Astronomy

What is the maximum possible separation between sun and moon in the earth sky for an eclipse to occur?

What is the maximum possible separation between sun and moon in the earth sky for an eclipse to occur?


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How do we calculate the maximum angular separation between sun and moon during:

  1. Solar Eclipse
  2. Lunar Eclipse

We'll need the angular diameter of the Sun: 31.6-32.7 arcminutes; the Moon's is between 29.3 and 34.1 arcminutes (found on Wikipedia).

The solar eclipse case is 0 degrees; it can only be an eclipse if the Moon is touching the Sun. In that case, their centers are at most (32.7 + 34.1) / 2 = 33.4 arcminutes apart.

A lunar eclipse would occur if the Sun and Moon are diametrically opposite in the sky; the separation of their centers is then 180 degrees. The actual separation is at least (31.6 + 29.3) / 2 = 30.45 arcminutes less than 180 degrees.


All Of Your Questions Answered About Next Week’s Unique Solar Eclipse: The Only Guide You’ll Need

12-year-old Alex Frye checks his special viewing glasses prior to viewing the partial solar eclipse . [+] from a highway overpass in Arlington, VA, Thursday, Oct. 23, 2014, . Photo Credit: (NASA/Bill Ingalls)

Next week there’s a rare kind of solar eclipse in North America, the first one since 2017 and the only one this century to cross the North Pole.

It will be visible as a “ring of fire,” a “crescent sunrise” and a “smiley face Sun,” depending on your precise location. As well as looking different depending on place, it will happen at different times, and be both dangerous and safe, impactful and not so interesting—all depending on where you are on the planet, and when you look.

You have questions? Here they are—the only guide you’ll need to June 10, 2021’s annular solar eclipse, how to see if safely and how to photograph it:


How to watch the Partial Solar Eclipse on Thursday 10th June

On Thursday this week (10th June) we’re treated to a special celestial event – an eclipse. Eclipses are a regular if infrequent occurrence – a natural result of the movement of the Moon around the Earth.

As the Moon orbits the Earth the three bodies line up every now and again. Because the Moon is 1/400th the Sun’s diameter and 1/400th the distance away the two objects look about the same size on the sky – by sheer fluke! This makes it possible for one to block out the other. Thursday’s eclipse is solar – the Moon is in between the Sun and the Earth, casting a shadow on the Earth’s surface.

As the Moon orbits the Earth, Earth Sun and Moon regularly line up as in the image below.

The Moon completes an orbit of the Earth around every 28 days – however the Moon’s orbit is inclined at an angle of about 5⁰ to the Earth’s orbit around the Sun, which is why eclipses do not occur every month.

Above: Geometry of a solar eclipse – image from ESA

From the UK, this solar eclipse will be partial– as the Moon passes in between the Earth and Sun the three bodies won’t be lined up exactly from our viewpoint, so the Moon will cover just a small section of the Sun. Weather permitting, from the UK it will appear as below (timings are for the location of Jodrell Bank):

First contact – the Moon grazes the edge of the Sun

Precise timings vary depending on your location – check out this page Solar & Lunar Eclipses Worldwide (timeanddate.com) to find the exact timings for where you are (you may see timings in the media for ‘UTC’ which is Coordinated Universal Time and can be considered as the same as GMT).

From some other parts of the world the eclipse will be ‘annular’ – this is where the Moon’s disk doesn’t entirely cover the disk of the Sun (that would be a total eclipse) but leaves a bright ring visible at the moment of maximum coverage. This happens because neither the Earth’s orbit around the Sun nor the Moon’s orbit around the Earth is exactly circular, so that the apparent sizes of the Sun and Moon vary somewhat – this means that sometimes, as in this case, the Moon can look a bit smaller in the sky and so unable to cover the Sun’s disk completely.

For more info about this week’s eclipse check out Annular Solar Eclipse on 10 June 2021 (timeanddate.com) and for a comprehensive guide plus predictions for future eclipses check out MrEclipse.com

Safe observing

Never look at the Sun directly as it can severely damage your eyes. To view the eclipse safely you can either use a pinhole viewer which is super simple to make How to View a Solar Eclipse: Make a Pinhole Projector (timeanddate.com) or – even easier – you can experiment with using things that already have holes in them such as a colander. Just line the colander up with the Sun so that it casts a shadow on the ground and move it towards or away from you until the lines are sharp – during the eclipse you will see lots of crescents as in the picture below.

Above: Image courtesy of Wikimedia Commons : Steve Elliott from UK, CC BY-SA 2.0

These are fun DIY ways to observe but you can also buy special eclipse glasses which allow you to look at the Sun safely – otherwise observation should never be direct as looking at the Sun can severely damage your eyes. In previous years there have been rumours suggesting that you can look at the Sun’s reflection safely in a pool of water – this is untrue and risks eye damage.

In case of cloudy skies there will also be a live stream available here

And if you’re free on Thursday morning and fancy a bit of astronomy with your morning coffee, book a ticket to visit us at Jodrell Bank Discovery Centre where, weather permitting, we will have safe observing by projecting the Sun’s image. As ever, our friendly and knowledgeable engagement team will be on hand to answer your astronomy questions.


Type: Total Solar Eclipse

Would you travel halfway across the world to experience one minute of totality? For eclipse chasers, that’s more than enough, so the tiny Exmouth Peninsula – the only part of Australia crossed by the path of totality – is sure to be bursting with observers from around the world. Exmouth is also the place to swim with whalesharks, the ocean’s biggest fish at 40ft.

For more Aussie stargazing, read our guide to astronomy in Australia.


Winter Solstice – First Day of Winter or Midwinter?

Now is the time that we should talk about the meteorological definition of the winter solstice. Well, technically speaking, if we go by the meteorological definition of the winter solstice, it marks the end of the half of the winter or winter season i.e mid-winter.

However, on the other hand, if we go by the astronomical definition of the winter solstice, it marks the arrival of the first day of winter. Therefore, the question arises that why we have two different definitions for a single event. More importantly, which one of these is the correct one? Let’s find out.

Let’s Go Back in Time

Before the arrival of the scientific revolution, humans didn’t know how to calculate the change in the season in terms of astronomical calculations. WHY? Because they didn’t have the telescope to do such nasty observations.

Therefore, what they used to do is to calculate the change in season as humanly as possible. With time, early humans understood that the sun seems to cross over the horizon after a fixed interval of time. Additionally, they also understood the pattern of the annual temperature cycle.

In other words, what early humans used to do is to calculate the relative things, like what they felt and observed with the naked eyes, which is in fact in the modern notation is known as the meteorological definition of winter solstice or simply meteorological winter.

On the other hand, what our astronomers and scientists calculate with their super-sophisticated technology is defined as the astronomical definition of winter solstice or simply astronomical winter.

Therefore, to conclude, I would say that both definitions are correct in their own sense. Hence, as a result, some people define winter solstice in the southern hemisphere as the first day of winter.

On the contrary, some people define it as the end of the half of the winter or winter season. Hence mid-winter. Not to mention, the meteorological seasons always arrive approx 20 days before the arrival of astronomical seasons. To understand it more clearly, refer to the below table.


SOLUTION: So Lost Please Help. A total solar eclipse occurs when the moon passes between the earth and the sun, and the darkest shadow cast by the moon, called the umbra, hits the surfac

Notice how I made the segment OO' a red segment and I made O'P a green segment.
I've also added in segments OD and O'C shown in blue
In addition, I marked a new point R which is the intersection between the circle for the earth and the segment OO''

"the distance from the center of the sun to the center of the earth is approximately 93,000,000 miles"
So, OO'' = 93,000,000

"the diameter of the sun is 870,000 miles", so the radius is half that: 870,000/2 = 435,000
So, OD = 435,000

"the diameter of the moon is 2160 miles", so the radius of the moon is 2160/2 = 1080
So, O'C = 1080

"the diameter of the earth is 7920", so the radius of the earth is 7920/2 = 3960
So, RO'' = 3960
Using the segment addition postulate, we can say

OO'' = OR + RO''
93,000,000 = OR + 3960
93,000,000 - 3960 = OR
92,996,040 = OR
OR = 92,996,040

During lunar apogee, the moon is 252,700 miles away from the earth. This means the length of segment O'O'' is 252,700
Using the segment addition postulate, we know
OO' + O'O'' = OO''
Let y be the length of OO' and solve for y

OO' + O'O'' = OO''
y + 252,700 = 93,000,000
y = 93,000,000 - 252,700
y = 92,747,300

Therefore, the distance from the center of the sun to the center of the moon during a lunar eclipse and during a lunar apogee is roughly 92,747,300 miles.

Summary so far
OD = 435,000
O'C = 1080
RO'' = 3960
OO' = 92,747,300
OR = 92,996,040

Let's go back to the drawing. Focus on just triangle ODP and the smaller triangle O'CP and add in the measurements you see in the summary above (well with the exception of RO'' and OR)

Now let x be the length of O'P shown in green . We need to find the length of x to help us solve this problem.

From the drawing, we see that OP is the sum of OO' and O'P.
OP = OO' + O'P
OP = 92,747,300 + x

We have similar triangles, so we can set up a proportion and solve for x

(OD)/(OP) = (O'C)/(O'P)
(435,000)/(92,747,300 + x) = (1080)/(x)
435,000x = 1080(92,747,300 + x)
435,000x = 1080(92,747,300) + 1080x
435,000x = 100,167,084,000 + 1080x
435,000x - 1080x = 100,167,084,000
433,920x = 100,167,084,000
x = (100,167,084,000)/(433,920)
x = 230,842.28429

The length of O'P is approximately 230,842.28429 miles.
Use this to find OP

OP = OO' + O'P
OP = 92,747,300 + 230,842.28429
OP = 92,978,142.28429

That's a lot of work, but we know these two important pieces of info
OP = 92,978,142.28429
OR = 92,996,040

If OP > OR, then P will be to the right of R and P will be inside the circle of the earth.
However, above we see that OP is actually less than OR. So P will actually be located to the left of point R.

Therefore, the eclipse is NOT possible. No shadow from the moon is cast at all. The moon is simply too far away from the earth.


"How far is P from the center of the earth during lunar apogee?" It's asking for the length of PO'', so let's find that

OO'' = OP + PO''
93,000,000 = 92,978,142.28429 + PO''
93,000,000 - 92,978,142.28429 = PO''
21,857.7157099992 = PO''
PO'' = 21,857.7157099992

Question: How far is P from the center of the earth during lunar apogee?
Answer: Roughly 21,857.7157099992 miles


Two Moons? What would happen?

Depends on the moons.
Mars's moons are very small and so have almost no effect mars.

Two Earth moons sized moons (!) would have an effect, especially on tides.

20500 km (1/3 the Hill sphere to be conservative).

If we assume that the moon's are of equal mass, Each will swing a little closer to Earth and a little further from Earth as it orbits the other, This means that when one is at its closest to the Earth, the other is at its furthest. This will tend to smooth out differences in tidal force due to the individual moons changing distance from the Earth. Any remaining difference would be very small compared to the difference due to the fact that our Moon already changes its distance by more than the separation of the two, due to the eccentricity of its orbit.

So, having two moons orbiting each other in binary fashion would not be much different than having one moon of the same combined mass.

20500 km (1/3 the Hill sphere to be conservative).

If we assume that the moon's are of equal mass, Each will swing a little closer to Earth and a little further from Earth as it orbits the other, This means that when one is at its closest to the Earth, the other is at its furthest. This will tend to smooth out differences in tidal force due to the individual moons changing distance from the Earth. Any remaining difference would be very small compared to the difference due to the fact that our Moon already changes its distance by more than the separation of the two, due to the eccentricity of its orbit.

So, having two moons orbiting each other in binary fashion would not be much different than having one moon of the same combined mass.

Sorry, I should have elaborated on what I meant rather than the two moons moving far and close to earth in their orbit, I meant that they would rotate from the north pole to east to the south to the west. so both moons would generally be the same distance from the earth at all times. though as you explained, with the maximum distance between the two moons being so small I'd imagine that moons in a binary configuration have much more effect than a single moon.



Comments:

  1. Medwine

    Indeed, and how I had not thought about it before

  2. Tuvya

    And then that.

  3. Beverly

    This is nothing more than a convention

  4. Crispin

    Surely. I agree with all of the above-said. Let us try to discuss the matter. Here, or in the afternoon.

  5. Dunixi

    All good. Thanks for the post!



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