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How much extra daylight per day?

Most of us are aware that from December 21st to June 20th, days get ever longer. From miserably short snippets of Winter sun, to the seemingly endless days of Summer our planet’s Northern hemisphere slowly tilts towards our Sun. I remember reading a book during a mid-summer trip up to the Isle of Skye which lies at 57.5° latitude, roughly as far North as Hudson’s Bay. It was almost midnight and I did not need any light other than the sun to be able to read. It’s very strange!

I love noticing that it is staying lighter until later in the evenings as spring advances, and this is accompanied by the return of migratory animals and the return to life of trees and flowers. It’s a lovely time of year that brings us hope and the sprouting of healthy food.

This got me thinking: we all love this extra daylight, but how much do we actually get from one day to the next? So I decided to pose this problem, as I really enjoyed solving it, and I intend to make full use of this bonus time from now until…

Using this graph ONLY, how many extra minutes of daylight do we get each day on average from the summer to the winter equinox, in Halifax?

Sun graph for Nova Scotia from www.timeanddate.com
graph showing daylight hours for Halifax, Nova Scotia, for 2019 from www.timeanddate.com.

HINT: I used Geogebra to get accurate measurements from which to perform my calculations.

Extra Questions

  • Do we gain the same number of minutes of daylight per day?
  • How does this situation change as we go from Summer to winter equinox?
  • Is this value the same at all places on planet Earth?
  • If not, where would it be greatest? Where least?
  • Why does the Ecuadorian tourist board describe Ecuador as: “The land of perpetual spring”?
  • What do the discontinuities in the graph show? (HINT: Your country may not do this!)

LINKS

Earth, Moon distance solution!

This is my solution to this problem. I have not finished yet…

NB: I know we could just Google the distance from the Earth to the Sun, but please do not – who would benefit from that? This is eduation kids!

So to solve this I used ideas I picked up from teaching ‘enlargements’, a subset of ‘geometric transformations’, in highschool Math classes. Some people would call it Thales theorem, to give credit to the chap who originally figured this out about 2500 years hence.

Step 1
I loaded up the image and used the ‘circle through 3 points’ tool in Geogebra to construct a circle which modelled the outlines of both Earth & Moon. I zoomed in a lot to enable me to position the 3 points as close to the circumferences as possible, to minimise errors.

Worked out the ratio of their actual diameters, which is in proportion to their
actual radii.

Used the ratio of diameters to divide radius of Earth in photo to get what the moon’s radius would be if it were at the same distance from the camera as the Earth.

Then I looked at the difference and figured it….

the Moon appears 1.327 times larger than it should were it the same distance as the Earth. So it must be….errr. Trouble is, we don’t know where the observer is… think on Dan!

How far is the moon from the Earth in this NASA photo?

Big thank you to NASA for allowing the use of its images for our education

Okay so we will use the (quickly Googled) ‘fact’ that Earth’s diameter is about 12 742Km.
TIDBIT: If you measure around the equator, Earth’s diameter is actually about 21Km greater than measured through the Poles, because the Earth is a huge spinning ball of molten metal that bulges out as it spins like a water-filled balloon!

Also we can use that the Moon’s diameter is about 3474Km

And I’m going to advise you to use my favourite software for this kind of visual modelling problem, Geogebra. Or maybe your brain works better than mine!

The moon transits across the face of planet Earth, photographed by a NASA satellite DISCOVR
Our Moon passing in front of our planet – DISCOVR satellite image courtesy of NASA

FYI this beautiful photo was taken by the Earth Polychromatic Imaging Camera ( truly “EPIC” ) on NASA’s DSCOVR satellite. Nice work everyone!

Here is my solution – do try it first though


How is this beautiful image of the Solar System dangerous?

The classic school poster of the Solar System. Pretty planets all in a row!
Loads of information here, but also a large dose of disinformation!

When I heard a loyal listener to the BBC’s More or Less podcast recently ask, “which planet is Earth’s nearest neighbour,” I honestly thought I knew the answer already. How wrong I was! As a teacher, I know all about ‘growth mindset’, so I am prepared to admit that I am poorly educated about our solar system (and I was lucky enough to have the opportuntity to study an Astronomy course at University a while back – even worse!).

Could my ignorance have had anything to do with unhelpful diagrams like the one below? The word ‘model’ has many meanings, but here we are talking about “a representation of current understanding”. For example “the model of gravity in the 19th century did not include quantum effects.”


What do you think is wrong with the ‘model’?

Loads of interesting information, but try to not remember it too clearly!

Let me first say I really like this image as a ‘poster’. In fact, having this kind of awe-inspiring scene displayed on classroom walls, gave me a great deal of relief and pleasure when I was bored in lessons, and probably made my teachers’ lives far easier. It gives an idea of how the planets appear visually, with all their wondrous rings & storms, and also shows their approximate relative sizes. No moons, but I guess they would have cluttered it up.

This beautiful image undeniably makes a dramatic and memorable impact, but because it is such an over-simplification, it might actually hinder our capacity to think accurately in geometrical terms about our star system. Can anyone really have a intuitive ‘feel’ for distances greater than the size of our planet?
Personally, I think I need accurate pictures to help my little brain reach up to such massive proportions.

Scale models show us the somewhat uglier truth!

Take a look at this image of a model of the Sun-Venus system made in Geogebra, which is actually drawn to scale (Mercury is the closest planet to the Sun).
QUESTION: The actual distance is about 58 million Km – can you figure out what scale this model uses?

Not half as pretty, but arguably more correct than the first model

ANSWER: So 58 million Km or 58 000 000 Km is shown by 5800 units. So 1 unit on the axes represents 10 thousand Kilometers in real-life. Roughly!

Take a look at the following image of a scale model showing the Earth with our Moon orbiting around us.
QUESTION: How many planet Earth’s do you think could fit in between Earth and the Moon?:


The distance from Earth to the Moon is shown to be 384.4 units above, where each unit is a million kilometers! How many Earths could fit in that gap?

ANSWER: Earth’s diameter is 12 742Km (WIKI); Earth-Sun distance is 384 402Km;
384402 / 12742 gives us about 30, so 30 planet Earths could fit side by side in the gap. This would look better in Latex!

Finally let’s take a glance at 3 images of a scale model that includes Earth, Moon and eventually the Sun. We’ll start focused on the Earth & Moon and gradually pull back to show how far away the sun is relatively . I apologise in advance – it’s kind of hard to see, but I will include links to the Geogebra applets below so you can go and explore at leisure.

Earth and the Moon’s orbital path
Zooming out…


The actual Solar System is far less photogenic!

Ahh, there is the sun! This distance is 1 AU (astronomical Unit) which is about 150 million Kilometers.

Have you seen any other ‘educational’ images that might be conceptually misleading?

Please submit a comment below with a link to the image in question.
My sincere thanks for reading folks!

LINKS

Who is our nearest planetary neighbour?


Our fellow wanderers, Venus, Mars & Mercury. But who is the closest?

A loyal listener to the BBC’s excellent “More or Less” podcast asked the other day about which planet is our nearest neighbour. He had heard on TV that it was Mars, but he himself thought it was Venus, so he asked them to investigate. 50 years of data were duly collected and dispatched, to an illustrious Professor, who revealed the answer on the show (link below!), so well done More or Less!

But hang on a moment. I am pretty sure that regardless of your existing astronomical knowledge, you will be able to figure this answer out for yourself, with just 50 seconds of data if you read on… What’s more, for the vast majority of human history nobody at all could have answered this question, and now we can do it on our ‘phones’. Simply wow!

HINT: The planets are named after the Greek word “planetes”, which means “wanderers”. Bear this in mind as you think about this problem.

So which planet is our nearest neighbour?

Mars’ Mariner Valleys – thanks to NASA for the gorgeous photo

Isn’t it Mars? Humans have been sending rovers to survey the place, and do plan on sending a manned, one-way mission at some stage. But it will take some 300 days to get there, and that is if you launch when our two planets are at their closest. Mars was also described as “planet Earth’s closest neighbour” on the BBC’s ‘Sky at Night’ program the other day too. Hmmmm.

Could it be Venus? I am pretty sure I have been told that Venus is the closest planet, and that is what my instinctive answer would be. There were loads of stories about aliens on Venus coming to invade Earth back when sci-fi was first starting to become popular many decades ago, so it would make sense as a choice.

Venus. This image was created using combined data from the Magellan, Pioneer and Venera data. Three separate missions were needed to create this image!

Why not Mercury? (The planet, rather than the metal AKA quicksilver) Named after the winged messenger of the gods from Greek mythology, and closest planet to the Sun, it sounds fast and it is hot enough to melt lead at its equator. Surely too hot to be the closest neighbour of our beautiful blue-green Mother Earth?

The classic school poster of the Solar System. Pretty planets all in a row!
Does this beautifully neat image help us answer the solve the problem? Afraid not! See this article.

If you are looking for the solution, the picture above does not help, at least not much. And sure I could just tell you, but wouldn’t you rather figure it out for yourself? If you just visit this amazing model of the Solar System provided by Solar Scope and play around for a few minutes you will be able to solve this mystery for yourself – I promise! Zoom in until you can see all the contenders, speed up time a few notches, and watch carefully… You may be surprised!

If you don’t have time to figure it out for yourself, feel free to watch this short video where I reveal the truth!
If you are really short of time, scroll down to see the answer! I recommend that you also listen to the recent BBC More or Less program to hear a great discussion of this, but please make sure to also check out the amazing model from Solar Scope. It’s one of the highlights of the internet and it makes the problem super easy to solve.

Go play with this model and find out the answer to this riddle, and so much more!

Links to models – go play!

The solution…..⅄ɹ∩ƆɹƎW!

Earth’s nearest planetary neighbour, at least for the majority of the time, is Mercury. Venus spends less time than Mercury as our nearest but actually approaches closer than any other planet, while Mars is occasionally the closest, and has the most similar orbital velocity.

Thanks for reading!