$$\def\|{&}\DeclareMathOperator{\D}{\bigtriangleup\!} \DeclareMathOperator{\d}{\text{d}\!}$$

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## 1. Loose in Space

On Earth, many things have a fixed place, such as mountains and seas and cities and roads and buildings and mile posts. Those things have a fixed place because they are fixed to the Earth. It would take a lot of force and effort to move those things to different places. If you see and recognize such a thing, then you know where you are relative to the other (fixed) things on Earth.

When you're floating freely in space, then it is empty around you. Space is not sticky and provides no friction, so you cannot feel if you're moving. Nothing in space has a fixed location. There aren't mile posts or traffic signs in fixed places in space from which you could tell where you are. There are no fixed places in space. Separate things in space all move relative to each other.

If you float in space, then gravity from the other things in space pulls at you, and that makes you change direction or speed or both. You cannot stand still in space.

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## 2. Measuring Speed in Space

On Earth, there are different ways in which you can measure how fast a car goes. One way is to measure how quickly the wheels rotate. If you know how many times a second the wheels go around, and if you know how big the wheels are, then you can calculate how fast you go. The speedometer in cars is based on this principle. You can't use this method in space, because spaceships don't have wheels that go around faster when the spaceship goes faster.

Another way is to check how long it takes to get from one mile marker to the next mile marker. The shorter it takes to get to the next mile marker, the faster you go. You can't use this method in space, because there are no mile markers in space, and everything moves all the time anyway, so even if there were mile markers then they'd move around.

A third way is to use radar to measure your speed relative to the ground or to fixed things along your way, by sending radar waves to them and measuring how long it takes for some reflected radar waves to return or how much Doppler shift the reflected waves have. The police use this method to check if you're speeding. You can't use this method in space, because everything is so far away that it takes very long (minutes or hours or longer) for the reflected radar signal to return, and also because radar waves get weaker with distance, so pretty soon they'd get too weak for you to detect anymore.

The only method that really works in space for determining your location is to triangulate based on the directions in which you see things that you recognize. And if you know where you are now and where you were a known amount of time ago, then you can calculate what your speed is. This is similar to how sailors figure out what their position is from looking at the Sun and stars and landmarks on the horizon, except that in space there isn't even an "up" or "down".

Triangulation works as follows: Suppose that I notice that the railway station is due west from me and that I have a map of the town. I can then draw a line on the map that goes due east from the railway station, and I must then be in a place that is on that line on the map, because only from the places on that line does the station appear due west. Suppose that I also notice that the big oak tree is due south from me. If I then draw a line on the map that goes due north from the location of the big oak tree on the map, then I know I must be somewhere on that line, too. So, I must be on the line that goes east from the station, and also on the line that goes north from the oak tree. There is only one place that is on both of those lines, and that is the point where those lines cross, so that must be my location. I may have trouble measuring the directions very accurately, so I'll do well to look for some more tall things and add more lines to the map for them as well. Where most of these lines cross, that's where my location must be on the map.

Triangulation only works if you know where the things really are that you triangulate (like the station and the oak tree in the example). Everything in space moves around, so in space you'll have to be able to calculate where the planets and other things are that you want to use to navigate by, so you'll have to know their orbits.

Actually, most spaceships that we've sent into space don't measure their own speed, but we know their speed anyway because we've sent them on the exact orbit that we want, for which we could predict what their speed would be (using the equations that describe gravity).

For example, the Space Shuttle in a low orbit around the Earth always has a speed of about 7.5 kilometers per second or 4.7 miles per second, because that's the speed of things in low orbits around the Earth, according to the laws of gravity.

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## 3. Failed Rockets Are Usually Doomed

A rocket is always given just enough fuel to perform its duties, because it is so very expensive to launch extra kilograms or pounds into space, even if they are extra kilograms of fuel. The route that a rocket follows is planned very carefully so that the rocket requires as little fuel as possible to perform its tasks. If something goes wrong and the rocket does not follow the planned route, then it is almost certain that the rocket has too little fuel to complete its mission, because every route other than the planned one requires more fuel.

If a rocket should end up in orbit around a planet but something goes wrong which makes the rocket end up in an orbit around the Sun, then it is almost certain that the rocket has too little fuel to go to the planet again along a new trajectory.

If the rocket flew past the planet but could not brake and it ended up in an orbit around the Sun instead, then the rocket can continue completing orbits around the Sun until the planet and the rocket happen to be at the intersection of their orbits at the same time, and then the rocket could try again to get into an orbit around the planet. However, if the orbit of the rocket happens to be a bad one, then it can take very many years before such a chance comes again.

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## 4. Drag forces from the Air

If something like a bird or an airplane or a rocket flies through the air, then it notices drag forces from the air. The drag forces try to make the speed more equal to the speed of the air itself. Drag forces are bad for a rocket, because they take speed away, so the rocket has to use more fuel to get above the atmosphere than it would if there were no atmosphere.

If there were no drag forces from the air, then airplanes and birds would not be able to fly, so for them friction with the air has advantages, too. If the air around the Earth did not slow down falling objects, then we'd be in big trouble. The biggest raindrops (with a diameter of about 6 mm) hit the surface at a speed of about 36 km/h, and smaller raindrops go slower. If these drops were not slowed down by the air, then they might reach speeds of more than 160 km/h and hurt us.

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## 5. In Space Without a Space Suit

If you were in space without a space suit or oxygen tanks, then you would suffocate within a minute or so, because there is no oxygen in space. You wouldn't notice this, however, because you would get unconcious already after about ten seconds. Your body would not explode or anything like that. If you look for "explosive decompression" on the internet, then you'll find several articles about this.

If you brought oxygen but no space suit, then you would get terrible sunburn on any exposed skin, because there is no ozone layer in space to protect you from the full blast of the ultraviolet light from the Sun. You'd also be irradiated by harmful cosmic rays and by X-rays coming from the Sun, which would give you radiation sickness if you stayed outside for long enough. And at least your dark side (that points away from the Sun) would get really, really cold.

I cannot recommend going into space without a space suit.

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## 6. Escape Velocity

The escape velocity is the lowest speed that you need to have to escape from the gravity of a celestial body without needing a rocket engine or other form of propulsion anymore, if there is no atmosphere or other source of friction to slow you down. Escaping here means that you can get as far away from the celestial body as you want.

Once you've reached the escape velocity, you can turn off your rocket engines and yet get as far from the planet as you want, without using any more fuel, at least if you don't go the wrong way and hit the planet.

The escape velocity depends on where you are. The further you are from the planet, the lower the escape velocity is, in just the same way that your speed gets less when you get further from the planet. If you're going at exactly the escape velocity at some location, then you'll everywhere go at exactly the escape velocity of the place where you are then (if you don't use a rocket engine or other propulsion, and if there is no friction from air or something else to slow you down).

This works in just the same way as when you try to kick a ball over a dike or hill: The lower you are, the harder you need to kick the ball to get it over the top. The "escape velocity" of the ball depends on where you are.

"The" escape velocity of a planet is the escape velocity that you'd need at the surface of that planet (if you ignore the atmosphere of the planet). If the planet has an atmosphere, then you need to keep the rocket engines going for longer, to also beat the friction of the atmosphere which slows you down.

At distance $$r$$ (in kilometers) from the center of a planet that has $$M$$ times as much mass as the Earth, the escape velocity $$v_\text{escape}(r)$$ (in kilometers per second) is equal to

$$v_\text{escape}(r) = 893 \sqrt{\frac{M}{r}}$$

Multiply the speed in km/s by 3600 to get the speed in km/h (kilometers per hour). Multiply by 0.6 to transform kilometers to miles.

For example, the Earth has a radius $$r$$ of 6378 km and a mass $$M$$ of 1 earth mass, so the escape velocity at the surface of the Earth is equal to $$893 \sqrt{\frac{1}{6378}} = 11.2$$ km/s. This is approximately equal to 40,300 km/h or 24,200 mph.

If you go exactly at the escape velocity, then you can get arbitrarily far away from the planet, but then your speed will get smaller and smaller, but it will reduce to zero only when you are infinitely far away. If you go faster than at the escape velocity, then you'll have some speed left over even when you are at infinite distance. If we call that speed $$v_∞$$, then we have for the speed $$v(r)$$ at distance $$r$$

$$v^2(r) = v^2_\text{escape}(r) + v_∞^2$$

If you don't want to get infinitely far from the planet, then you don't need to attain the escape velocity. If, for example, you want to get in a circular orbit around the planet, then you need about 71 % (or $$1/\sqrt{2}$$) of the escape velocity at that distance. The other way around, the escape velocity at a particular distance is equal to about 141 % (or a factor of $$\sqrt{2}$$) of the circle orbital speed at that distance.

For example, for a low orbit around the Earth, you need 71 % of 11.2 km/s, or 11.2 × 0.71 = 8.0 km/s, and the orbital speed of the Earth around the Sun is about 30 km/s so the escape velocity (to escape from the Sun) at that distance is equal to about 30 × 1.41 = 42 km/s.

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## 7. Jumping off a Planet

Large planets have strong gravity and small planets have weak gravity. If the planet is small enough, then its gravity is so weak that you can jump up from that planet and disappear into space.

If you can jump 1 meter high on Earth, then your initial upward speed is about 4.5 m/s. I do not think that you'll be able to reach a very much greater initial speed if you jump up from another planet, even if it is a much smaller one, because you just cannot move your legs much faster. If you want to escape from the planet by jumping, then the escape velocity of that planet must be less than about 5 m/s.

The escape velocity from the surface of a round planet with a radius $$R$$ and average mass density $$ρ$$ is about equal to

$$v_\text{escape} = k R \sqrt{ρ}$$

where $$k$$ is a number that depends on the chosen units. The following table shows some examples.

 $${R}$$ $${ρ}$$ $${v_\text{escape}}$$ $${k}$$ km g/cm³ m/s 0.75 km g/cm³ km/h 2.69 mi g/cm³ mph 2.69 mi g/cm³ ft/s 3.9

For example: The average mass density of the Earth is about 5.5 g/cm³ (5.5 times that of water), and the radius of the Earth is about 6400 km or 4000 mi, so the escape velocity from the surface of the Earth is about $$0.75 × 6400 × \sqrt{5.5} = 11,300$$ m/s or 11.3 km/s, and also about $$2.69 × 4000 × \sqrt{5.5} = 25,200$$ mph.

For a planet with a mass density of twice that of water (which seems reasonable for a small planet), this means that the escape velocity measured in meters per second is about equal to the radius of the planet measured in kilometers. For the escape velocity to be not more than 5 m/s, the radius of such a planet must be not more than about 5 km.

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## 8. Travelling to the Other Planets

### 8.1. Cheap Journeys

If you want to travel from planet 1 to planet 2 and do not pass any other planets along the way, and planets 1 and 2 both follow circular orbits around the Sun in the same plane, then it turns out that the cheapest ways to travel (with the least total extra velocity difference) are:

1. If the ratio of the diameters of the orbits is at most about 11.9, then follow a Hohmann transfer orbit directly from planet 1 to planet 2.
2. If the ratio of the diameters of the orbits is between about 11.9 and about 15.9, then first take a Hohmann transfer orbit from planet 1 to a certain circular orbit beyond both planets, and then a second Hohmann transfer orbit from that orbit to planet 2.
3. If the ratio of the diameters of the orbits is greater than about 15.6, then first take a Hohmann transfer orbit from planet 1 to infinite distance, and then a second Hohmann orbit from infinity to planet 2.
4. You can try the "Interplanetary Transport Network" for arbitrary orbits, which makes use of the chaotic structure of the solutions of the three-body problem or n-body problem. These orbits require very little propellant, but are very difficult to calculate, and take a lot longer to travel along.

### 8.2. A Hohmann Transfer Orbit

A Hohmann transfer orbit is an elliptical orbit of which the perifocus lies on the orbit of the one planet and the apofocus on the orbit of the other planet.

Fig. 1: Hohmann Transfer Orbit

Figure 1 shows a Hohmann transfer orbit in red, which touches the small orbit (e.g. of planet 1) at the bottom and the large orbit (e.g. of planet 2) at the top. The small blue circles show the locations of the planets when the spacecraft leaves planet 1, and the small yellow circle shows the position of planet 2 when the spacecraft arrives.

The trick of a Hohmann orbit is to use the engines of your spacecraft only twice: once to transfer from the orbit of planet 1 into the Hohmann transfer orbit, and once more to transfer from the Hohmann transfer orbit into the orbit of planet 2.

A journey to another planet via a Hohmann transfer orbit cannot start at just any time you want, because the travel time is fixed (for planets in circular orbits) and you would probably like for the target planet to be at the end of the Hohmann transfer orbit just when your spacecraft is there, too, so you must leave the home planet at just the right time. The next table shows some numbers of such journeys starting from the Earth. These numbers were calculated under the assumption that the planets follow circular orbits, but that is not entirely correct, so the values for real journeys can deviate somewhat from the numbers given in the table.

$${t_\text{h}}$$$${t_\text{c}}$$$${t_1}$$$${t_₂}$$$${φ_0}$$$${Δ_0}$$$${ψ_0}$$$${φ_1}$$$${Δ_1}$$$${ψ_1}$$$${∆v_1}$$$${∆v₂}$$ $${∆v}$$
year
   °
AU
   °
   °
AU
   °
km/s
Mercury 0.2888 0.3173 0.4720 0.7608 108.3 1.18 18.1 −76.0 0.981 −22.5 −7.53 −9.61 17.15
Venus 0.3999 1.5986 1.679 2.079 −54.0 0.821 −45.5 −36.0 0.594 −45.7 −2.50 −2.71 5.20
Mars 0.7087 2.1353 1.953 2.661 44.3 1.07 85.2 75.1 1.59 67.5 2.95 2.65 5.59
Jupiter 2.731 1.0920 3.319 6.050 97.2 5.42 72.3 83.1 5.18 85.9 8.79 5.64 14.44
Saturn 6.062 1.0350 6.969 13.03 106.1 9.88 68.3 −157.7 10.5 −20.2 10.29 5.44 15.74
Uranus 16.07 1.0120 16.94 33.01 111.3 19.6 65.9 −154.4 20.1 −24.4 11.28 4.66 15.94
Neptune 30.67 1.0061 31.33 62.00 113.2 30.5 65.1 63.0 29.7 64.7 11.66 4.05 15.71
Pluto 45.64 1.0040 46.37 92.00 113.9 40.0 64.8 48.6 38.9 49.7 11.82 3.69 15.50

• In the table, $$t_\text{h}$$ is how long the journey in the Hohmann transfer orbit between the Earth and the planet (or the other way around) lasts, measured in years.
• You can only start your journey to or back from the planet when the planet is in the proper position relative to the Earth. That happens once every synodical period, which is called $$t_\text{c}$$ in the table.
• $$t_1$$ is the moment (measured from the departure from Earth) at which you can start your trip back to Earth for the first time. Every $$t_\text{c}$$ after that is also possible.
• $$t_2$$ is the moment at which you can be back on Earth again for the first time.
• $$φ_0$$ indicates how far the planet is from Earth in the sky, as seen from the Sun, when you depart from the Earth (see the diagram), measured in degrees. This angular distance is also correct at the moment that you return to Earth (but then in the opposite direction).
• $$Δ_0$$ is how far the planet is from the Earth then, measured in AU.
• $$ψ_0$$ is then the elongation of the planet, measured in degrees relative to the Sun. A positive elongation means that the planet is then visible at night after sunset, and a negative elongation that the planet is visible in the morning before sunrise.
• Similarly, $$φ_1, Δ_1, ψ_1$$ hold for the moment of departure from the planet back to Earth.
• $$∆v_1$$ shows how much speed difference your rocket engines must produce near the Earth to get into the Hohmann transfer orbit.
• $$∆v_2$$ is likewise the speed difference that your rocket engines must produce near the planet to switch from the Hohmann transfer orbit into the orbit of the planet.
• $$∆v$$ is the total speed difference that is needed during the outbound trip to the planet, but that does not include the launch from Earth or the planet, or your landing on Earth or the planet. The landing can be relatively cheap if you land on a planet with an atmosphere (such as Venus, the Earth, or Mars) because you can use that atmosphere to brake cheaply.

For example: A trip to Mars takes about 0.7 years or 8 1/2 months. You then have to wait on Mars for 1.24 years or almost 15 months before the Earth and Mars are in suitable positions for the return trip to begin. Then it takes again about 8 1/2 months to return to Earth. All in all, the trip takes 2.66 years or 32 months. If you like, you can stay away for an additional multiple of the synodical period of 2.14 years or just over 25 months.

If you want to calculate the numbers from this table for yourself, then look at the Calculation Page about Gravity and Space Travel.

If you fly by a planet in just the right way, then the gravity of that planet gives you extra speed that remains even when you are again very far from that planet. Using these "gravity assists", you can make a journey to a far-away planet last shorter and require less fuel. A one-way journey to Pluto lasts at least about 30 years if you do not use gravity assists, but if you fly by Jupiter in just the right way, then you can get to Pluto in only about 9 years.

$${∆v}$$$${δ_\text{max}}$$$${q_1}$$$${q_2}$$$${a}$$ $${Q_1}$$$${Q_2}$$$${δ_∞}$$
km/s
  °
AE
°
Mercury −7.5 10 0.33 0.39 0.39 1 1.25
Venus −2.5 123 0 0.72 0.72 1
 ∞
37
Mars +2.9 80 1 1.32 1.52 1.52 1.65
Jupiter +8.8 158 1 5.14 5.20 5.20 1101
Saturn +10.3 145 1 9.16 9.55 9.55
 ∞
127
Uranus +11.3 132 1 17.38 19.22 19.22
 ∞
112
Neptune +11.7 141 1 28.19 30.11 30.11
 ∞
106
Pluto +11.8 6 1 1.04 39.54 39.54 39.69

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## 9. Weight during a Journey to Mars

If you travel to another planet, such as Mars, then you'll not feel the same weight all the time. While you're being launched into space, you'll feel much heavier than on the ground, because of the strong acceleration. When the engines of the rocket turn off and you start to coast to Mars, then you'll be weightless. When you descend into the atmosphere of Mars, then you'll start feeling weight again, because of the drag forces that slow your spaceship down. When you've landed on Mars, then you'll weigh about 40 % of what you weigh on Earth, and you'll be able to jump about 2.5 times higher than you can on Earth (at least, you would if you didn't have to wear a heavy space suit).

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## 10. Space Travelers

### 10.1. How Many?

Traveling into space is very expensive. For each extra kilogram or pound that you want to bring along, you need 25 or more extra kilograms or pounds of expensive fuel. And if the extra weight is in the shape of an extra person, then it becomes even more expensive, because a person also needs to bring extra food and drink for the whole trip, and also an extra space suit and all kinds of other things.

If too few people go, then you can get into trouble if one of them gets sick or perhaps even dies, and then the whole mission may fail, for example if it was the pilot. You need to bring enough people, but not too many. I expect that five people is a nice number to send to Mars.

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### 10.2. What Can You Bring Along?

During the launch from the ground your rocket is accelerated very strongly so that you are pushed hard into the back of your seat. That acceleration and the accompanying vibrations also work on all other things in the rocket, so you can only bring things that can take the launch. Other than that, you can bring anything you want on a space trip, but because every additional kilogram requires more expensive fuel and room, there is bound to be a limit to how much you are allowed to bring and how much space that may occupy, just like when you travel in an airplane.

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Journeys to other planets take a very long time. You can prevent people getting into arguments during such trips in various ways: (1) by only sending people who don't get into arguments quickly, (2) by making clear beforehand who is in charge of each part of the mission, (3) by making the travelers get to know each other very well already when they are still on Earth, (4) by teaching the travelers how to cope with irritation and with other potential reasons for arguments.

There will probably be fewer arguments than usual, because a mission to another planet is quite dangerous. If you're in a dangerous situation, then you're probably less likely to argue about small things, because those are then less important.

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### 10.4. What If Someone Gets Ill?

If someone gets ill during a space journey, then you do the same things that you would do if someone got ill on any other trip through an inhospitable region far from hospitals: you'd try to cure the patient with the things that you brought along. Probably someone with medical knowledge will be sent along on any space trip, and medical equipment as well. It is not possible to turn around halfway through some trip to another planet, or to quickly send a medical doctor from Earth in a different rocket, so space travelers must deal with these things themselves.

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### 10.5. What About Food and Drink?

During a long space journey, you cannot go to a supermarket once in a while, so you have to bring along all food and drink that you might need during the whole trip. That food and drink must therefore keep for a long time, be easy to prepare, contain enough nutrients and vitamins, and preferably be as light-weight as possible (because each extra kilogram makes the trip more expensive). People are studying how to bring along a vegetable garden, but I'm not sure that that would work already today.

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## 11. Problems Due to Weightlessness

Astronauts that are weightless for many weeks suffer from loss of calcium and other minerals from their bones, so that their bones become more brittle and break more easily. You can try to prevent this by adjusting your diet, but the affected bones do not completely recover when you return to the ground. The calcium that disappears from your bones ends up in your blood and can cause bladder stones. Astronauts also usually have less appetite and do not eat enough when they are in space.

The return to Earth after a long period of weightlessness is extra tough because during the strong deceleration at the end of the descent you temporarily weigh more than you do on the ground, so your weak muscles go in a few minutes from having to bear no weight at all to having to bear extra weight on top of your usual weight. Russian cosmonauts who spent 8 to 11 months in space got very tired and fatigued even if they did not do very much during the day.

For an overview of these (and other) problems, you can look at //www.permanent.com/s-nograv.htm.

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## 12. Space Suits

//science.howstuffworks.com/space-suit4.htm says that the space suit that the NASA astronauts used on the Moon had a mass of 82 kg (180 lb). Gravity on the Moon is only about 1/6th as strong as on Earth, so the weight of the suit on the Moon would be about as much as the weight of 14 kg (30 lb) on Earth.

## 13. Rockets and Space Ships

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### 13.1. Propulsion

You can change your speed or direction or move forward in three different ways:

1. You can push off from something, such as the side of a swimming pool. If you apply force to the side of the pool, then (according to the First Law of Newton) that side applies a counterforce of the same magnitude to you (except if you have broken the side by pushing off from it), so then you go in the opposite direction.
2. You can pull yourself along something (such as along the ground, when you are walking). When you walk, then you pull your foot backward that's on the ground, and because of friction with the ground your foot doesn't slide backward, but instead the rest of your body goes forward.
3. You can send (shoot, let escape) something that you brought along. Because of the Law of Conservation of Impulse, you yourself must then go in the opposite direction.

The first two methods work on Earth but not in space, because there isn't anything in space to push off against or to pull yourself along. In space, you can only use the third method to change your speed or direction. Unfortunately, that method requires that you lose something (because you must always send something in the opposite direction from where you want to go), so you must especially bring something along that you don't mind losing and that you can use to propel yourself: the propellant.

Because you must bring along the propellant (or its components) until you need them, you want a propellant that gives as much speed as possible. It turns out that for this the speed at which the propellant leaves you is the most important: that speed must be as great as possible. It is also important that all of the propellant goes in the same direction: If it goes equally in all directions, then it does you no good at all. The measure that is used in the professional literature for the effectiveness of a propellant is the specific impulse. The specific impuls says how long a kilogram of propellant can provide a kilogramforce (about 10 newton) of thrust. The escape velocity of the propellant in meters per second is equal to ten times the value of the specific impulse measured in seconds.

Great speeds occur, for example, in gases that are formed in certain chemical reactions, so those are used a lot to provide propulsion in space. The formed gas must go as much as possible in the same direction, so then you quite naturally get a design for a spaceship with one or more nozzles through which the formed gas escapes. We call something like that a rocket.

In a chemical reaction, electrons are exchanged between the atoms in the compounds, so you need two different kinds of compounds for a chemical reaction: one that can provide electrons (an oxidizer) and one that want to take up electrons (a fuel).

Oxygen is freely available as an oxidizer in the atmosphere of the Earth, so a car or an airplane needs to bring along fuel but no oxygen. However, there is no oxygen or other oxidizer in space, so you have to bring that along yourself as well.

Many different kinds of propellant have been used in rockets so far, and for large rockets different kinds of propellant can be used all at the same time or in succession. The next table mentions a couple of them.

Table 1: Propellants

Fuel Oxidizer Type Specific Impulse Rockets
liquid hydrogen liquid oxygen liquid, cold 425 - 444 Ariane 5, Centaur, Saturn 1B, Saturn V, Space Shuttle
kerosine liquid oxygen liquid, cold 220 - 260 Atlas/Centaur, Saturn V
monomethyl hydrazine nitrogen tetroxide liquid 260 - 313 Delta, Space Shuttle, Titan
dimethyl hydrazine nitrogen tetroxide liquid 360 Proton
aluminum powder ammonium perchlorate solid 242 - 270 Delta, Space Shuttle, Titan
Propellant Engine Type Specific Impulse Rockets
xenon ion engine 3300 Deep Space 1
xenon experimental ion engine 6000 HiPEP
hydrogen proposed magnetoplasma engine "high" VASIMR

The top half of the table describes chemical rockets. For such rockets, the combination of liquid hydrogen and liquid oxygen provides the greatest specific impulse, and so the greatest escape velocity for the gases, so it is the most effective. Hydrogen and oxygen are both gases at room temperature. However, it is much better to make those gases so cold that they condensate into liquids, because those take up about 800 times less space. Hydrogen is liquid only at temperatures below −253 (20 K, −423), and oxygen only below −183℃ (90 K, −297℉). Those temperatures are so very low that you must make all kinds of special arrangements to deal with them.

The bottom half of the table describes non-chemical rockets. Ion engines provide a much greater specific impulse than chemical rockets, but their thrust is in general too small to be able to launch a rocket from the ground. An ion engine is therefore mostly useful for rockets that are already in space.

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### 13.2. Ion Engine

An ion engine emits ions. Because the ions go in one direction, the rocket is accelerated in the opposite direction. An ion engine works by splitting neutral atoms (often xenon atoms) into electrons and ions, using electricity (generated, e.g., using solar cells). The ions are then accelerated (again using electricity), and then sent into space. Ion engines have already been used in space, for example in the "Deep Space-1" mission (//nmp.jpl.nasa.gov/ds1/). Ion engines are only useful when you are already in space, because the acceleration that such engines can provide is too small to beat the gravity at the surface of the Earth. The advantage of an ion engine is that it requires less fuel than a chemical engine for the same acceleration.

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### 13.3. Photon Engine

A photon rocket emits photons (i.e., light). Because the photons go in one direction, the rocket is accelerated in the opposite direction. A photon engine is really just a very large flashlight that shines towards the back, but you need to emit an enormous amount of light to get a noticeable amount of acceleration. If you want to launch a rocket using only a photon engine, then the photon engine must emit at least 3 gigawatt of light for each kilogram of mass of the rocket. If we take the complete energy consumption of the Netherlands (about 100 gigawatt for a country of 16 million people) and provide it to a photon engine, then you can launch about 30 kilogram (100 lb) with that, which must include the mass of the engine itself. And if you want to extract that much energy from sunlight, then you need about 500 square kilometers of solar cells, and those add up to much more than 30 kilogram. Photon engines are only useful if you are already in space, because the accelerations that they can provide is much too small to beat gravity at the surface of the Earth.

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## 14. A Return Trip to the Moon

For each extra kilogram or pound of things that you want to take with you into space, you need a certain number of extra kilograms or pounds of fuel. How many extra you need depends on many things, including the type of fuel that you use and the shape of your rocket. For a launch from the Moon, you need far less fuel than for a launch from the Earth, because the Moon has less gravity and because the Moon has no atmosphere to slow the rocket down, and because you're on your way back when you launch from the Moon.

That last bit goes as follows: When you start your trip from the Earth, then you need to bring not just the spaceship that eventually returns to Earth, and all of the fuel that you need for your trip to the Moon, but also all of the fuel that you'll need for your return trip. That fuel is heavy, too, so you need extra fuel on your trip to the Moon just to bring the fuel for the return leg to the Moon.

An an example, I provide some numbers that I found for the Apollo 11:

1. From launch from Earth until an orbit around the Earth: 52 times as much fuel as payload.
2. From an orbit around the Earth to an orbit to the Moon: 0.3 times as much fuel as payload.
3. From an orbit to the Moon to an orbit around the Moon: 0.02 times as much fuel as payload.
4. From an orbit around the Moon to landing on the Moon: 1.1 times as much fuel as payload (because you have to use the rocket engines to slow down your fall to the surface).
5. From launch from the Moon until an orbit around the Moon: 0.9 times as much fuel as payload.
6. From an orbit around the Moon to the Earth: 0.3 times as much fuel as payload.
7. For landing on Earth you need no fuel, because you can use the atmosphere of the Earth to slow the space ship down.

In total, Apollo 11 used about 550 kg of fuel for each kg that returned to Earth. The launch from Earth by itself required about 52 kg of fuel for each kg of payload, and the launch from the Moon by itself required about 0.9 kg of fuel for each kg of payload.

Every time a part of the rocket is spent, it is decoupled and discarded, so the part of the rocket that reaches the Moon is much smaller and less massive than the rocket that launched from Earth. The part that launches from the Moon again is smaller still, so no big launch construction is needed to launch from the Moon. The Saturn V rocket that brought the Apollo 11 to the Moon weighed about 3 million kg at launch and was about 110 m tall, but the Lunar Module that landed on the Moon was only 7300 kg and the part that launched from the Moon again was only 4900 kg and only about as tall as a house.

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## 15. Space Shuttles

The US Space Shuttles that have flown many missions around the Earth since the 1980s cannot get higher than about 1000 km above the Earth, because they do not bring enough fuel.

The Saturn V rocket that flew the Apollo missions to the Moon could put 230,000 lb (104,000 kg) in an orbit close to the Earth, or 110,000 lb (50,000 kg) close to the Moon, so it needed 2.1 times as much fuel per delivered pound to go to the Moon than to go to an orbit close to our planet.

You can get an indication of how much fuel is needed to go to space by comparing the launch and end weights of the Space Shuttle and the Saturn V rockets. The Space Shuttle weighs about 4.5 million pounds (2.0 million kilograms) at liftoff, and some 230 thousand pounds (100 thousand kilograms) at landing, so for each pound (kilogram) delivered to a low orbit in space it needs about 20 pounds (kilograms) of fuel. The Apollo/Saturn V combination weighed about 6.1 million pounds (2.8 million kilograms) at liftoff, and only some 110 thousand pounds (50 thousand kilograms) of that (namely the Apollo spacecraft) actually reached the Moon, so the Saturn V needed about 55 pounds (kilograms) of fuel for each pound (kilogram) delivered to the Moon. Travelling into space takes a lot of fuel.

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## 16. Travelling Forever in the Same Direction

If you leave Earth and keep going along a straight line to the north or south in space, then you won't get to any planets in our Solar System. None of the planets of the Solar System ever stand to the north or south of the Earth; they are never more than about 25 degrees north or south of the equator. If a spaceship were to keep going north or south, then it may encounter planets around another star, but space is very empty, so the spaceship may have to travel thousands of lightyears before it encounters another star (unless the spaceship may adjust its course, then it becomes easier).

"Going north" means going away from the equator (toward the north) as efficiently as possible. In space, this means going in a straight line parallel to the rotation axis of the Earth, in the direction around which the stars appear to circle when seen from Earth at night. The Pole Star stands close to but not exactly in that direction. "Going south" means the same thing, but toward the south.

If we allow the spaceship to deviate a bit from the straight line (once it has left the Solar System), then it will be able to meet another planet more quickly. If the spaceship can move away from the straight line by a distance equal to 50 AU (50 times the distance between the Sun and the Earth − which distance comfortably includes all of the Sun's planets), and if the stars were distributed randomly across space with about the same average distance between the stars as there is near the Sun, then the spaceship could expect to have to travel about 15 million lightyears before it would meet another planet.

At that distance in real space it would be far outside of our Milky Way Galaxy, and between the galaxies the average distance between the stars is a lot greater than it is near the Sun, so in real space the spaceship can expect to have to travel much further than 15 million lightyears before it meets another planet (if it cannot move away from the original straight line by more than 50 times the distance between the Sun and the Earth).

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Last updated: 2021-07-19