Next Lunar Eclipse

Poster’s Note: One of the many under-appreciated aspects of NASA is the extent to which it publishes quality science content for children and Ph.D.’s alike. NASA Space Place has been providing general audience articles for quite some time that are freely available for download and republishing. Your tax dollars help promote science! The following article was provided for reprinting in September, 2015.

By Dr. Ethan Siegel

2013february2_spaceplaceThe moon represents perhaps the first great paradox of the night sky in all of human history. While its angular size is easy to measure with the unaided eye from any location on Earth, ranging from 29.38 arc-minutes (0.4897°) to 33.53 arc-minutes (0.5588°) as it orbits our world in an ellipse, that doesn’t tell us its physical size. From its angular size alone, the moon could just as easily be close and small as it could be distant and enormous.

But we know a few other things, even relying only on naked-eye observations. We know its phases are caused by its geometric configuration with the sun and Earth. We know that the sun must be farther away (and hence, larger) than the moon from the phenomenon of solar eclipses, where the moon passes in front of the sun, blocking its disk as seen from Earth. And we know it undergoes lunar eclipses, where the sun’s light is blocked from the moon by Earth.

Lunar eclipses provided the first evidence that Earth was round; the shape of the portion of the shadow that falls on the moon during its partial phase is an arc of a circle. In fact, once we measured the radius of Earth (first accomplished in the 3rd century B.C.E.), now known to be 6,371 km, all it takes is one assumption—that the physical size of Earth’s shadow as it falls on the moon is approximately the physical size of Earth—and we can use lunar eclipses to measure both the size of and the distance to the moon!

Simply by knowing Earth’s physical size and measuring the ratios of the angular size of its shadow and the angular size of the moon, we can determine the moon’s physical size relative to Earth. During a lunar eclipse, Earth’s shadow is about 3.5 times larger than the moon, with some slight variations dependent on the moon’s point in its orbit. Simply divide Earth’s radius by your measurement to figure out the moon’s radius!

Even with this primitive method, it’s straightforward to get a measurement for the moon’s radius that’s accurate to within 15% of the actual value: 1,738 km. Now that you’ve determined its physical size and its angular size, geometry alone enables you to determine how far away it is from Earth. A lunar eclipse is coming up on September 28th, and this supermoon eclipse will last for hours. Use the partial phases to measure the size of and distance to the moon, and see how close you can get!

This article was provided by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

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Image credit: Daniel Munizaga (NOAO South/CTIO EPO), using the Cerro Tololo Inter-American Observatory, of an eight-image sequence of the partial phase of a total lunar eclipse. Click for a larger view.

About NASA Space Place

The goal of the NASA Space Place is “to inform, inspire, and involve children in the excitement of science, technology, and space exploration.” More information is available at their website: http://spaceplace.nasa.gov/

Total Lunar Eclipse, Mars Just Past Opposition And A Very Early Observing Event At Baltimore Woods on April 15th

Greetings fellow astrophiles!

The next few weeks are busy ones for CNYO and amateur astronomers in general.

April 10th (just this morning)STEM Career Day At National Grid (image below)
April 15th (from midnight to 3:30ish)Total Lunar Eclipse & Mars Just Past Opposition
April 12th and 13thCNYO and New Moon Telescopes (NMT) At NEAF
April 19thMOST Climate Day (And CNYO Lecture)
April 24th – Seasonal Observing At Beaver Lake Nature Center

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A piece of Mars, some meteors, several magnets, terrestrial rocks with larger meanings, four things we didn’t know “when I was their age,” and additional makings of a set of STEM astro demos.

But back to the eclipse and opposition. It is my opinion that lunar eclipses don’t get the respect they deserve. Yes, solar eclipses are much more exciting and it has been well-documented that people have previously responded very strongly (and not always pleasantly) to solar eclipses. The sudden darkening of the sky and noticeable temperature drop can cause all shades of responses (no pun intended) in people. That said, all we really get (besides a view of the solar corona) is an example of what happens when you put a black disc in front of the Sun. Lunar eclipses, on the other hand, tell us a bit about how the Earth itself interacts with the Sun by how this interaction alters our view of the Moon.

Both solar and lunar eclipses tell us something about the Sun/Earth/Moon relationship. Specifically, we learn that the Sun/Earth orbital plane (the oval made as the Earth goes around the Sun each year) and the Earth/Moon orbital plane (our local oval) are not the same – the Earth/Moon plane is tilted slightly off the Sun/Earth plane by 5.2 degrees (small, but just enough). That is, the Moon spends some time above and some times below the Sun/Earth orbital plane, while sitting right in the plane only two times each orbit (where the two planes intersect). How do we know this? Simple. If the Earth/Moon plane were exactly in the Sun/Earth plane, there would be a total solar eclipse and total lunar eclipse every month because there would be a time each month (New Moon) when the Sun, Moon, and Earth made a straight line (Sun-Moon-Earth = solar eclipse) and a time each month (Full Moon) when the Sun, Earth, and Moon made a straight line (Sun-Earth-Moon = lunar eclipse). As the two planes are slightly off, the New Moon is simply “off the radar” of most people because it can’t be seen during the daytime. The Full Moon, on the other hand, is brilliantly bright most of the time because it only infrequently enters the Earth’s shadow.

The image below shows this very nicely (and it’s always better to find and cite a good image than to have to roll your own). Give it a look for 30 seconds to make sure each of the four cases make sense to you.

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The Sun/Earth and Earth/Moon orbital planes. Note the top and bottom orientations that are perfect for eclipses (and the left and right that are not). Image taken from www2.astro.psu.edu (from Chaisson & McMillan Publishing). Click for a larger view.

Total solar and lunar eclipses, then, occur on special, but periodic and predictable, occasions when the Moon finds itself exactly in the Sun/Earth plane. When it’s just ever-so-slightly off this plane AND still between the Sun and Earth (or still falls into the Earth’s shadow in the Sun-Earth-Moon arrangement), we get partial eclipses. Just that simple.

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What to expect on April 15th (the government’s cashing in on its short wavelength tax!). Image from this article at io9.com.

Perhaps the most striking difference between a solar and lunar eclipse is that a solar eclipse obstructs the disc of the Sun, leaving only a view of its wispy exterior (corona), while a lunar eclipse alters the color of the Moon while still allowing us to see it in its entirety. Those watching the lunar eclipse will see the Moon go from its usual bright grey to orange, then a dark red before reversing the color order. The reason for this dark red coloring is the same reason why our sky is blue – the scattering of light in our atmosphere. Recalling our handy scattering relationship – that scattering (I) is proportional to 1 / wavelength4, we see that shorter wavelengths scatter more than longer wavelengths (because the wavelengths are in the bottom of the proportion, so larger numbers decrease the value of “I”). The image below was taken from one of the great non-wikipedia physics sites (well worth several afternoons to explore), hyperphysics.phy-astr.gsu.edu.

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The scattering relationship. See hyperphysics.phy-astr.gsu.edu/…/blusky.html for much, much more.

We see that shorter wavelength light gets “bounced around” more, while longer wavelength light passes for longer distances unimpeded by interactions with molecules and larger particles (like soot after big volcanic eruptions) in our atmosphere. Light going straight from the Sun hits our atmosphere and gets increasingly scattered as wavelength gets shorter – blue scatters more than red, so we see the blue strongly when we look up during the day. With the blue light strongly scattered, those people on the edges of where the Sun’s light falls – those just starting or ending their days – see more red light because that wavelength wasn’t as strongly scattered – effectively those at sunrise and sunset get the filtered-out leftovers of the light that those at high noon see as blue. The “lit” side of the world experiences a range of different colors depending on where they are during the day, but all are being illuminated by waves of light from the Sun that left at the same exact time (plus or minus a nanosecond or two).

Because it’s a busy week and the author is feeling lazy, he refers you to the top image of the three-panel image below, showing how the scattering of sunlight in our atmosphere occurs sooner after entry (on average) for blue, a bit later (on average) for green, then a bit later (on average) for yellow, then out to red, some of which is and isn’t scattered (on average).

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The scattering of light by Earth’s atmosphere (shorter wavelengths scatter sooner). The other two images are placed into context by your reading about extrasolar planetary atmosphere studies. See www.universetoday.com/…-in-blue-light/ for that info.

And so, we know that blue is scattered strongly and red is not. This red light then races to the edges of our illuminated globe and the red light not scattered directly down to Earth or scattered in the opposite direction (out into space right above you) races past Earth at various altered (scattered) angles. During the most complete part of the lunar eclipse, the red color you see is, in fact, the red light that is passing through the edges of our atmosphere at those places experiencing sunrise and sunset (the sunlight performing a “grazing blow” of our atmosphere). As you might guess, if Earth were to lose its atmosphere (but don’t give any of your industrious friends any ideas), our lunar eclipses would appear quite different. Instead of a dark red Moon, we’d simply see a black disc where no stars shone (like placing a quarter at arms length and obscuring anything behind it).

This lunar eclipse just happens to coincide with another special event in our Solar System that just passed on April 8th – Mars at Opposition. Earth-centric oppositions occur when the Sun and a planet (from Mars out to Neptune, then dwarf planets, comets and asteroids also fit the description) are on opposite sides of the sky to one another (this cannot happen for Venus and Mercury to an observer standing on Earth – this also means that Earth is never “at opposition” for Mars). This necessarily means that, when this occurs, the Earth and that other object are as close as they will get for that Earth year. Because our orbits are not circular around the Sun, our distances at opposition do vary. The slightly outdated image below shows this difference of opposition distances for Mars from 1995 to 2001. August of 2003 was our closest approach (34 million miles) to Mars in roughly 60,000 years, making for some impressive views through even medium-sized scopes.

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Mars distances at four oppositions. Image taken from the Hubble Space Telescope website. Click for a larger view.

What does this opposition mean for us? For those attending Baltimore Woods for Bob Piekiel’s special Lunar Eclipse observing session on the (really early) morning of April 15th (that is, we’ll be set up from 11:00 p.m. on the 14th and hanging out until it’s over), this means that Mars will be just a few days past its closest approach to Earth, making for especially good views through the scopes in attendance. Add Jupiter and Saturn over the course of the lunar eclipse, and we’ve a small feast of planetary observation for the evening. We hope you can join us!

Bob Piekiel Hosts Observing Sessions At Baltimore Woods (And More!) – 2014 Observing Schedule

I’m pleased to have obtained the official schedule for Bob Piekiel’s growing observing and lecture programs for the 2014 season and have added them to the CNYO Calendar. For those who have not had the pleasure of hearing one of his lectures, attending one of his observing sessions, or reading one of his many books on scope optics (or loading the CD containing the massive Celestron: The Early Years), Bob Piekiel is not only an excellent guide but likely the most knowledgeable equipment and operation guru in Central New York.

Notes On Baltimore Woods Sessions:

The Baltimore Woods events calendar is updated monthly. As such, I’ve no direct links to the sessions below. Therefore, as the event date nears, see the official Calendar Page for more information and any updates on the event.

Also…

* Registration for these events are required. Low registration may cause programs to be canceled.
* $5 for members, $15/family; $8 for nonmembers, $25/family.
* To Register By Email: info@baltimorewoods.org
* To Register By Phone: (315) 673-1350

Green Lakes:

* February 8 (Fri.)/9 (Sat. weather alternate), 1-3 p.m.

Solar viewing session at the main office parking lot. See the Green Lakes website for directions.

Baltimore Woods:

* February 21 (Fri.)/22 (Sat. weather alternate), 7-9 p.m.

The giant planet Jupiter will be in prime viewing position all night long, as well as the brilliant winter skies surrounding the constellation Orion. Uranus and Neptune will also be visible early.

* February 22 (Sat.)/23 (Sun. weather alternate), 1-3 p.m.

A solar viewing program, featuring our nearest (and favorite) star! Come and enjoy safe views of the Sun through a variety scopes and several wavelengths.

* March 21 (Fri.)/22 (Sat. weather alternate), 7-9 p.m.

Jupiter will be visible high in the sky for excellent viewing in the evening, then come and bid farewell to the Winter Skies.

Montezuma Wildlife Refuge:

* March 28 (Fri.)/29 (Sat. weather alternate), 7:30-9:30 p.m.

Come and enjoy the late Winter / early Spring skies, featuring views of Jupiter.

Baltimore Woods:

* April 15, VERY Early Tuesday A.M. – Midnight to 2:30 am

Again, assume this starts at 11:59 p.m. on Monday, April 14th and goes through about 2:30 a.m. Tuesday morning. This is the first Lunar Eclipse CNY has had in several years, and it will be visible in its entirety for all in NY State. Watch the Moon get covered by the Earth’s shadow and turn a deep shade of orange or red. Saturn and Mars will be in good viewing positions as well for scope viewing.

Mohawk Valley Astronomical Society:

* May 14 (Wednesday)

Bob Piekiel gives the lecture “Collimating Cassegrains and Two-Mirror Scopes” for our friends in the Mohawk Valley Astronomical Society (MVAS).

Baltimore Woods:

* May 23 (Fri.)/24 (Sat. weather alternate), 8:30-10:30 p.m.

Join Bob Piekiel for a possible Meteor Storm! In the early morning hours of Saturday, May 24, the Earth will pass through the debris field left behind by a small comet known as P/209 LINEAR. Astronomers are predicting that this interaction may result in a brief but intense burst of meteor activity that could range from dozens to hundreds of meteors per hour. Nothing is certain, but many mathematical models are predicting that this could be the most intense meteor shower in more than a decade. Saturn will also be at its biggest for its best viewing of the whole year, plus good views of Jupiter and Mars are to be had. Come and say “hello” to the Spring Skies!

* June 6 (Fri.)/7 (Sat. weather alternate), 8:30-10:30 p.m.

Join Bob Piekiel for an in-between Baltimore Woods sessions during this weekend’s Mars and Moon Conjunction.

Baltimore Woods:

* July 18 (Fri.)/19 (Sat. weather alternate), 8:30-10:30 p.m.

Look into the heart of our Milky Way galaxy to see the finest examples of rich star clusters and gaseous nebulae. Also fantastic views of Mars and Saturn.

Green Lakes:

* July 25 (Fri.)/26 (Sat. weather alternate), 8:30 – 10:30 p.m.

Summer Milky Way, at the Frisbee Golf field.

Baltimore Woods:

* August 12 (Tues.)/13 (Wed. weather alternate), 8:30-11:00 p.m.

The annual Perseid meteor shower, one of the year’s finest, plus Summer Skies and the Milky Way. Look into the heart of our Milky Way galaxy to see the finest examples of rich star clusters and gaseous nebulae. Also fantastic views of Mars and Saturn.

Green Lakes:

* August 15 (Fri.)/16 (Sat. weather alternate), 8:00 – 10:30 p.m.

Summer skies and left-over Perseids.

Baltimore Woods:

* August 16 (Sat.)/17 (Sun. weather alternate), 1:00-3:00 p.m.

Solar observing program

Seneca Meadows:

* August 22 (Fri.)/23 (Sat. weather alternate), 8:30-10:30 p.m.

Summer skies

Clark Reservation State Park:

* August 29 (Fri.)/30 (Sat. weather alternate), 8:00-10:00 p.m.

Baltimore Woods:

* October 8 – EARLY MORNING 4:30 – 6:30 am.

Lunar Eclipse, NO BACKUP DATE.

* Monday, November 17 (backup Tuesday 18th) 8 – 10 p.m.

Leonid meteor shower and hello to fall skies. Also the planets Uranus and Neptune.

* Saturday, December 13 (backup Sunday the 14th) 7 – 9 p.m.

The Geminid meteor shower and hello to winter skies.

Barlow Bob’s Corner x 2 – The Sunspotter Solar Telescope & Activity For The Sunspotter Solar Telescope

The following two articles have been provided by Barlow Bob, founder & organizer of the NEAF Solar Star Party and regional event host & lecturer on all things involving solar spectroscopy. You can read more about Barlow Bob and see some of his other articles at www.neafsolar.com/barlowbob.html.

Barlow Bob’s Corner #1 – The Sunspotter Solar Telescope

Galileo demonstrated that the Sun rotated by observing sunspot movements and argued that, based on these imperfections on the surface of the Sun, that the Sun was not perfect. This statement angered the Roman Catholic Church during the Renaissance. The church stated that God was perfect – therefore, the Sun was perfect, without blemishes. Unfortunately, he lost his sight caused by illness. He might have lost his sight by observing the Sun through his telescope without a safe solar filter. However, there is now a safer way to observe the Sun.

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The Sunspotter (image from www.pha.jhu.edu/dept/lecdemo/)

The Sunspotter Solar Telescope can be used to safely recreate Galileo’s solar observation. You can confirm this rate of rotation and observe that the number of sunspots change over the Solar Sunspot Cycle. The Astronomical League even has a Sun Spotters Observing Award.

The Sunspotter product is the safer solar telescope for observing sunspots.

This unique solar telescope projects an image of the solar surface on a small piece of paper. Sunlight passes through a lens and is reflected off three mirrors and passing through an eyepiece that projects the solar image on to a small piece of paper. A group of people of all ages can observe the solar image at the same time.

The Sunspotter creates an image of the Sun by eyepiece projection. After you align it with the Sun, light passes through the 61.7 mm objective lens, stopped down to 57.0 mm. It is reflected off of three mirrors into the 12.5 mm FL field lens.

A 3.5-inch image of the Sun, magnified 56 times, is projected on to a white viewing screen. You can observe features on the Sun, in all wavelengths of light, as they would appear in a small refractor. The triangle-shaped wooden telescope sits in a semicircle cradle. You can observe the Sun from 0 to 30 degrees.

When you reverse the telescope in the cradle, you can observe the Sun from 30 to 90 degrees.

This wooden folded-Keplerian telescope is constructed using techniques found in a fine piece of furniture. Perhaps the manufacturer should consider selling this product in a furniture gallery store. The Sunspotter appears to have been created by Al Nagler, in a seventh grade wood shop class, while the other students made salad bowls.

The Sunspotter was created for use in a classroom for a short period of time. However, to use it longer requires the ability to track the motion of the Sun across the sky. Upon arrival at a solar observing session, I set up a small canvas camp table on level ground. A two-foot-square thick piece of sturdy plastic or plywood is placed on the table, to create a stable platform. A television swivel stand sits on this platform. The Sunspotter is placed on the swivel stand, to create a simple mount to manually move the solar telescope to track the movement of the Sun.

You do not notice the movement of the Sun across the sky over a short period of time. However, you do notice the movement of the Sun at sunrise or sunset, when it is against the horizon. Kids of all ages are fascinated by the projected image of the Sun in the Sunspotter, dancing across the white viewing screen. Most people are surprised to see how fast the solar image moves across the viewing screen, caused by the rotation of the Earth under the Sunspotter. Students and teachers have taken a video of this movement of Earth for science projects.

It is very easy to align this cleverly designed solar telescope with the Sun. There is a gnomon, consisting of a short wooden rod on the front, above the objective lens. Simply point the front of the telescope in the direction of the Sun and move the telescope until this gnomon no longer produces a shadow on the front of the telescope. Two points of light are projected on the back inside through two small holes on the right and left of the objective lens. Two small circles are drawn on the rear inside. When you align the tow point of light inside of these circles, an image of the Sun is projected on the white viewing screen under the eyepiece.

This product is extremely easy to operate. I shared the Sunspotter at a Boy Scout Summer Camp – while a father was reading the operating instructions on the back of the Sunspotter, his six-year old son aligned the telescope. The son watched the previous scouts align it.

YOU DO NOT GET A SECOND CHANCE IN SOLAR ASTRONOMY!

How much are your eyes worth?

While the Sunspotter is the safer solar telescope, it is also the cooler lunar telescope. You can also use the Sunspotter as a Moonspotter to observe the Moon from First Quarter to Third Quarter. I even used this product to observe a Lunar Eclipse.

The wooden Sunspotter solar telescope has an extremely unusual shape. The central part has a triangular shape, containing an objective lens, three mirrors, and an eyepiece. The mount has a crescent shape with feet on the bottom.

Manufacturers of cases for astronomy telescopes and accessories do not make a padded case for the Sunspotter, with its unique shape. This product was shipped in a large cardboard carton, with a hard fitted foam interior. The Sunspotter fits securely inside of this shipping carton.

I carried the Sunspotter into a music store. People who are not amateur astronomers look at you funny when you carry a weird looking wooden object into a music store. I told the store employee that I was looking for a large padded drum case to hold this wooden telescope. The employee showed me several cases. The Sunspotter fit perfectly into one case.

When I placed the Sunspotter on its side in the bottom of the drum case, there was additional empty space in the top. I bought a round foam pad in a housewares store. I placed this pad over the Sunspotter and I now store clothing in the top half of this case.

Since I now store various small cases containing the parts of my other solar telescopes in the large drum case, I had to find another case to hold the Sunspotter. I left the Sunspotter in its shipping carton. However, this large box is difficult to carry from my vehicle to the observing field of an event.

The bedding sales area of a local retail store had comforters on display stored in heavy plastic cases with zippers. These large plastic cases appeared to be the same size as the Sunspotter shipping carton. I considered buying a comforter, just to get this plastic case.

While observing the Sun with Chuck and Carol Higgins, I mentioned my idea to buy a comforter to get a plastic case to hold the Sunspotter. They gave me an empty heavy duty plastic comforter case. The Sunspotter shipping carton fit perfectly inside of this plastic case with a handle.

At an art supply store, I bought a small and large portfolio case used to carry art works. The television swivel stand and two-foot square piece of heavy plastic or plywood fit into these cases. I now can protect the Sunspotter and easily carry it plus the mount at a solar star party.

This product was created for the vertically challenged. It has been rumored that elves us the Sunspotter at the North Pole. However, they can only use it for six months – during summer vacation.

I set the Sunspotter up at the annual NEAF – Northeast Astronomy Forum – in Suffern, New York. Amateur astronomers were fascinated with this product. Some ATM people photographed it or used a video camera. Others took measurements or made drawings of how it was constructed. They probably stopped at Home Depot on the drive home to build their own wooden Sunspotter.

The Sunspotter
Ref: SKE:654-0145
price: USD $349.95.

For additional information contact:
Science First
86475 Gene Lasserre Blvd.
Yulee, FL 32097

www.sciencefirst.com
(800) 875-3214
(904) 225-5558
Fax: (904) 225-2228

If Galileo had used the Sunspotter, he still would have been in trouble with the church. However, he could have retained his eyesight.

Barlow Bob’s Corner #2 – Activity For The Sunspotter Solar Telescope

The Sunspotter product is the safer solar telescope for observing Sunspots.

This unique solar telescope projects an image of the solar surface on a small piece of paper. A group of people can observe the solar image at the same time. Kids of all ages are amazed at how fast the solar image moves across the piece of paper. You can also observe the Moon through this telescope.

Several years ago, someone told me about an additional educational activity using the Sunspotter. When you observe the Sun, where is the solar equator?

You can use the Sunspotter to find the solar equator.

A six-inch embroidery hoop will fit on the piece of paper. A wooden or plastic embroidery hoop can be bought at a craft store. Make a pen mark at the top and bottom of the hoop. Make another pen mark on the right and left sides of the inside hoop. Drill four small holes in the inside hoop at the pen marks. Finally, pick up a spool of the thin green wire used to attach gardening plants to wooden stakes – sold in hardware, craft or gardening stores.

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The completed embroidery loop and green wire.

Thread the green wire through the first hole from the outside into the second hole on the opposite side. Continue to move the wire across the top of the inside hoop and into the next hole. The wire is finally threaded into the last hole. Wrap the two ends of the wire through the first and last holes several times to secure the ends. Once the wire has been threaded through the four holes, two perpendicular wires form a crosshair inside of the hoop. Attach the larger outside hoop to the smaller inside hoop and tighten the bolt to secure the two hoops together.

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The completed loop with Sunspotter.

Place the altered embroidery hoop on top of the small piece of paper displaying the projected solar image. You will usually see two groups of sunspots between that equator and solar North and South Poles. As the solar image drifts across this piece of paper, keep moving the horizontal wire until the sunspots move in a line following the wire. This will show you the orientation of the Solar Equator.

Sue French provided the following information and is used here with permission.

The plane of our Solar System is defined as the mean plane of the Earth’s orbit. Earth is the only planet whose orbit isn’t inclined to the plane of the Ecliptic. If you still count Pluto as a planet, it has the highest inclination, Mercury the second highest, and Venus the third. The Sun’s axis is tipped with respect to the plane of the Ecliptic, so even if the Earth had no axial tilt, the Sun’s equator would appear high, low, or tipped depending on where Earth is in its orbit around the Sun (take a normally tilted globe of the Earth. Pretend that it’s the Sun and you are the tilt-free Earth. Walk around the globe to simulate your orbit around it, and see how the view of its equator seems to change). And the apparent tilt of the Sun’s equator with respect to the observer’s horizon would also change as the Sun takes its daily path across the sky for anyone that didn’t live somewhere along the Earth’s Equator.

This will show you the orientation of the solar equator. You could also try this with solar eyepiece projection.