What Time Is It on Mars?

I’m puffing a little after hiking up a dozen flights of stairs. That whole bank of Acme Building elevators is closed off while the repair crew tries to free up the one that trapped us. The crowd waiting for the other bank is forgetaboutit. I unlock my office door and there’s Vinnie, tinkering with the thermostat. “Geez, Sy, it’s almost as cold in here as it is out in the hall. Hey, ya think there’s anything to the rumor that building management is gonna rent out that elevator as office space? And how does time work on Mars?”

“Morning, Vinnie. You’re right, I don’t think so, and where’d that last question come from?”

“I been thinking about those ultra-accurate clocks and how they’d play into that relativity stuff we talked about with Ramona.” <short lull in the conversation as we both consider Ramona> “Suppose there’s one of those clocks in a satellite going around Earth. If I remember right, it’s going ZIP around the planet so its clock ought to run faster than my wristwatch, but it’s further out of Earth’s gravity well so its clock ought to run slower. Which would win?”

“You remembered right — you’ve got Special Relativity and General Relativity in a couple of nutshells, and yes, they sometimes work in opposite directions. You have to look at the numbers. Give me a sec to work up a few examples on Old Reliable… OK, let’s start with the speed part. That’s Special Relativity because they both start with ‘SP’.”

“Cute.”

“I thought so.  OK, here’s a handful of locations and their associated straight-line speeds relative to some star far away. That last column shows a difference factor for a clock at each location compared to a far-away motionless clock in a zero gravitational field. Multiply the factor by 86,400 seconds per day to get the time difference per day. The fastest thing on the list is that spacecraft we’re sending to the Sun by way of some slingshot maneuvers around Venus to speed it up. The Special Relativity difference comes to less than two nanoseconds per day. That’s barely in the range we can detect. It’s way less for everyplace else. ”

“Hey, Mars is down at the bottom. Lemme think why… OK, slower rotation than Earth’s, AND smaller radius so you don’t move as far for the same degrees of spin, so the formula barely subtracts anything from 1.0, right?”

“Yup, the slower you go compared to lightspeed the smaller the time adjustment. The difference between unity and the ratio for a point on Mars’ surface is so small that Old Reliable suffered a floating-point underflow trying to calculate it. That’s hard to make it do. Bottom line, the SR effect doesn’t really kick in unless you’re going faster than practically everything larger than an atom.”

“So how about the gravity wells? I’ll bet the deeper the well, the more time gets stretched.”

“Good bet. The well gets deeper as the attracting mass increases. But your clock feels less of a squeeze if it’s further away. The net effect is controlled by the mass-to-distance ratio inside that square root. Worst case in this table is at the top. A clock embedded in the Sun’s photosphere loses 0.00212*(86400 sec/day)=183 seconds compared to a far-away motionless clock in free-fall. We here on Earth lose 912 milliseconds a day total, but the astronauts on the ISS lose about 3 milliseconds less than we do because they’re further away from Earth’s center.”

“Yeah, I read about those twin astronauts. The one flying on the ISS didn’t get older as fast as the one that stayed on Earth.”

“About a second’s-worth over a year. So, do you have your relativity and Mars-time answer?”

“Sorta. But what time is it up there right now?”

“Hey, Mars is a whole world and has different times at different places just like Earth does. Wherever you are on Mars, ‘noon’ is when the Sun is overhead. Mars spins about 3% slower than Earth does — noon-to-noon there is Earth’s 24 hours plus 37 minutes and change. Add in the net 340-millisecond relativistic daily drift away from Earth time. No way can you sync up Earth and Mars times.”

“Nothin’s simple, huh?”

~~ Rich Olcott

Advertisements

Why So Big?

“How come so big, kid?”

“Beg pardon, Mr Feder?”

“Mars has the biggest volcanoes and all, like that canyon you can’t even see across.  Earth’s bigger than Mars, right?  How come we don’t have stuff like that?”

“Maybe we do but we’ve not found it yet.  Earth’s land area is only 4% greater than the surface area of Mars.  Our ocean floor and what’s beneath the Greenland and Antarctic ice sheets are like a whole second planet twice as big as the land we’ve explored so far.  Some people refer to the Mid-Atlantic Ridge as a 10000-mile-long volcano.  No-one knows for sure what-all else is down there.  Even on land we’ve probably had enormous landforms like Alba Mons but on the geologic timescale they don’t last long here.”

“So like I said, how come?”

“Because of what we have that Mars doesn’t.  Massive forces of erosion — wind, water, Goldilocks temperatures — that grind down landforms something fierce.”

Watney_s route 420
Mark Watney’s travel route in The Martian.
Image by ESA/DLR/FU Berlin
under Creative Commons license

“Wait, Mars has winds.  What about those dust storms, and that windstorm that damn near destroyed Watney’s spaceship?”

“Um, Watney’s a fictional character.  The dust storms do exist, though —  one of them created a blackout that may have killed the Opportunity rover’s solar power.  But Martian dust grains are about the size of smoke particles.  Doesn’t take much of a wind to get those grains into the air and keep them there even in Martian atmosphere that’s only 1% as thick as Earth’s.  A 120-mph wind on Earth would blow you over, but one on Mars would just give you a gentle push.  Martian winds can barely roll a sand grain along the ground.  They definitely can’t sandblast a volcano like Earth winds can.  Which, by the way is why planetologists panned that storm scene in your The Martian movie.  Couldn’t happen.  The film production team admitted that.  The rest of the science was pretty good, though.”

“OK then, water.  You talking like dripping water can wear a hole in a rock?”

“More like water in quantity — glaciers carving off mountaintops and rivers digging canyons and ocean waves smashing shorelines to sandy powder.  Dripping water works, too — water’s corrosive enough even at low temperatures that it can dissolve most kinds of rock if you give it enough time.  But Mars has no glaciers or rivers or oceans.  Probably no dripping water, either”

“You were kidding about Goldilocks, right?  Talk about fictional characters!”

“Not in this case.  To planetologists, ‘Goldilocks’ is a technical term.  You know, ‘not too cold, not too warm…”

“‘Just right,’ yeah, yeah.  But just right for what?  What’s Mars got that’s Goldilocks-ish?”

“Sorry, it’s Earth that has the Goldilocks magic, not Mars, and what’s just right is that we’re in the right temperature range for water to exist in gas and liquid and solid forms.  Mars’ surface is way too cold for liquid water.”

“Wait, I read that they’d found liquid water there.”

“Not on the surface.  The radar experiment aboard European Space Agency’s Mars Express spacecraft found an indication of liquid water, but it’s a kilometer below the surface.  Twenty kilometers wide, maybe a meter thick — more of a pond than the ‘lake’ the media were talking about.”

“Why should it make a difference that Earth’s Goldilocks-ish?  I mean, we’re comfortable but we’re not rocks.  What’s that got to do with the volcanoes?”

“Recycling, Mr Feder, recycling.  On Mars, if enough gaseous water molecules could get together to make rain, which they can’t, they’d freeze to the ground and stay there for a long, long time.  On Earth, though, most rain stays liquid and you get ground water or run-off which eventually evaporates and rains down again.  The same molecules get many, many chances to grind down a mountain.”

“But Earth water can freeze, too.”

“Remember we’re Goldilocks-ish.  Liquid water soaks into a cracked rock where it freezes, expands to pry off a chip or two, and thaws to freeze again.  Water’s freeze-thaw cycle can do a lot of damage if it gets to repeat often enough.”

“So Mars has big stuff because…”

“The planet’s too cold to wear it away.”

~~ Rich Olcott

Raindrops landing in a red-brown puddle
Adapted image from Clipart-library.com

The Big Splash? Maybe.

You’ve not seen half of it, Mr Feder.  Mars has the Solar System’s tallest volcano, most massive volcano, biggest planetary meteor strike, deepest and longest  canyon…”

“Wait, kid, I’ve been to the Grand Canyon.  Thing is … BIG!  What’d they say?  A mile deep, 18 miles wide, 250 miles long.  No way Mars can beat that.”

“Valles Marineris is 4½ miles deep, 120 miles wide and 2500 miles long.  The Grand Canyon meanders, packing its length into only 150 miles of bee-line distance.  Marineris stretches straight as a string.  No river carved that formation, but the planetologists can’t agree on what did.”

Labeled Mars map 2 420
Mars map from NASA/JPL/GSFC

“They got evidence, don’t they?”

“Not enough.  Different facts point in different directions and no overall theory has won yet.  Most of it has to do with the landforms.  Start with the Tharsis Bulge, big as a continent and rising kilometers above Mars’ average altitude.  Near the Bulge’s highest point, except for the volcanoes, is a fractured-looking region called Noctis Labyrinthus.  Starting just west of  the Labyrinth a whole range of wrinkly highlands and mountains arcs around south and then east to point towards the eastern end of Marineris.  Marineris completes the arc by meeting the Labyrinth to its west.  Everything inside that arc is higher than everything else around it.  Except for the volcanoes, of course.”

“Looks like something came up from underneath to push all that stuff up.”

“Mm-hm, but we don’t know what, or what drove it, or even how fast everything happened.  There are theories all over the place”

“Like what?”

“Well, maybe it’s upwellng from a magma hotspot, like the one under the Pacific that’s been creating Hawaiian Islands one at a time for the past 80 million years.  Some people think the upwelling mostly lifted the existing crust like expanding gas bubbles push up the crust of baking bread.  Other people think that the upwelling’s magma broke through the crust to form enormous lava flows that covered up whatever had been there before.”

“You said ‘maybe.'”

“Yeah.  Another group of theories sees a connection between Tharsis and Hellas Basin, which is almost exactly on the other side of the planet.  Hellas is the rock-record of a mega-sized meteorite strike, the third largest confirmed one in the Solar System.  Before you ask, the other two are on the Moon.  Like I said, it’s a group of theories.  The gentlest one, if you can call it that, is that energy from the impact rippled all around the planet to focus on the point opposite the impact.  That would have disrupted the local equilibrium between crustal weight and magma’s upward pressure.  An imbalance like that would encourage uplift, crustal cracking and, ultimately, Valles Marineris.”

“Doesn’t sound very gentle.”

“It wouldn’t have been but it might even have been nastier.  Another possibility is that the meteorite may not have stopped at the crust.  It could have hit hard enough, and maybe with enough spin, to drill who knows how far through the fluid-ish body of the planet, raising the Bulge just by momentum and internal slosh.  Worst case, some of Tharsis’ rock might even have come from the intruder.”

Realistic Orange-red Liquid Splash Vector
Adapted from an image by Vecteezy

“Wow, that would have been a sight to see!”

“Yeah, from a distance.  Any spacecraft flying a Mars orbit would be in jeopardy from rock splatter.  We’ve found meteors on Earth that we know originated on Mars because they have bubbles holding trapped gas that matches the isotope signature of Martian atmosphere.  A collision as violent as the one I just described could certainly have driven rocky material past escape velocity and on its way to us.  Oh, by the way and speaking of sights — you’d be disappointed if you actually visited Valles Marineris.”

“How could anything that ginormous be a disappointment?”

“You could look down into it but you probably couldn’t see the far side.  Mars is smaller than Earth and its surface curves downward more rapidly.  Suppose you stood on one side of the valley’s floor where it’s 4 miles deep.  The opposite wall, maybe 100 miles away, would be beyond your 92-mile horizon limit for an object that tall.”

“Aw, phooey!”

~~ Rich Olcott

Holes in The Ground — Big Ones

Al’s stacking chairs on tables, trying to close his coffee shop, but Mr Richard Feder (of Fort Lee, NJ) doesn’t let up on Jim.  “What’s all this about Gale Crater or Mount Sharp that Curiosity‘s running around?  Is it a crater or a mountain?  How about it’s a volcano?  How do you even tell the difference?”

That’s a lot of questions but Jim’s got game.  “Gale is an impact crater, about three and a half billion years old.  The impacting meteorite must have hit hard, because Mount Sharp’s in the middle of Gale.”

Mud drop
Adapted from a photo
by Davide Restivo, Aarau, Switzerland
[CC BY-SA 2.0] via Wikimedia Commons
“How’s that follow?”

“Have you ever watched a rain drop hit a puddle?  It forces the puddle water downward and then the water springs back up again to form a peak.  The same general process  happens when a meteorite hits a rocky surface except the solid peak doesn’t flatten out like water does.  We know that’s the way many meteor craters on the Moon and here on Earth were formed.  We’re pretty sure it’s what happened at Gale — the core of Mount Sharp (formal astronomers call it Aeolis Mons) is probably that kind of peak.”

“Only the core?  What about the rest of it?”

“That’s what Curiosity has been digging into.”  <I have to smile — Jim’s not one to do puns on purpose.>  “The rover’s found evidence that the core’s wrapped up in lots of sedimentary clays, sulfates, hematites and other water-derived minerals of a sort that wouldn’t be there unless Gale had once been a lake like Oregon’s Crater Lake.  That in turn says that Mars once had liquid water on its surface.  That’s why everyone got so excited when those results came in.”

“Oregon’s Crater Lake was from a meteorite?”

“Oops, bad example.  No, that one’s a water-filled volcanic caldera.”

“How do you know?  Any chance its volcano will blow?”

“The best evidence, of course, is the mineralogy.  Volcanoes are made of igneous rocks — lava, tefra and everything in between.  Impact craters are made of whatever was there when the meteorite hit, although the heat and the pressure spike transform a lot of it into some metamorphic form.”

“But you can’t check for that on Mars or the Moon.”

“Mostly not, you’re right, so we have to depend on other clues.  Most volcanoes, for instance, are above the local landscape; most impact structures are below-level.  There are other subtler tests, like the pattern and distance that ejecta were thrown away from the event.  In general we can be 95-plus percent sure whether we’re looking at a volcano or an impact crater.  And no, it won’t any time soon.”

“What won’t do what?”

“You asked whether Crater Lake’s volcano will erupt.  Mount Mazama blew up 7700 years ago and it’s essentially been dormant ever since.”

“There’s some weasel-wording back there — most volcanoes do this, most impacts do that.  What about the exceptions?”

“Those generally have to do with size.  The really enormous features are often hard to even recognize, much less classify.  On Mars, for instance the Northern Lowlands region is significantly smoother than most of the rest of the planet.  Some people think that’s because it’s a huge lava flow that obliterated older impact structures.  Other people think the Lowlands is old sea bottom, smooth because meteorites would have splashed water instead of raising rocky craters.”

Labeled Mars map 420
Mars map from NASA/JPL/GSFC

“I’ll bet ocean.”

“There’s more.  You’ve heard about Olympus Mons on Mars being the Solar System’s biggest volcano, but that’s really only by height.  Alba Mons lies northeast of Olympus and is far huger by volume — 600 million cubic miles of rock but it’s only 4 miles high.  Average slope is half a degree — you’d never notice the upward grade if you walked it.  Astronomers thought Alba was just a humungous plain until they got detailed height data from satellite measurements.”

“The other one’s more than 4 miles high?”

“Oh, yeah.  Olympus Mons rises about 13.5 miles from the base of its surrounding cliffs.  That’s more than the jump from the bottom of the Mariana Trench to the top of Mount Everest.”

“Things on Mars are big, alright.”

~~ Rich Olcott

 

Symphony for Rubber Ruler

“But Mr Moire, first Vera Rubin shows that galaxies don’t spread out like sand grains on a beach…”

“That’s right, Maria.”

“And then she shows that galaxy streams flow like rivers through the Universe…”

“Yes.”

“And then she finds evidence for dark matter!  She changed how we see the Universe and still they don’t give her the Nobel Prize??!?”

“All true, but there’s a place on Mars that’s named for her and it’ll be famous forever.”

“Really?  I didn’t know about that.  Where is it and why did they give it her name?”

“What do you know about dark matter?”

Rubin inspecting dark matter“Not much.  We can’t see it, and they say there is much more of it than the matter we can see.  If we can’t see it, how did she find it?  That’s a thing I don’t understand, what I came to your office to ask.”

“It all has to do with gravity.  Rubin’s studies of dozens of galaxies showed that they really shouldn’t exist, at least on the basis of the physics we knew about at the time.  She’d scan across a galaxy’s image, measuring how its red-shifted spectrum changed from the coming-toward-us side to the going-away-from-us side.  The red-shift translates to velocity.  The variation she found amazed the people she showed it to.”Pinwheel Galaxy NGC 5457 reduced

“What was amazing about it?”

“It was a flat line.  Look at the galaxy poster on my wall over there.”

“Oh, la galaxia del Molinete.  It’s one of my favorites.”

“We call it the Pinwheel Galaxy.  Where would you expect the stars to be moving fastest?”

“Near the center, of course, and they must move slower in those trailing arms.”

“That’s exactly what Rubin didn’t find.  From a couple of reasonable assumptions you can show that a star’s speed in a rotating galaxy composed only of other stars should be proportional to 1/√R, where R is its distance from the center.  If you pick two stars, one twice as far out as the other, you’d expect the outermost star to be going 1/√2 or only about 70% as fast as the other one.”

“And she found…?”

“Both stars have the same speed.”

“Truly the same?”

“Yes!  It gets better.  Most galaxies are embedded in a ball of neutral hydrogen atoms.  With a different spectroscopic technique Rubin showed that each hydrogen ball around her galaxies rotates at the same speed its galaxy does,  even 50% further out than the outermost stars.  Everything away from the center is traveling faster than it should be if gravity from the stars and gas were the only thing holding the galaxy together.  Her galaxies should have dispersed long ago.”

“Could electrical charge be holding things together?”

“Good idea — electromagnetic forces can be stronger than gravity.  But not here.  Suppose the galaxy has negative charge at its center and the stars are all positive.  That’d draw the stars inward, sure, but star-to-star repulsion would push them apart.  Supposing that neighboring stars have opposite charges doesn’t work, either.  And neutral hydrogen atoms don’t care about charge, anyway.  The only way Rubin and her co-workers could make the galaxy be stable is to assume it’s surrounded by an invisible spherical halo with ten times as much mass as the matter they could account for.”

“Mass that doesn’t shine.  She found ‘dark matter’ with gravity!”

“Exactly.”

“What about planets and dust?  Couldn’t they add up to the missing mass?”

“Nowhere near enough.  In out Solar System, for instance, all the planets add up to only 0.1% of the Sun’s mass.”

“Ah, ‘planets’ reminds me.  Why is Vera Rubin’s name on Mars?”

“Well, it’s not strictly speaking on Mars, yet, but it’s on our maps of Mars.  You know the Curiosity rover we have running around up there?”

“Oh yes, it’s looking for minerals that deposit from water.”

“Mm-hm.  One of those minerals is an iron oxide called hematite.  Sometimes it’s in volcanic lava but most of the time it’s laid down in a watery environment.  And get this — it’s often black or dark gray.  Curiosity found a whole hill of the stuff.”

Vera Rubin Ridge labeled
Adopted from a Curiosity Mastcam image from NASA

“Yes, so…?”

“What else would the researchers name an important geologic feature made of darkish matter?”

~~ Rich Olcott