Estimating Surface Gravity on a Fictional Planet

WARNING: MATHS CONTENT!!!

One of the things I had to do as part of the rework of my novel The Tau Ceti Diversion, is to try and work out the surface gravity of my fictional planets. From the Kepler data, there are two exoplanets located in the Tau Ceti system that are likely to be in the system’s habitable zone, or where there is the possibility of liquid water on the surface, and perhaps life as we know it.

To play around with my estimates of gravity, I used ratioed rearrangements of Newton’s law of gravity (law of universal gravitation) and a simple formula relating the density of a spherical planet to its mass and radius (these are at the bottom of the post in the ADDENDUM).

Here’s Newtons famous law:)

law of gravity

The two planets thought to be in Tau Ceti’s habitable zone are denoted Tau Ceti e and Tau Ceti f. What is known about these two planets is their likely orbit, eccentricity, and their mass. All of these properties have been derived by calculation, based on observed data, so are all known to within appropriate error bounds, but I’m leaving the error off my scribblings so things don’t get too messy.

Tau Ceti e is thought to be around 4.3 Earth Masses, or Me (i.e. 4.3 times as heavy as Earth), while Tau Ceti f, the planet that orbits a bit further out, is thought to be around 6.67 Me. For the astronomically minded, these two planets orbit at around 0.55 and 1.35 AU from Tau Ceti respectively.

So, here’s where I cheated a bit, like any good engineer. I started with the answer I wanted and calculated backwards to see if the answer I wanted led to reasonable base assumptions. This is not as cheeky as it sounds, because when you have an insoluble problem (i.e. not enough data is known for an explicit result), an iterative approach is often used.

For my story to work, I needed a surface gravity on my planet of no more than 1.2g – that’s twenty percent higher than Earth’s. But how could I get a gravity that low on a planet that was over 4 times the mass of Earth? The answer is that surface gravity is a function of mass and radius, or going a step further along the calculation path, mass and density.

I used a ratioed form of Newton’s law that allowed me to relate the ratio of two planets gravitational forces to the ratios of their masses and radii. I already knew the ratio of the gravities ( assumed at gTCe/gE= 1.2) and the ratio of the masses (MTCe/ME =  4.3), so could calculate the ratio of radii (rE/rTCe) at 1.89.  Using another formula that related the ratio of the two planet’s densities to their ratioed mass and radii, I could then calculate their ratioed densities (dens TCe/ densE) at 0.63. So at the end of all that, to have a surface gravity of 1.2 g, Tau Ceti e would have to have a density of 63% of Earth’s. Is that reasonable?

The density of Earth is 5.514 g/cm3, not too much different from the density of a rocky planet like Mercury (5.427 g/cm3), but a lot higher than other solar system planets like Jupiter and Uranus (1.326 g/cm3 and 1.27 g/cm3 respectively), comprised of lighter materials. A surface gravity of 1.2g on Tau Ceti e would put its density at around 3.5 g/cm3, less dense than our own rocky planets, but certainly in a feasible range.

So what sort of densities would you expect for the Tau Ceti system? One clue is the metallicity of the system, which is a measure of the ratio of iron to hydrogen in the star’s makeup. In the case of Tau Ceti, this is estimated to be around one third of our own sun. This indicates the star is likely to be older than the Sun, made up of stellar remnants left over from less evolved stars that have not had time to form as much of the heavier elements in their internal fusion factories.

So Tau Ceti is made up of lighter elements. Based on this, it was reasonable to assume that the planets in the Tau Ceti system would also be made up of proportionally lighter elements, and quite possibly in the range I had estimated. Tau Ceti e and Tau Ceti f are also large planets – much larger than our own Earth – so having a density in between Earth and our own gas giants also made sense to me.

Using the same planetary density I had calculated for Tau Ceti e, for the larger Tau Ceti f, gave me a surface density of around 1.4g for the bigger planet – just a little too high for feasible human colonisation – and that fit nicely with my story as well.

It was a lot of fun playing with these calculations, and thankfully the known science fit with my story, at least with some comfortable wiggle room!

The Tau Ceti Diversion is due to be launched on September 1st 2016! Read more about what happens in the story here!

Tau-Ceti-Diversion-severed-ebook-cover (Medium)

 

ADDENDUM

For those interested in the maths. . .

Density formula:  densp= Mp / (4/3*pi()*rp^3)

Where:

densp= Density of Planet (kg/m3)

Mp = mass of planet (kg)

rp = radius of planet (m)

In ratio form: densp1/densp2= Mp1/Mp2 *(rp2/rp1)^3

 

Ratio of Newtons law relating gravity, mass and radius of two planets:

gp1/gp2= Mp1/Mp2 *(rp2/rp1)^2

 

Thank You Kepler! Thousands of New Exoplanets Now Confirmed

The number of new confirmed exoplanets – planets located outside our own solar system – continues to grow at an impressive rate.

A massive amount of data is collected by space-based telescopes, which has to then be analysed and verified by astronomers. In the largest single announcement yet, NASA scientists have released information on 1,284 new verified planets, pared down from 4,302 potential candidates. When only decades ago there was not a single verified exoplanet, that number becomes staggering.

kepler - thousands of new planets

This announcement more than doubles the number of confirmed planets identified by the Kepler space telescope. And with every new verified planet identified, the odds of identifying a true Earth-analogue increase.

Before Kepler was launched, astronomers had no idea how common planets really were. Now it is thought that there are likely to be more planets than stars. When you realise there are billions of galaxies, each with millions of stars, that’s a lot of planets! Even if the chance of life was extremely low, the likelihood of life, possibly even intelligent life out there somewhere starts to look good.

Missions like Kepler, combined with new technologies for getting actual pictures, spectrographic analysis and thermal maps of exoplanets (check out this post on capturing planetary snapshots), all point to some very exciting discoveries in the not-so-distant future.

Of the newly identified Kepler planets, around 550 could be Earth-like rocky planets. Nine of these orbit in their sun’s habitable zone, now making a total of 21 confirmed exoplanets in the so-called ‘goldilocks’ zone where liquid water can exit on the planet’s surface, allowing the potential for the formation of life as we know it. Two of these habitable zone planets are in the Tau Ceti system (see here). The potential for life on one of these planets is explored in my novel The Tau Ceti Diversion, due to be launched on September 1st 2016! Read more about what happens in the story here!

Kepler truly is the workhorse of planet-finding. Of the 3.200 exoplanets identified to date, more than 2,325 of these were discovered by Kepler. Launched in March 2009, Kepler spent four years monitoring the same patch of sky – some 150,000 stars – watching for the telltale tip in a star’s brightness that indicates a transiting planet.

Let’s hope that Kepler, and other missions like it, continue to increase our knowledge of exoplanets far into the future.

 

Capturing our First Planetary Snapshots

 

Kepler has confirmed more than 1000 planets outside our solar system, but so far only a few of Earth-like size and in the habitable zone — rocky planets with just the right temperature for liquid water. And none of those potential Earth-analogues have been observed directly, but through the interpretation of astronomical data, such as the wobble of the star, or the dimming on the star’s light due to planetary transit.

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So far, some pictures of other planets have been taken from ground-based telescopes, but those planets are large, bright and orbit far from their suns — not like potential Earth-twins which will be far smaller and orbit closer to their suns.

NASA scientists and engineers are working on two new technologies to help look for new planets, a starshade and a coronagraph, which will both work to block the light of the star, allowing the telescope to examine the reflected light of the planet itself.

This means we can not only take pictures of prospective Earth-like planets, but also use spectrographic analysis to analyse what in their atmospheres as well. This will give us clues to what might exist there. For example, evidence of plant life and animals similar to those on our Earth would show up as a series of simple signature compounds in the planet’s atmosphere: such as oxygen, ozone, water and methane.

A starshade is a type of spacecraft that actually flies in front of the telescope to block the light of the sun under observation. Despite the fact it will be only tens of metres wide, it will fly quite a bit in front of the telescope — in fact around 50,000 km away — more than four Earth diameters. Getting it into space is a challenge. It will be folded up like a super-origami prior to launch to unfurl in space,  somewhat like an unwinding spring, into to a crazy-sized sunflower. The pointed petals are crucial to its design: they control the light the right way to reduce the glare to levels where planets can be seen. The petal-fringed shape creates a softer edge that causes less bending of the light waves.

Both the starshade and the telescope will be independent spaceships, allowing them to move into just the right position for observations. The petals of the starshade need to be positioned with millimetre accuracy.

Blocking out the starlight while preserving the light emitted from the planet is called starlight suppression.

The light of a sun can be billions of times brighter than the reflected light from the planet. Our own sun is 10 billion times bright than Earth.

Coronagraphs were originally introduced in the early 20th century to study our own sun, blocking out the light from the sun’s disk to allow scientists to study its outer atmosphere, or corona; hence coronagraph. They are much smaller than the starshade, located within the telescope itself.

These starlight-blocking coronagraphs will be more sophisticated.

These new generation coronagraphs uses multiple masks as well as smart mirrors that can deform, to suppress starlight in sequential stages. There are many other challenges in delivering the coronagraph technology, including being able to suppress or compensate for the warping and vibrations that all space telescopes experience.

New Calvanni Review

Writer Tracy Joyce recently published a great independent review of The Calvanni. Here’s the whole review from Tracy’s blog:

The Calvanni (Book 1, The Jakirian Cycle) by Chris McMahon – Monday 27th July 2015

Calvanni front cover (Small)

“If you’re after a fast paced, complex adventure with detailed world building, politics and characters, then The Calvanni may be just what you’re looking for.

The Calvanni is set upon the world of Yos – a world where all metal is magical and cannot be forged. The weapons and armour must be made from natural materials and special ceramics – a nice point of difference from other novels I’ve read. The magic system has been well thought out and for those who like a lot magic in their reading, this book has plenty and some excellent battle sequences.

When the story opens the reader is plunged into the scene dealing with the assassination of the Sarlord of Athria. The depth of the political intrigue and old rivalries within the novel are quickly revealed. McMahon has also created a world with complex social and religious classes and many unusual animals.

This detail is one of the greatest strengths of The Calvanni, yet it may also be an initial obstacle to reading enjoyment for some. There is an array of unique terminology for this world within the novel. Fortunately, there is a glossary at the beginning of the book, which many may find useful. I actually enjoyed all the new terms and creatures that McMahon adds to the world of Yos – for me it added to its sense of authenticity. If you find this initially difficult, then persevere because your patience will reward you with a great read. The pace and the construction of the story are such that you just keep reading and pick up the terminology, or what is implied by it quickly.

On first glance the cover of The Calvanni seemed to me to be more akin to the type of illustration one would see on the cover of an romance novel that masquerades as epic fantasy – Don’t let that fool you because this is a high fantasy with some of the most original and intricate world building I have read in long while.

I’m looking forward to reading the rest of the series.

Four Stars!”

Back to Dune

I recently set myself the task of reading all of the Frank Herbert Dune books, and the additional prequels written by Kevin J Anderson and Brian Herbert. Fourteen books in all. What spurred me on to do this was coming across the first set of Dune prequels in a second-hand bookstore and reading them for the first time. These prequels — House Atreides, House Harkonnen and House Corrino — sustained my interest and re-ignited my enthusiasm for the Dune Universe.

So here I go. This is not a formal review — I don’t pretend to be a SF critic — this is just me with a journal, sitting in a coffee shop, writing down my thoughts after reading the book; as insightful, incomplete or tangential as they were . . .

Dune – Frank Herbert

Dune Ciover

Herbert’s world has amazing scope, and its creation is an incredible achievement.

Re-reading this book after so many years was a different experience. I can see now how frustrated I would have been as a younger reader at the lack of action.

As an older reader, I could appreciate Herbert’s writing much more.

I would have to say though, for all the confusing wordage of his pre-chapter ‘wisdom’ excerpts and his in-prose philosophical insertions — which occupy much of the prose and dialogue — I have taken away no powerful insights. For me there was no true transfer of wisdom, no higher knowledge. At worst I felt the Herbert was sewing confusion and word-games that sounded profound, but which he himself had no personal stake in. His own beliefs and thoughts remain unstated. Basically, these extended sections of dialogue were literary smoke and mirrors. I concluded that this is in effect a form of delayed resolution to draw the reader on, where many questions are raised, yet no conclusion is ever delivered. And no truth.

The main focus of Dune’s narrative is the inner experience and transformation of Paul. I was impatient with this when I first read Dune. On this second read, may years later, I appreciated Herbert’s prose expression, yet felt he failed to convey a true transformative experience, falling back into word-puzzles and a philosophical mish-mass that implied significance without delivering.

The fact of genetic memory is a central premise of this world. I cannot accept this as a credible basis. This does not make sense to me from a scientific point of view.

Herbert’s novel implies telepathy through contact in the spice ritual that creates the Reverend Mothers, yet the mechanism or actuality is unclear.

The idea of a Mentat is sound, yet Thufur fails to convince me as a character. We are told he is a master assassin and mentat, yet he never actually shows us anything to convince us of this. And believe me — I wanted to believe it! I wanted to see it!

The Bene Gesserit are done well – you can see directly how their training gives them advantages. You can credit this, and it is shown directly through Jessica as a character. The Bene Tleilaxu are vaguely presented in this first book, but intriguing.

All up I enjoyed the return to the world of Dune, and enjoyed Herbert’s prose. He has created a in-depth and convincing world that has remarkable texture and is a pleasure to visit.

My SF Short Time Pump Just Published in Dimension6

I’m very excited to announce my SF short Time Pump has just been published in Keith Stevenson’s Dimension6 ezine! Click here to download a free, DRM-free epub or here to download a mobi file!

D6cover4-218x300

The story was born from an intriguing SF idea and gradually took shape through various edits and critique sessions. I’m sure quite a few of my former Vision and Edge writing group partners will remember this one.

Time Pump has always been one of my favourite stories. I don’t want to give too much away, but suffice to say it raises some interesting questions about time travel. Time Pump was great fun to write, and the SF idea aside, it is a classic survival story set on a frigid ice-world. Originally it had a lot more backstory about the central character MacPherson and why he ended up on the planet like that (and who betrayed him), but various critique partners encouraged me to focus and shorten the story. So if you’re wondering about that deeper mystery . . . blame them for never finding out:)

The prequel novella to my three-book Heroic Fantasy series Jakirian Cycle, Flight of the Phoenix, is also available as a free download from my website. Haunted by terrible visions, and battling his own fear of Sorcery, the aging weaponmaster Belin must face the magical assassins that stalk the capital Raynor and bring the newborn son of the fallen Emperor — the last of the Cinanac line — to safety. Check it out — it’s a great way to get a taste for the series.

Here is the cool cover by Daryl Linquist

FotP4Kindle

The Jakirian Cycle is Heroic Fantasy in a world of ceramic weapons, where all metal is magical. It’s had some great reviews and is available through my website in either print versions or in a variety of electronic formats and platforms. My favourite review tag line is ‘Think Kill Bill meets Dune!’ – I mean, how cool is that? Here are the covers, also by Daryl.

Calvanni front cover (Small)Scytheman front cover (Small)Sorcerer front cover (Small)

 

Judging Your Own Work

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Now this is something I find almost impossible to do.

Every single time I sit down to write I make the journey from ‘My God this sucks’ to ‘this is starting to hang together’ to ‘I’m liking this!’ and back to ‘this is total crap.’

Somewhere through that process I actually get a buzz – usually when I forget to think critically at all.

I’ve won prizes and been shortlisted for genre awards. Other writer friends say I write well. Every now and then I will get a shock when a dedicated critiquer who does nothing but criticize me and my work introduces me as a ‘fine writer.’

It seems that I have no capacity for objectivity. When I look at the work that I have done I see the prose through a microscope (showing ugliness usually) and the story from a lightyear away – focused on the shape of the whole thing and its various subplots.

Getting critique is one way to get feedback. Reviews on published work are another. I’m not sure which one is crueler, probably the reviews since they are public and liable to effect sales.

On a day-to-day basis, how are you supposed to get any sort of handle on your work? I guess writing is a never-ending series of judgements you make – is the sentence too long, is there enough description, should the clown really kill the president, how big are his shoes etc. Yet when the high of actually being in the flow fades, all I am left with is a sense of unease.

How do you go about judging your own work as you progress? Is it actually impossible?

 

Tattoos in Fantasy

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I’ve always been intrigued by tattoos. The awesome finality of having your skin inked has made me even more fascinated by traditions where tattoos carry a special meaning, such as the Polynesian cultures.

In my fantasy world of Yos, tattoos carry very particular meanings. Men and women are tattooed with a totem on coming of age, which has a religious meaning and marks inclusion in a particular sect and tradition – men inked on the chest and women on the cheek.

Then, both men and women gain tattoos that show their chosen path in life, their achievements and honours. This is so central to the cultures of Yos that to cover your chest (it’s a warm world) is a sign of deceit. Warriors will only wear armour in full-scale conflict.

In a world where many cannot read or write, the tattoos give a person’s history at a glance, where honour – and dishonour – is written in ink.

Here’s the cover from The Calvanni, that shows some of the tattoos of the Way of the Calvanni – or knife-fighter.

Calvanni front cover (Small)

Do you have any special tattoos that carry a particular meaning for you?

What’s Your Favourite Fantasy Weapon?

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One of the great things about writing fantasy is the fun you can have with weapons:)

In my fantasy world Yos, where my three-book Jakirian Cycle is set, all metal is present as a magical crystal called a glowmetal. These glowmetals are a naturally occurring blend of light and metal that cannot be created or destroyed. So in the development of weapons, swords and metal armour were out. Instead I developed various classes of composite ceramic.

Lanedd – which can be used for blades. This holds a razor-sharp edge, yet avoids the brittleness of pure ceramics.

Mought – incredibly tough material that can be cast into shape as armour or used for the haft of various weapons.

The longest practical lanedd blade that can be cast using the techniques available to Glassmiths in Yos is the ‘calv’ or long-knife. This is where the world ‘calvanni’ or knife-fighter derives.

On Yos the dualist’s weapon of choice is the greatscythe. This is a staff-like weapon with twin concealed blades, one at either end. The blades shoot out and lock into place. It is operated by a mechanism central to the haft . It is also the weapon of the Suul nobility.

I had a lot of fun trying to figure out how the greatscythe worked. After all – with no forged metal – I could not very well have conventional coiled springs.

Here’s what I came up with:

The greatscythe has a central fighting grip and a release grip slightly wider than this which is operated by twisting two rings. These have a thread on the inside that operates a rod moving parallel with the axis of the greatscythe. This movement switches what is known in knife-talk as an Out-The-Front or OTF mechanism.

To make this work I needed two separate types of springs in the internal mechanism, both which had to be some sort of natural material. The first I solved with small bone ‘leaf’ springs for the catches that lock the blade into position. For the main spring that drives the blade back and forward I used a rubber strap-spring.

The greatscythe itself tapers to the ends. Two cover plates attach to a hollow cast core and cover the dual mechanisms – sealed in place with a special mought (ceramic) that melts at a much lower temperature than the mought of the haft. So if the mechanism needs to be fixed the sealing mought can be melted away to free the plate.

What your favourite Fantasy weapon?