Uncategorized

How to Get to Mars

This is going to be the first in a series on issues surrounding colonizing Mars.  I will talk about why it is so incredibly difficult to actually get there and get back as well as some ideas on how we should realistically be looking at minimizing the costs to do this.

Ever since the 1960s, we have been trying to get to Mars and take pictures and explore.  Mars has always captured our imagination, since it seems to tantalizing that it could contain life. It is right there within our grasp.  But, still, it is so far away.

Almost 2/3 of all missions that have been slated to go to Mars have failed.  Some of these include rockets that have blown up.  Others include a Russian lander that returned about half of one image before it stopped working.  Viking was the first lander that actually took pictures and really worked.

We can go to Mars about every other year.  This is because a Mars year is pretty close to two Earth years, so Mars and Earth have the correct positions once every Mars year.

In this post, I will walk through how we actually get to Mars right now, independent of cost or any real consideration – just the basic facts.  In the next post, I will walk through some of the costs in terms of rocket fuel needed to actually do this. Here we go!

The first thing that the spacecraft has to do is to get off the Earth.  The easiest way to do this is to pick a good direction and just accelerate up to just over the escape velocity of the Earth.  This is about 11.2 km/s (about 25,000 MPH) on the surface of the Earth.  That means if you launch something with >11.2 km/s, it will escape Earth’s gravitational field and won’t return. (Hmmm, I need to write a post on escaping Earth and other gravity wells.)

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To escape the Earth gravitational well, pick a direction and go at a speed larger than 11.2 km/s. You will get away with it!

Now that the spacecraft has escaped Earth, let’s switch frames of reference.  It may seem like 11.2 km/s (25,000 MPH!) is super fast and our spacecraft is definitely on its way to Mars.  Nope.  It has escaped Earth, but that just means that it is going around the sun with the Earth.  Take a look at the illustration below.  This shows that if a spacecraft ONLY escapes Earth, it will just orbit the sun with the Earth, staying in roughly the same position with respect to the Earth. Interestingly, the Earth is moving at 29,800 m/s, which is about 66,650 MPH.  So, our spacecraft went from moving 0 MPH with respect to the Earth to moving 66,650 MPH with respect to the sun.

Slide2
If the spacecraft escapes the Earth, but doesn’t do anything else, it will just orbit the sun next to the Earth.  Something more is needed!

In order to go towards Mars, you have to do what is called a Hohmann transfer.  This is where you go from having a roughly circular orbit to having an elliptical orbit, with one side of the ellipse being at Earth’s orbit, and the other side being at Mar’s orbit. In order to do this, you have to go to a higher orbit, which requires the spacecraft to accelerate and increase its velocity.  To get to Mars, the spacecraft has to speed up to 32,700 m/s, or 72,150 MPH.  This is a difference of 2,900 m/s or 6,500 MPH, so the spacecraft has to speed up by this amount in order to change trajectories towards Mars.

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In order to get on an Earth-Mars transfer orbit, the spacecraft has to increase its velocity once it escapes the Earth.

Time passes.  The worlds and our spacecraft move.  We don’t need to use any fuel at all, since the spacecraft is just coasting towards where Mars is supposed to be in a few months.Slide4

After about 8 months, the spacecraft arrives at Mars!  Yeah!

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The spacecraft arrives!

Now, if we do nothing, the spacecraft will continue to be on an elliptical orbit, and will fall back towards the Earth.  This is very bad, so we have to do something about it!

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Interestingly, in order to stay in Mars’s orbit, the spacecraft has to accelerate again.  This is because Mars’s orbit is above the elliptical orbit, so it demands an increase in velocity. Mars is moving at about 24,100 m/s or about 54,000 MPH. Our spacecraft, when it arrives at Mars, is moving at about 21,500 m/s or 48,100 MPH.  This means that the spacecraft has to speed up by about 2,600 m/s or 5,900 MPH.

Slide7

In order to not fall back toward Earth when the spacecraft arrives at Mars, it needs to speed up again!

Now, the spacecraft is in a very similar circumstance as when it was near the Earth.  If we do nothing, it will just orbit the Sun next to Mars.  We want to either have the spacecraft orbit Mars, or we want to have it land on Mars.  In order to do that, the spacecraft has to slow way down. If it orbits Mars, it has to slow down a fair bit, but less than if it were going to land.

The change in velocity needed to get into orbit is a bit complicated to figure out.  First we have to figure out the escape velocity of Mars.  The reason for this is that if the spacecraft is way far away from Mars and doesn’t do anything at all, it will smash into the surface at the escape velocity, which is 5,000 m/s or about 11,200 MPH.  To stop this from happening, the rocket has to slow down by this much (assuming that there is no atmosphere!)

Orbital velocity at 400 km above Mars’s surface is about 3,360 m/s or 7,500 MPH. From a long way away from Mars, the spacecraft can fall toward Mars, and slow down to about 3,360 m/s from the hypothetical escape velocity of 5,000 m/s.  That means that the spacecraft has to slow down by about 1,640 m/s or about 3,700 MPH. The spacecraft will then be in orbit around Mars.

To get to the surface (assuming that there is no atmosphere), the spacecraft has to slow down another 3,360 m/s or 7,500 MPH.

One of the cool things about spacecraft around Mars is that they often use aerobraking to change their orbit or slow down enough to land.  Aerobraking is where the spacecraft enters the upper atmosphere a tiny bit to experience drag and will slow down.  It is a time consuming, but very inexpensive way to slow down enough to get into Low Mars Orbit, or to land.  The spacecraft could save about 5,000 m/s by using aerobraking.  But it is complicated to do that.

Slide8
Now, when it is close to Mars, it has to slow way down in order to not be slammed into the planet.

In summary, the total delta-V that is needed to get to Mars, including escaping from Earth, getting into an elliptical orbit towards Mars, then getting out of the elliptical orbit near Mars, and landing on the surface (not using aerobraking!), is close to 22,000 m/s or about 49,000 MPH. This is a huge amount of delta-V, and almost all spacecraft end up using aerobreaking to save around 5,000 m/s.

In the following post, I will talk about how much fuel is needed in each of these steps and we can figure out how large of a spacecraft we can land on Mars.

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Rockets

Max-Q and Why Does it Matter?

In a rocket launch, they almost always talk about Max-Q, which is the point in the launch sequence where the rocket experiences the maximum dynamic pressure. First, let’s talk about what that actually means.

The rocket, as it is going up into space is experiencing three forces: gravity (down), thrust (up), and atmospheric drag (down).  Gravity is probably obvious, since you are probably sitting in a chair or on the couch and are feeling its effects (well, you are probably feeling the normal force from the chair that is pushing up on your backside, but let’s just say that you are feeling gravity). Thrust is what the rocket does as it expels fuel to make it go up. I have a post on that.

I also have a post on drag and terminal velocity if you would like a refresher on what all of that means. But, as a tiny backstory, atmospheric drag is like friction that an object feels as it moves through a fluid. So, when you are riding a bike, you feel drag, which makes it so you have to pedal harder into a headwind than a tailwind. This force is proportional to the density of the medium (it is MUCH harder to ride a bike underwater than it is in the atmosphere!), and the velocity squared (when you go twice as fast, you have to pedal four times as hard).

Returning to the subject at hand:

When the countdown ends and the rocket starts to fire, but before it starts to move, there are two forces acting on the rocket: gravity and thrust.  Thrust has to be a bit bigger than gravity for the rocket to start moving, otherwise the rocket will just sit there.  When the rocket starts moving upwards, it gain speed, and starts to experience a drag force.

Now, if the rocket flew horizontally, or if the atmosphere extended upwards forever, the drag force would increase and increase and increase as the rocket got faster and faster and faster.  As it happens in reality, the rocket launches mostly in a vertical state, and the atmospheric density decreases quite rapidly with altitude.  By about 23 km altitude, the atmosphere has decreased down to about 10% of its density.  For reference, airplanes fly at about 1/2 of this altitude, so the density is about 33% of its sea-level value.

The situation with the rocket, then, is that it starts to accelerate and the drag force starts to grow dramatically, since the force is related to velocity squared:  whenever the speed doubles, the force quadruples.  But, at the same time, the density is decreasing, so the force is weakening because of this.  At some altitude, the decreasing density wins out over the increasing velocity, and the drag force starts to decrease.

It is this point – where the increasing velocity is balanced by the decreasing density of the atmosphere and the drag force starts to decrease that is called Max-Q.

Screen Shot 2018-06-24 at 4.27.21 PM
A plot of the drag on the rocket as a function of altitude (in meters). The drag force is negative at this stage, since it is towards the ground.  Max-Q happens around 11 km in altitude in this simulation.

Now the question is – why do people care?

Well, rockets are really unstable. The thrust is coming out the back end and they are extremely long and narrow.  The thrust vector has to be right through the center of mass of the rocket in order for it to not rotate.  If the thrust vector is off, it could easily start to roll over.  If thrust and gravity were the only forces, it would be a bit complicated to control, but when you add in aerodynamic forces, it becomes even more complicated.  Older rockets (and model rockets!) used to have fins in order to help with this.  The fins made it so that if the rocket tipped at all, the aerodynamic forces on the fins would help correct for the tipping and apply a restorative force back into a non-tipping orientation. See the picture below.  There are aerodynamic forces all along the rocket, but the fins have the largest forces, so those forces win, and the rocket will rotate around the center of gravity and restore back to vertical.  With no fins, this restorative force doesn’t exist, since the forces along the rocket are all roughly equal, which makes it so that the rocket may or may not rotate one way or the other around the center of gravity.  Because of this, the rocket motors have to solve the issue all on their own.

Slide1

So, the drag force makes is a bit harder to control the rocket. Most rockets use computers to figure out how the rocket is tilting and adjust the thrust vector of the engine to rotate the rocket back to vertical.

If the computer stopped working and the rocket couldn’t adjust back to vertical, what would the problem be? The problem is that the rockets are not exactly super rigid and made out of super-strong materials, since they are designed to be as lightweight as possible.  It is designed to fly like an upright pencil through the atmosphere.  If you were to turn the pencil over and try to shove the pencil in a sideways configuration through the atmosphere, the rocket would probably shred to bits.  This is very bad.  So, the rocket needs to be aimed upwards as much as possible.  Any deviation from this upright position, and the aerodynamic forces could rip the rocket apart.

Slide2
If the rocket tilts too far, the forces on both sides of the center of gravity with cause the rocket to break apart. That is not good.

Max-Q is the time during the rocket’s flight in which the aerodynamic (drag) forces are the strongest.  So, you really don’t want the rocket to tip or do anything wonky during this time.  After Max-Q, the force decreases quickly, and the engineers can relax a bit.

It is around Max-Q, where the rocket starts to tilt a bit and rotate towards the horizontal direction.  This is because rockets only go upwards to get to their correct altitude.  They really need to go horizontally at about 7.6 km/s (that is fast).  If the rocket were to go straight up to like 500 km, then tilt over, it wouldn’t work very well, since it takes a long time to accelerate up to 7.6 km/s. Turning down low allows the rocket to take a while to get up to 500 km and take a while to get up to 7.6 km/s speed.  The rocket times it just right so that both are met at about the same time.  The location of Max-Q is where this tilting starts.

 

 

 

 

Satellites, Space Stations

It Fell From the Sky

Recently, a news article talked about China’s “Failed” Space Station (Tiangong-1) re-entering Earth’s atmosphere.  There are several aspects of this that are interesting:

  1. China launched a Space Station!  That is sort of cool and crazy.  The article calls it a “failed” space station, but really, it was just about as successful as any country’s first space station. Really, only three countries have launched space stations, besides the International Space Station: Russia, USA, and now China.  All of them had problems with their first stations. But, this post isn’t about space stations.  I will write about those some other time!
  2. The space station is going to re-enter Earth’s atmosphere, as most objects in low Earth orbit do.
  3. Researchers don’t know exactly when it will re-enter the atmosphere.  They gave an estimate of around April 2nd, with a two-week window size.  It seems like this is a really large window size.
  4. The article discusses that the space station could land in the United States! Should you run for the hills and hide for the entire two-week period that it could re-enter the atmosphere?
Tiangong-1
Tiangong-1 Space Station

First, let’s talk about how many objects there are in low Earth orbit.  There are a LOT – about 22,000 that are larger than a softball.  There are even more that are smaller than this size, but we don’t really have the ability to track those objects.  Very few of these objects are operational satellites, like less than 1,000.  You can find the most objects at an altitude around 700 km.  We put a lot of satellites in this range for pretty much the same reason that you find a lot of stuff there – the atmosphere above about 700 km is super weak, so that the drag is extremely low.  Objects at 700 km altitude will take well over 50 years to be pulled back down into the atmosphere.  This means that anything put up there will stay for a really long time.

 

Objects below about 500 km altitude will re-enter the atmosphere within about 10 years.  Anything put there or lower is just sort of swept into the atmosphere relatively quickly. This is why there is not much stuff at these altitudes – it all re-enters the atmosphere.

osohtdst
Altitude distribution of objects in low Earth orbit around the Earth. NASA Orbital Debris Program Office (ODPO).

About one object re-enters the atmosphere every day.  Most of these objects are really small and burn up completely.  Others are very big and make it through the re-entry process and land on Earth.  Things like first and second stages of rockets are examples of relatively large objects that don’t always burn up in the atmosphere.

The Department of Defense (DoD) tracks all of these objects, and attempts to predict exactly when and where they will enter the atmosphere.  This is really difficult to do.  First, the orientation of the objects are not really well known, and they could be tumbling. Therefore, it is really hard to predict the area that they are presenting to the incoming air, so the drag is difficult to calculate.  Also, the objects may have lots of protrusions, like antennas and solar panels.  If the satellite is tumbling, the area could change dramatically.  Or, if there is enough force to rip the panels off, then the area could change quite suddenly and stay at a lower value.  Think about driving a minivan down the road with a mattress strapped onto the top.  The minivan feels a lot of drag while the mattress is attached, but suddenly feels quite unburdened when the mattress flies off onto the cars behind it.  The same happens when satellites or space stations are unburdened of their solar panels as they enter the atmosphere.  Just like a minivan with a mattress strapped onto the top, it is difficult to predict if and when this unburdening event may happen, so determining the exact drag for the last few weeks of the object’s life is quite difficult.

Another thing that adds to the difficulty of predicting the drag is that there are a lot of aspects of the atmosphere between about 100 and 150 km that we don’t really understand that well.  For example, in this region, the temperature goes from being the coldest part of the atmosphere (about -75°C at 100 km) to the hottest part of the atmosphere (about +700°C at about 200 km).  That exact transition is not well understood.  Part of the reason is that it is impossible for a satellite to survive there and take measurements.  It is also impossible for an airplane to fly there, or a balloon to ascend to there.  Really, the only way to take measurements is either with rockets (so about 10-20 measurements a year at most), or through remote sensing, which has a lot of assumptions.

One of the great ironies in NASA is that when the Upper Atmosphere Research Satellite (UARS) was going to re-enter the atmosphere, NASA researchers also had a window of a couple of weeks.  One would think that given the name of the satellite, we would be able to specify the atmosphere well enough to predict when it was going to de-orbit!  But, not so much.  It is a hard problem!  Another interesting thing about UARS is that it actually re-entered the atmosphere over the United States! UARS was about the size of a school bus, so a lot of pieces may not have burned up in the atmosphere and may have made it all the way to the ground. No one was hurt.

NASA has come computers codes that you can run that will predict what will make it to the ground.  You actually have to runs these codes before you can get permission to launch a satellite. Most stuff like aluminum and plastics burn up,  but things like tungsten and other really dense metals may not.  You can then predict how fast the objects will hit the ground by estimating the surface area and mass, and predicting the terminal velocity.

Given how much stuff has re-entered the atmosphere, why has no one ever died due to getting hit my something? Well, the surface of the Earth is really, really large.  One website estimated that the percentage of area that we humans have covered with artificial surfaces is about 0.6%.  That is not much.  If the objects were falling randomly over the Earth, then one might expect about 2 objects a year to re-enter the atmosphere over a populated area.  Since the vast majority of objects burn up in the atmosphere, there is not too much to worry about.

orbit_debris_on_ground
A rocket stage that made it back to Earth. And not the way Space-X get’s their stages back.

There have been objects like meteors that have recently entered the atmosphere over populated areas.  For example, on January 16, 2018, a meteor landed just north of the University of Michigan.  This meteor was large enough to cause a huge boom and could be seen by thousands of people.  Still, no one was hurt. Even in a relatively dense population center, there is a lot of empty land.

 

So, there is not very much chance that when the Chinese Space Station re-enters the atmosphere and some of the bits make it back to Earth, they will land on anyone or cause much damage.  Most likely the pieces will land in the ocean or over land where there are not too many humans.  But, I guess there is always a first time.

Engines, Rockets

Why the Falcon Heavy Makes Good Business Sense

This week, Space-X had a test launch of the Falcon Heavy, the largest rocket ever launched besides the Saturn-5. It was a great success, putting a Tesla Roadster into trans-Martian orbit. Space-X has taken a fantastic first step. If you have not seen the launch, you should definitely watch it – it is fantastic.

fh-staticfire
Falcon Heavy at liftoff (Elon Musk via SpaceNews).

While the Falcon Heavy is very cool and a great achievement, it is also a good business investment.  There are two reasons for this.

The first reason is that the Falcon Heavy is a good business decision is that the Falcon Heavy is simply three Falcon-9s strapped together. Other rocket companies have different lines for different weight classes.  For example, Orbital/ATK has the Pegasus rocket, which last launched the eight CYGNSS satellites.  The next mission that will use the Pegasus is ICON, which will launch later this year.  That is about 1.5 years between launches.  The Pegasus launches off of an airplane, which is super cool.  The next size up from the Pegasus that Orbital makes is the Minotaur-C, which is capable of of carrying about four times as much mass to orbit as the Pegasus.  The Minotaur-C uses some of the same components as the Pegasus, but they are pretty different.  This means that Orbital needs to keep up two lines of production, which is quite difficult and costly.

The Falcon-9 uses 9 Merlin 1D engines in the first stage and 1 Merlin 1D (Vacuum) engine in the second stage. So, it uses essentially 10 of the same engines.  The Falcon Heavy uses 3 Falcon-9 first stages for a total of 27 Merlin engines in the first stage, with a second stage that is identical to the Falcon-9 second stage, for a total of 28 Merlin engines.  The engines and first stages can be used as Falcon-9s or Falcon Heavies.  This makes the production costs much lower, since they don’t have to maintain different manufacturing lines for different rockets.

What would be super awesome is if they could have a rocket that used one Merlin engine (a Falcon-1 rocket, which used to exist) that could compete with the super small rockets, like the Pegasus or the Electron (as discussed in a previous post).  But, Space-X made a choice that their smallest rocket would be the Falcon-9, which was a good decision, since the Falcon-1 could not really be expanded, like the Falcon-9 to the Falcon Heavy.

(Side Note: The Falcon Heavy is a relatively small rocket compared to the BFR that Space-X is planning for going to Mars.  There are plans for more, extremely large, rockets. The BFR is going to be a fundamentally different design than the Falcon Heavy, which is somewhat sad, since I just wrote a bunch of words above about how awesome it is that Space-X are combining the same rockets to get bigger rockets. I have no real idea how much development has gone into the BFR yet.  I will find out and get back to you!)

9m_BFR_vs_12m_ITS_vs_NG_vs_SLS
The future of rockets compared to the Saturn V. The Falcon Heavy is the biggest rocket available today, but it is very small compared to what is needed to go to the moon or Mars with humans. (https://en.wikipedia.org/wiki/BFR_(rocket))

The other thing that Space-X has done is to make the Falcon-9s reusable. The fact that they can fly back down and land makes them very valuable.  While the reusability of the rocket engines, and the number of times that they can be reused, is still questionable, it is quite certain that they will get there and the engines will be able to be used many times.

The other reusable space vehicle has been the Space Shuttle.  The problem with the shuttle was that it was extremely costly to reuse it – about $500,000,000 to launch the shuttle. (I will write a post on this soon!) The Space-X rockets are fundamentally different things.  They do not have a super complicated heat shield, or relatively complicated solid rocket boosters.

Interestingly, the primary reason that the Falcon-9 lands the way that it does, standing up using thrust, is that this is the way that it would have to land on Mars. Because Mars has such a weak atmosphere, it is very hard to land with parachutes or with wings, like the shuttle. Space-X therefore designed the Falcon-9 so that it could land vertically.  Not that there will be any Falcon-9s on Mars, but the vertical landings are great tests of the technology so that when rockets do land on Mars, they will have undergone significant real-world tests. That is in addition to making the rockets reusable, which drives the price down significantly.

In summary, Space-X is making really good business decisions in its Falcon-9 and Falcon Heavy lines: using the same engines and the same structures is really smart, and making the rockets reusable is genius.

Satellites

Two Reasons Why the Humanity Star is Not a Complete Waste of Time

If you have not seen this, you should look at this web page that describes The Humanity Star.  It is basically a nearly spherical object that was launched into space in January of 2018.  It has 65 reflective surfaces that will reflect sunlight while it is in orbit. The general idea is that whenever it is in the sun, it will be so bright in the sky that you can see it.

Normal satellites can be seen in orbit around the Earth from the ground.  What happens is that when it is dark on the ground, but still light at orbital altitudes (around 250 miles high and above), sunlight can reflect off the satellite and it can look like a star in the sky.  This happens just after sunset or just before sunrise.  If you are very patient and look up at the sky during these times (preferably from an outdoor hot tub), you can sometimes see objects that look like stars that are moving from south to north or north to south. To give you an idea, it should take them about 10 minutes to go from horizon to horizon.

The Humanity Star is so bright that it should be be visible during the day.  The web page talks about how this will be a beacon to draw humanity back together and to make them look to the stars.  I personally don’t think that a tiny star-like object in the sky will bring humanity back together unless the star-like object is getting bigger and bigger every day and has the potential to wipe out humanity.  Other people that I have talked to have a similar feeling, and so it seems like The Humanity Star really has no real value. Except it does. There are a few good reasons, some intended, and others maybe not.

Humanity-Star-2
The Humanity Star. It is not in orbit in this picture. It is sitting on the ground. (From the website).

The true purpose of The Humanity Star was really to test the Electron rocket by Rocket Lab. This was the first flight of the Electron.  While Space-X just launched the Falcon Heavy, Rocket Lab launched a small rocket that can take only 150-225 kilograms to orbit for an estimated price of $5M.  This is a huge deal because constellation missions would like to spread out satellites.  It is incredibly difficult to truly distribute a constellation of satellites from a single launch vehicle (rocket).  If you could buy 8 tiny rockets that could take one or two satellites to orbit for the price of one medium sized rocket that could take 8 satellites, it would allow you to distribute the satellites immediately.

When you test a rocket for the first time, the probability of failure is quite high (like, explosively high).  Some companies give a special deal to satellite companies to launch their satellite on a very risky rocket launch. If it blows up, then everyone loses, but they are not out a huge amount of money.  If it doesn’t blow up, everyone wins – the rocket is proven to work, and the satellite gets to orbit for cheap. Other companies just launch dummy payloads in order to prove that the rocket works.  If it works, then they have a proven rocket.  If it doesn’t, no one is harmed.  This path doesn’t make the company any money (if the rocket works), but also doesn’t make people really angry (if it doesn’t work).

The Humanity Star was a dummy payload for the first test launch of the Electron rocket.  This is similar to Space-X launching a Tesla on the Falcon Heavy (another dummy load with an actual dummy in the driver’s seat). Instead of just saying that it was a test load, Rocket Lab made a big deal about The Humanity Star instead of talking about their super cool and super small rocket.

The second interesting thing about The Humanity Star is that it can actually be used to do science, even though it has no power or sensors or anything. The Air Force has many dummy spheres like this in orbit. The reason for this is that all objects in low Earth orbit feel atmospheric drag.  Since the projected area of a nearly spherical object is known exactly and basically never changes (since it looks exactly the same from every angle) the only change in the drag force that the object feels is due to changes in the atmospheric density. Normal satellites are strange shapes and have lots of protrusions, like antennas and such.  If the orientation of the satellite changes, the drag changes. It is often extremely difficult to model this behavior accurately.  So, simple spheres are used and are tracked with radars from the ground.

The Humanity Star will allow us to more accurately track the thermospheric density since it is really big (about 1 meter across) and pretty light (about 8 kg).  Its area to mass ratio means that the drag that it feels will be pretty big, so it will reenter the atmosphere pretty quickly (less than a year). Because it feels such a large drag, the drag force will be easy to determine and any changes will be caused by only by changes in the thermospheric density.  This is the type of research that I do!

Another really minor thing about The Humanity Star is that because it can be visible from just before sunrise to just after sunset, including the whole day, it could be used for educational purposes.  You see, a satellite’s orbit can be determined just by tracking how it moves across the sky.  If you point a telescope at the satellite in the sky and mark down the direction that the telescope is pointed, and do this over and over again as the satellite moves across the sky, the math is relatively easy to do to determine the orbit (well, students do this in Junior-level Aerospace Engineering classes). This is a great real life example that students could use to put their education to use! In the daylight!

Hopefully this has convinced you that The Humanity Star is not a complete waste of time and money!

 

Star Wars

Why Does the Millennium Falcon Fly the Way it Does?

Since we are all humans (well, maybe), who have been raised on planet Earth (again, maybe), we pretty much understand how things work in an atmosphere. We end up thinking about a wide variety of things with an atmosphere in mind. Take airplanes for instance.

Airplanes fly by generating lift with their wings. There is an air pressure difference between the top of the wing and the bottom of the wing that causes an upward pressure difference, giving the plane lift.  When this lift is larger than gravity, the airplane goes up.  When it is less than gravity, it goes down. When it exactly balances gravity, it flies level.

Since an airplane typically has two engines, one on the left and one on the right, you may think that an airplane can turn by adjusting the engine speeds.  Like, in order to turn right, the left engine thrusts a bit harder and the airplane is rotated to the right. Any who has flown on an airplane knows that this is not the case.  As you probably are well aware, an airplane turns by tilting one way or the other: it banks to make a turn. This banking, or tilting, points the lift vector from being perfectly vertical to being directed in one direction or the other. The airplane literally uses air pressure to change directions!  This force then causes an acceleration that is perpendicular to the direction of motion (centripetal acceleration). Interestingly, tilting the airplane reduces the effective lift, so the plane will start to descend if it doesn’t speed up to compensate for this. Take a look at the diagram below.

Slide1
(Left) When an airplane is flying in a straight line, the lift balances the gravity.  (Right) When the airplane tilts, some of the lift force is directed perpendicularly to the velocity, so that the airplane starts to turn.  This is called “banking”.

If an airplane wants to turn a 90° turn, it tilts in the direction that it wants to go, causing a force (and acceleration) that points towards the center of the turn (centripetal acceleration).  It continues like this until it is done with the turn, then stops tilting.

Slide2

It would be incredibly difficult for airplanes to not fly like this.  Pretty much by definition, they use the atmosphere to help with flight: Air-Plane.

In space, this is not the case at all, since there is little to no atmosphere.  This means that spaceships (in space) can’t fly like airplanes. They don’t use air pressure to give them lift, since there is no air. They use thrusters to move from one place to another.

This means that spaceships don’t have the atmosphere to allow them to make banking maneuvers. So, how do they make turns if they can’t bank? Well, ships that fly in space have thrusters that cause an acceleration in the direction that they want to move. If a spaceship wants to move to the right, it has to thrust towards the left, which will accelerate it to the right. If the ship wants to reverse course, it doesn’t make a big circle, it just turns around and starts accelerating in the opposite direction that it is moving. This would look like it is slowing down, eventually stopping completely, then moving in the other direction, getting faster and faster all of the time.

Spaceships don’t have to turn in giant circles like airplanes have to. Airplanes can’t simply turn around like a spaceship, since the air puts a huge amount of pressure on the forward facing side of the airplane.  It would be very bad if you simply rotated a 747 by 180° while it was still moving at 600 miles per hour.  Very bad. Like, wings being ripped off and fuselage breaking in half type of bad. Seriously, don’t do it.

But, in space, there is (essentially) no atmospheric pressure to rip the wings off of the ship or break the fuselage in half. So, space ships can orient themselves in whatever direction they want when they are not thrusting.

The Millennium Falcon, on the other hand, banks all of the time.  Take a look at this youtube video of just the Falcon flying. It is constantly banking.  In an atmosphere, this way of flying totally makes sense (except it is not shaped like a wing at all, so I don’t understand the lift, but we will set that aside.) And, the Millennium Falcon does fly in the atmosphere, so maybe that is why it is portrayed as constantly banking.

Since ships like the Millennium Falcon have one large thruster, and not thrusters on each side of the ship, they have to rotate so it is facing the way that it wants to go, then thrust, thrust, thrust.  No banking!  Imagine, in reality, what it would look like for the Millennium Falcon to turn to the right.  It would be going in one direction (not even having to use thrust, since you don’t have to thrust to move in space – just to change velocity!). Then it would have to rotate around facing perpendicularly to the velocity, then thrust, continuously rotating, so it always thrusts towards the center of the turn.  When it is done turning, it can turn in whichever direction it wants to, but it would probably face the direction that it is moving. Take a look at the figure.

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If the Millennium Falcon wanted to reverse directions, it would simply flip over so that it was facing in the opposite direction, and would thrust, slowing down, and then accelerating in the opposite direction.  There would be no back flips or anything like that, since backflips are another form of maneuvering in an atmosphere.

One very cool thing about spaceships is that they don’t have to face in the direction that they are moving (if they are moving at a constant speed and want to continue moving in that speed).  This is very convenient if you want to shoot another ship – you can simply rotate your ship around and shoot in whatever direction you want. Battlestar Galactica did a really fantastic job of portraying this.  If you watch this video at around 7:30, you can see the ships moving in one direction while shooting in a different direction, then rotating around to thrust in another direction to change their velocity.  Pretty nice!  This is how ships should really move in space!

Ok.  I love the Millennium Falcon.  Who doesn’t?  But ships in the Star Wars universe really don’t follow the laws of physics.  I have often wondered why.  I think that back in 1975, George Lucas didn’t really understand the physics, and movies that were made back then didn’t really care as much about the physics.  Now though, people do care more, and they have started to take the pains to get it closer to correct. But, I have to imagine that George Lucas (or Disney) had to make a decision about whether he (they) should change the physics to be more realistic, thereby changing some of the fundamental things about the universe.  It was most likely a hard choice.  I probably would have given in to the dark side and changed it.  I am weak.

 

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Lagrange Points

In orbital dynamics, there are very strange things that can happen.  One of those is the idea of Lagrange Points.  When you have two bodies that are orbiting each other (like the Earth orbiting the Sun or the Moon orbiting the Earth), you can get points in which the forces cancel such that you can put satellites there and they will basically stay in the same spot (mostly).  There are five Lagrange points, as illustrated below. These are very strange and sort of unexpected!  I thought that I would explain how L1 and L2 are created and wave my hands for the others, since the physics is exactly the same.

Lagrange_Points
The five Lagrange points between the Sun and Earth (from space.com)

To illustrate, we will consider the Earth-moon system, since that is a bit closer to home. Let’s start with the most basic thing: Earth’s gravity.  Earth has gravity that essentially goes outwards forever . Even Jupiter “feels” Earth’s gravity – it is just really weak.  Just to make sure that we are all on the same page, Earth’s gravity is towards Earth. 🙂

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Let’s switch to the moon. When you are standing on the moon, you are always being pulled towards the moon, but if you look at this from the Earth’s perspective, this “towards the moon” can be either “towards the Earth” or “away from the Earth”, depending on which side of the moon you are on.  If you are on the side facing the Earth, the moon is pulling you away from the Earth.  If you are on the “Dark Side of the Moon” (i.e., the side of the moon facing away from the Earth), then the moon is actually pulling towards Earth.  Weird, right? Take a look at the plot:

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So, if you next consider Earth’s gravity and the moon’s gravity together (plot below), you can see three things: (1) when you are close to the Earth, Earth’s gravity “wins”, and you are pulled towards Earth; (2) on the far side of the moon, Earth’s gravity and the moon’s gravity point in the same direction (towards the Earth), so they add together and you would be a little heavier on this side of the moon; and (3) when you are close to the moon, but on the Earth side of the moon, the moon pulls you away from the Earth and the Earth pulls you away from the moon, so you would weigh a bit less on this Earth side of the moon.  At some point between the Earth and the moon, there is a location in which Earth’s gravity (pulling you towards Earth) and the moon’s gravity (pulling you towards the moon) cancel each other and you have a gravitation null.

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Solving for this gravitational null (see below) is a pretty standard high school physics problem.

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Up until this point, we have only considered gravity.  This would be fine if Earth and the moon were fixed in place, instead of the moon orbiting around the Earth. But since this is not the case, we have to consider the orbital motion.  The moon goes around the Earth once every 28 days (roughly).  You can then ask the question about how much force is needed to keep the moon moving around in a circle instead of the moon flying off in a straight line.  This is the centripetal force.  You can experience this force if you go on a merry-go-round that is spinning fast. You have to hold on to something to keep from being flung off of it.  If you are standing at the exact center, then you don’t feel any force at all, but as you move further and further towards the edge, you end up feeling more and more force.  You should totally go and try this.

Well, the same force works in space.  If you have an object going around another object, it feels an outward force (well, the object wants to continue to move in a straight line, which we interpret as an outwardly directed force).  If we pretend that the moon is sitting on a gigantic merry-go-round at the position of the moon, and the merry-go-round is spinning exactly the same speed as the moon is going around the Earth (one revolution every ~28 days), the acceleration that you would feel at any point along the merry-go-round would be this:

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Notice that the acceleration is always away from Earth, just like on the merry-go-round, you always feel a force pushing you away from the center.  Now, the Earth and the moon are not sitting on a gigantic merry-go-round, so this is really a thought experiment, but you get the idea.

This ends up being a third force/acceleration that is felt in the Earth-moon system, and so it needs to be included in all of our accelerations that we talked about earlier:

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Notice that the centripetal acceleration is pretty much nothing compared to the Earth’s gravity until really close to the moon.  Is that a coincidence?  No!  What is the force that makes the moon orbit the Earth? Gravity balanced with centripetal acceleration!  If you trace the Earth’s gravity line (which turns into a dotted red line) and the centripetal acceleration line, they cross at the moon’s orbit (~60 Re)!  Physics!

But, we are really looking at the sum of the forces.  So, the centripetal acceleration becomes larger than all of the accelerations in the gravitational null point (since the gravity of the Earth and the gravity of the moon cancel so there is almost no acceleration there), and when you go on the other side of the moon and are far enough away, the centripetal acceleration becomes larger than the sum of the Earth and moon’s gravity.  Notice that the sum of the gravity is red (towards Earth), and the Centripetal acceleration is blue (away from Earth), which means that where they cross, the sum will be zero:

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The above plot shows the sum of all three of the accelerations: gravity from the Earth, gravity from the moon, and centripetal acceleration. Now you can see that there are two areas where the three accelerations cancel each other out: around 52 Re away from the Earth and about 71 Re away from the Earth, both along the Earth-moon line.  These are the first two Lagrange points (L1 and L2).

These Lagrange points exist in any system where you have one body orbiting another.  You can look at this plot and think of the sun as being the main body, and the Earth as being the second body, so that L1 is between the sun and Earth, and L2 is away from the sun on the dark side of the Earth. These Lagrange points are very useful, since we can place satellites near them so that they can look at the sun all of the time (this is useful for solar physics missions), or look back at the dayside of the Earth all of the time (for climate and weather missions), or be in the shade of the Earth all of the time (well, no missions really want this, since they need solar power to run, but they do want to be far away from the Earth and not have the sun be too large in their view).

There are three other Lagrange points that I have not discussed (as shown in the top picture as L3, L4, and L5).  All of these points result from the balance between the three accelerations, just like L1 and L2. L3 is very cool because it is on the opposite side of the sun, and we can’t really observe it.  Some people would argue that there could be a mirror Earth at L3, which is pretty funny.  We would be able to tell though, since the hidden planet would change the orbits of Venus and Mercury.  But, can we really trust science? 🙂

L4 and L5 are strange because they are in Earth’s orbital path around the sun, but about 60 degree behind and in front of the Earth.  The math is a tiny bot more complicated, since you have to consider two dimensions, but the concept is exactly the same. These two Lagrange points are really interesting, since you can observe the sun from unique vantages.