## Economics of Intra-Stellar Spacecraft

After seeing the discussion of spacecraft within our solar system in the textbook, and the impact the mission type has on the cost, I was curious to see how these discussions were reflected in actual data on these missions. So, I copied each mission from the book into Excel, and then researched each. Thanks mostly to Wikipedia and the Google search “How much did [MISSION NAME] cost?”, I came up with this table. Feel free to skip over it – the rest of the blog is more interesting.

 Name Launch Year Cost (inf. adj.) Launch Mass (probe) Type Planet Reached MESSENGER 2004 $504 Million 1110 kg Orbiter Mercury Magellan 1989$1155 Million 1035 kg Orbiter Venus Venus Express 2005 $128 Million 1270 kg Orbiter Venus Spirit 2003$1094 Million 1063 kg Rover Mars Opportunity 2004 $1600 Million 1063 kg Rover Mars Mars Express 2003$472 Million 1120 kg Rover Mars Mars Recon. Orbiter 2005 $928 Million 2180 kg Orbiter Mars Phoenix 2007$469 Million 670 kg Lander Mars Curiosity 2011 $2798 Million 3839 kg Rover Mars MAVEN 2013$725 Million 2454 kg Orbiter Mars Mars Insight 2018 $832 Million 694 kg Lander Mars Voyager 1 1977$1797 Million 825.5 kg Flyby Neptune Voyager 2 1979 $1797 Million 825.5 kg Flyby Neptune Galileo 1989$2766 Million 2562 kg Orbiter Jupiter Cassini 2004 $4336 Million 5712 kg Orbiter Saturn Juno 2009$1231 Million 3625 kg Orbiter Jupiter

Then, with all the boring data out of the way, I could make (relatively) pretty graphs to see how each part of the mission related to cost:

## Cost and Mass

The most intuitive finding of this data is that more massive probes are (quite literally) exponentially more expensive:

This makes sense. Here, “mass” refers to the mass of the final probe (including propellant for any maneuvers once it’s in orbit). So, a heavier probe would need a bigger rocket to bring it to space. But this is constrained by something called the rocket equation, which (in very rough terms) says that as you increase the final mass of what you’re bringing to space, the total mass of your rocket has to increase exponentially. So it makes sense that, the more massive your final probe already is, the greater the marginal cost of another kilogram.

## Cost by Probe Type

The book suggested that flybys are less expensive than orbiters which are less expensive than landers (and, presumably, stationary landers are less expensive than rovers). In practice, this isn’t reflected in the actual costs of these missions.

 Rover $1,490,865,000 Lander$650,132,000 Orbiter $1,471,548,000 Flyby$1,796,605,000

Of course, none of this shows the inherent cost of each mission type. But it may indicate how much priority different projects are given. A rover will be driving all over a planet’s surface, so it makes sense to have a lot of gadgets to comb through all that data. And if the best you can do is fly by a planet, you only have one chance to collect a lot of data, so you need to make it worth it (perhaps with very expensive equipment). Landers, meanwhile, can’t see as far as an orbiter, so they can only do a handful of experiments.

## Cost by Launch Year

The book didn’t discuss this directly, but I was curious if the price (adjusted for inflation) of missions within the solar system had come down. It has.

Excel’s trendline suggests that (after adjusting for inflation), the average cost of a mission within the solar system comes down by about \$22 million every year. But looking at the data, a lot of this seems to be caused by the missions from 2000-2010. It’s hard to say how much of this “trend” is caused by changes in technology vs. changes in available funding vs. changes in mission designs.

## Cost by Planet

We’ve sent missions to every planet in the solar system. I was curious which were most expensive.

Overall, missions to Saturn have been the most expensive on average. It’s not hard to come up with an explanation for why this could be. We’ve sent far more missions to Mars, and it’s cheaper to get back there. That means it may not be worth sticking everything you can on the ship and increasing the price. But with Saturn, it takes a lot just to get the rocket there. So if you have something going there, then everything to make the mission better – every extra hour of design, every special instrument to get more knowledge, every unique material to bring down the mass – becomes worth the cost. This doesn’t explain the trend in the opposite direction – that Mercury’s missions are cheaper than Venus’s, even though Venus is closer to Earth. That could be because we aren’t as interested in Mercury as we are Mars or Venus, but I really couldn’t say.

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## Composition of Solar System

The solar system is a planetary system consisted of star Sun, planets, comets and other objects orbiting around the Sun, and Earth is one of them. The major mass of solar system is from the Sun. The sun is a G2 main-sequence star at the center of solar system which contains about 99.86% of total mass in solar system. The sun generates its heat and light through nuclear fusion. It’s 4.6 billion years old as the rest of the solar system is, and it will continue to last for about 5 billion years.

The next thing in solar system are planets. Mercury is the planet that is closest to sun, followed by Venus, Earth, and Mars. These four planets are called terrestrial planets as they are rocky, small in size with little moons.

Between the terrestrial planets and Jovian planets is the asteroid belt. It’s a Circumstellar disc occupied by numerous asteroids between Mars and Jupiter.

Jupiter, Saturn, Uranus and Neptune are called Jovian planet which are gaseous, giant, with a lot of moons. Beyond Neptune, it’s the Kuiper belt which is also a Circumstellar disc but it’s much larger in size than asteroid belt — 20 times wider and 20 to 200 times more massive. It’s occupied by asteroids which are remnants from when the solar system formed.

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## Exploration and Geology of Mercury

Because it is so technically difficult to reach Mercury with spacecraft’s from Earth, the geology of Mercury is understood the least of all the terrestrial worlds. The main reason it is so hard to reach is due to how close Mercury is to the Sun.  When a spacecraft moves down Sun’s gravitational potential well to get closer to Mercury, its potential energy is converted to kinetic energy. In order to not pass by Mercury quickly, the spacecraft must rely completely on rocket motors to enter a stable orbit or land. This is very fuel intensive; in fact, a trip to Mercury from Earth requires more fuel than the amount required to escape the Solar System. I thought this was a very interesting piece of information to illustrate the concept of a potential well and just how much Sun’s gravity can affect space travel as objects travel closer to the Sun.

Since Earth-based observation of Mercury is made difficult because of its proximity to the sun, most of the information we have about Mercury’s geology is space-observed. All of the space-observed information we have about the geology of Mercury comes from two NASA space probes, the Mariner 10 (Nov 1973 – Mar 1975) and the MESSENGER (Aug 2004 – Apr 2015).  Less than 45% of the surface was mapped after the Mariner 10 completed 3 separate flybys, but more than 99% of the surface was mapped after the MESSENGER successfully entered Mercury’s orbit in 2011.

The surface of Mercury is mainly made up of plains and impact craters, and is overall very similar to the moon in appearance. These were created as a result of flood volcanism, which occurred fairly early in Mercury’s geological history. There are also vents located on Mercury’s surface, and they are thought to be the source of magma-carved valleys. Fault scarps showing thrust faulting are found inside craters at the poles of Mercury.  Based on what we know about Mercury’s density, it is implied that it has a solid iron-rich core that takes up about 75% of its radius. Its magnetic equator is shifted to the north nearly 20% of the radius, and this is thought to be caused by one or more iron-rich molten layers around the core or uneven weathering and deposition by solar wind. There has been an observed possibility of ice on Mercury’s poles, but this claim is not confirmed. If the ice observations are correct, astronomers believe that it must have originated from external sources like impacting comets.

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## Where is the Center of the Universe?

If you asked the ancient philosophers, they would have told you that Earth was the center of the universe. Perfectly stationary, the heavenly spheres revolved around Earth causing the celestial phenomenons we Earth dwellers witness each day and night. Modern science has debunked, rather profusely, the idea of geocentrism. Now, we can easily leave our atmosphere and witness the revolutions of the Earth around the Sun providing definitive proof that our planet is not at all special and the other bodies move throughout the cosmos without any care that we exist.

Cool. We are not the center of the universe. That makes sense and it is observable. But wait! Where is the center of the universe?

From a logical standpoint, one would look to the origin point and say, “Ah, yes. The center of the universe must be where the Big Bang took place.” This makes perfect sense if you assume that the geometry of the universe is a sphere; however, recently studies examining doppler shifts have suggested that the geometry of the universe, instead of being a solid, exists on a solid. This would make the “solid” that the universe rests on at least four dimensions since our world obviously exists in three dimensions.

The support for this comes from a large scale observation of doppler effects outside the Milky Way. Here’s a brief video that simply explains how that was observed.

So, now that the geometry has (somewhat) been determined we get to ask ourselves, again, “Where is the center of that shape?” Well, this turns out to be a difficult question. First, let’s ask the question, “Where is the center on the surface of a sphere?” If you think long enough, you might decide either that there is no center or that every point is the center. Start by picking any arbitrary point somewhere on the surface of the sphere. If you draw concentric areas around that point until the end of the surface you will discover that your arbitrary point provides perfect symmetry in every direction. This will hold for every possible point you could pick.

analysis via doppler

This concept translates to every regular surface of every solid, so we could apply this concept to our universe! This means that from an arbitrary standpoint we could choose any point in the universe to be the center, and in fact, this has been done for Tulsa, Oklahoma.

Turns out those ancient philosophers might have not been totally wrong.

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## You Honestly Believe We Live On A Ball?

The Earth is flat, and if you disagree you are blinded by science… In this blog post I’m going to unpack some of the most convincing arguments for a flat Earth, and provide a hopefully reasonable scientific response to these questions.

Look with your own eyes, look off into the horizon, if the earth is flat then you would no be able to see things that are far away, they would be lost from sight due to the curvature of the Earth. A simple misunderstanding of the scale of Earth relative to what an individual can perceive can lead to a real conundrum when approached with this question. Indeed from an individuals perspective, the curvature of the Earth is almost impossible to see for yourself.

Common sense will tell you that if we were really spinning on a ball at 1,000 mph while the ball itself orbits the sun traveling through space at many thousands of mph, then we would feel this incredibly fast motion, and most likely even be flung off of the earth into space. It is true that one’s common sense may lead them to this belief, but a scientific approach reminds us that what the human body really feels in regards to motion is acceleration, not velocity. So the fact of Earths orbital speed and the speed of its spin, does not mean that we should necessarily feel the motion, or be flung off the surface into space.

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## The 1 Shocking Discovery NASA Doesn’t Want You To Know…

VectorStock

For most, the discoveries of NASA are taken at face value and seen as trustworthy. However, for a growing number of conspiracists, alternative facts are rising into prevalence. I would like to introduce one of these alternative facts in this blog post. Although it may seem unbelievable, hopefully after a proper explanation, you can come to see how some people may come to adopt this mindset.

Alien life on mars is alive and well, and the government knows about it. This idea stems from an interesting photo taken of Mars’ surface.

Even a non conspiracist can recognize that this looks a lot like a face. Possibly the face of a monkey. And if there is a face of that magnitude on the surface of Mars, then there must be a sophisticated civilization on the planet capable of creating such a monument.

If you would like to travel further into this conspiracy you will have to conquer some pretty discouraging evidence. Further Mars missions have given us a much clearer view of the surface and NASA now confirms that the face was just an illusion caused by shadows and the angle of the original photos taken from the Viking 1 and 2 missions. However this could just be the claims of NASA trying to discourage the adoption of the knowledge of alien life on Mars. They could be releasing doctored photos specifically designed to cover up the alien existence.

The tendency to see patterns in placed where they are actually not intended is commonly known as pareidolia, and is a confirmed behavior that we recognize is humans in general. This is what NASA claims is happening with the face on Mars. Although there truly is no face, many people exhibit the pattern of pareidolia and perceive there to be a face. A properly entrenched conspiracy believer however may even come to the conclusion that the concept of pareidolia was itself invented to make people doubt the security of what they are seeing with their own eyes. So the people are so easily manipulated that they will believe NASA over what they see with their own eyes.

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## Gravity as the Driving Force

The Sun has a mass of 2 * 10^30 kg. Gravity exerts a compression force on the Sun proportional to this immense mass. So why doesn’t the sun collapse under the weight of its gravity?

The pressure of the center of the Sun is about 340 billion times the air pressure on Earth at sea level. Temperatures at the Sun’s core reach 15 million Kelvin. The conditions at the Sun’s core allow nuclear reactions to occur.

We will leave the exact reactions for a different time. Nevertheless, the basic reaction for stars the size of our Sun is called the proton-proton chain:

$4{_{1}^{1}\textrm{H}}\rightarrow{^{1}\textrm{He}^{2-}}+2e^{+}+2v_{e}$

The nuclear reactions inside the core result in energy and an outward pressure that combats the inward pressure of gravity. Gravity is the driving force behind the nuclear reactions that power the Sun, which in turn determines its size.

## Hydrostatic Equilibrium

While the core of the Sun is able to fuse hydrogen into helium, the size of the Sun will be relatively stable. The outward pressure of the reaction matches the inward force of gravity exerted on a star proportional to its mass.

During this period, the Sun is in “Hydrostatic Equilibrium” along the main sequence. Eventually, the Sun’s core will run out of hydrogen to fuse. The core will begin to contract and core temperatures will increase.

## Red Giants

Once the core of the Sun runs out of hydrogen material to fuse, the core will begin to collapse. The extreme temperature and pressure caused by the core collapsing allows layers of hydrogen just outside the core (which previously had no role in nuclear fusion) to begin reactions. This outer layer contains more volume. Additionally, the star uses a different fusion reaction that results in the star producing much greater net energy.

The Sun will expand and become a Red Giant due to the greater outward pressure exerted as a response to the force of gravity collapsing the star.

## Post-Red Giant

Our Red Giant Sun will eventually lose much of its mass and its emitted material will become a planetary nebula. It will become a white dwarf and slowly cool.

Gravity initiates the process that forms nebulae and stars, influences the formation and size of the star, and determines the life cycle and death of the star. In this way, gravity is the catalyst for change, and the driving force, in the life of our Sun.

### Sources

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## History of Constellations

Long before history has been recorded, humans have studied the stars in the night sky. Although we have looked at stars for thousands of years, it wasn’t until 1930 that the 88 constellations were officially named by the International Astronomical Union. 48 of these constellations were named by Ptolemy in his book The Almagest in 150 A.D. The rest of the 40 constellations were given names by various astronomers throughout the years. In modern terms, a constellation is an area or region in the sky. That area has stars within them to identifying the region, but the stars and the patterns they make are referred to as “asterisms.

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## Gravity Waves

Venus is the unfortunate victim of a runaway greenhouse effect. Not only does this make the planet uninhabitable, it also causes a tremendous degree of difficulty in observing the planet’s surface.

However, there are many interesting things to gain from Venus by just looking at the atmosphere, including a massive gravity wave. Gravity waves in an atmosphere (not to be confused with gravitational waves) are caused by some vertical force displacing otherwise stable air on the surface. Gravity tries to restore equilibrium and generates a visibly oscillating wave pattern.

A recent Japanese expedition of Venus in late 2015 with the probe Akatsuki noticed an enormous wave over a mountainous region. Note the brighter white streak across the atmosphere:

When the probe circled back a few weeks later, the wave was gone. Air likely passed over the mountains below that area, and moved on. What made this gravity wave interesting is that it was virtually stationary above the aforementioned mountains, in spite of Venus’s turbulent atmosphere.

Earth also has gravity waves! Here’s an interesting example from Antarctica:

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## Nuclear Fusion in the Sun

Nuclear fusion is the process in which the Sun and all other stars generate energy through the combination of light atoms into heavier ones. The nuclear fusion in most stars is carried out in proton-proton fusion. In the first step, two protons fused together to create a proton-neutron core and emitting a neutrino and positron. Then, the core is fused with another proton to form helium-3. Finally, two helium-3 atoms are combined together to create helium-4 with two additional protons. Since the mass of the final product in this process is lower than the mass of its original components, the “missing” mass was converted into energy. The quantity of this energy can be calculated by Einstein’s famous formula: e = mc^2. Because the speed of light is such a massive quantity, even the most tiny of masses converted into energy will yield very large outputs.

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