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Falling in Space

A comprehensive primer on the technique of space travel, i.e. how we travel from A to B in space.
Tags Astronomy, orbits, trajectories, orbital motion, gravity, gravitational constant, weightless, ISS, Newton, satellites, satellite orbit, geostationary, Earth orbit, Principia, ellipse, elliptic orbit, Kepler, escape velocity, conic sections, hohmann transfer, apsides, rendezvous, Buzz Aldrin, Mars, Curiosity, gravity assist, Jupiter, Lagrange, lagrangian points, L-points, two-body problem, three-body problem, Trojans, space missions, Cassini, Saturn, Juno, Jupiter, New Horizons, Pluto-Charon, Kuiper Belt, Messenger, Mercury, Grail, Moon, Luna, accelerated spaceflight, ion thruster, electric propulsion, Dawn, Vesta, Ceres, hall thruster, Roger Shawyer, EM drive, Cannae drive, Star shot.
Author(s) EV
First Published November 2016
This Edition - 2.1 January 2018

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Creative Commons logoby nc sa1 Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0)






Why are astronauts in the International Space Station (ISS) weightless? “Because there is no gravity up there” you often hear. “Astronauts and scientists themselves often talk about zero-gravity, don’t they?”.


weightlessness sandra magnus astronaut fruitWeightless in space. Image credit: NASA A satellite orbit in its simplest form can be compared with uniform circular motion, like when you sling a weight around on a string. This circular motion requires a constant force towards the centre of the circle. For a satellite, including of course the ISS, gravity of the Earth provides that “centripetal” force. If there was no gravity up there, the ISS would take of in a tangential straight line and disappear into space because of Newton’s first law of motion.

So there definitely is gravity up there demonstrated by the fact that the ISS nicely continues to travel in its orbit. And this holds for any satellite, even the natural satellite we have: the Moon. She has been “up there” for at least 4 billion years.


Let us do some experiments.
When a skydiver jumps out of a plane at high altitude it is advisable to have a parachute, but keep that folded up for a while. She falls down at increasing speed and experiences weightlessness. A disturbing influence here is the wind and air drag she experiences. Astronauts don’t have that of course, but otherwise the situation is quite similar.

Modify the experiment by putting the skydiver in a box and dropping the whole box out of the plane (This is a thought experiment. DON’T DO THIS AT HOME). Now the skydiver will not feel any wind and will be almost weightless inside the box. Almost, because the box itself experiences the air drag and therefore falls a little slower than the skydiver. She will feel a very slight weight force towards the bottom (in the direction of falling).

Let us now look at a thought experiment that was proposed in 1687. Isaac Newton published his Philosophiæ Naturalis Principia Mathematica often just referred to as Principia, in which he explains his ground braking theory of gravity (among other things).

newtmtnThe image we show here of a canon on top of a mountain is from a later popularised version of the Principia. The idea is to fire the cannon, which is supposedly well above the atmosphere, with increasing charge and thus initial speed of the cannon ball. The latter will fall down to Earth at increasing distance, but there will be a speed at which the cannon ball will never hit the ground; it will continue to fall around the Earth. In practice this is impossible because of the Earth’s atmosphere and mountains that are not that tall, but as a thought experiment it is quite illustrative. As a matter of principle the cannon ball, orbiting the Earth will come back to the same spot where it left the cannon, therefore if this was possible, the gunner would himself be struck by the projectile he had fired a while ago.

Look at the animation of this experiment
Gradually increase the firing speed and see what happens. At which minimum speed will the cannon ball come back to point V in the diagram? (At higher speeds the cannon ball will disappear from Earth. We will come back to that below).

This experiment illustrates that a satellite orbit actually is a perpetual free fall in the gravity field of the central body, the Earth in our case. But, as Newton realised, this holds for all orbital motion in space, e.g. the motion of the Moon around the Earth and of the planets around the Sun.


So why are astronauts in the ISS weightless?
Because they are in a constant free fall motion around the Earth. And the space station itself and everything else in it is in that same free fall. The Earth’s gravity is the very reason they are moving that way. The term “zero-gravity” is therefore misleading. It is much more accurate to say “weightless” because while everything in orbit is accelerating in the direction of the Earth’s centre (like the cannon ball), there is no weight force like you would experience while standing on the surface of the Earth.






Some basic principles
Without going into the mathematics [go here for that] the velocity of a spacecraft in a circular orbit around the Earth is given by

orbital motion equation

where G is the Universal Gravitational Constant, ME  is the mass of the Earth and R is the distance between the centre of the Earth and the centre of the spacecraft. We show this formula to draw some important conclusions about orbital motion:

  • The velocity decreases with increasing altitude above the Earth. Hence higher satellites move slower than satellites in lower orbits.
  • Velocity is independent of the mass of the spacecraft. This is a very important conclusion because it means that e.g. at the altitude of the ISS any object will move with exactly the same orbital velocity no matter how heavy or light. So the ISS itself (500 tons) will move exactly the same as any of the astronauts inside (or outside) or as any other object, say a paperclip inside the spacecraft.
  • We can calculate that at low orbit (marginally above the Earth’s atmosphere) the velocity is about 7.9 km/s.
  • With a little more calculation (knowing that the circumference of a circle is 2πR, we can calculate the altitude of a geostationary satellite (42,240 km) that has an orbital period of 24 hours, i.e. it orbits at the same angular velocity as the Earth itself. These satellites are extremely important in particular for telecommunication as they are always in the same position in the sky as seen from the surface of the Earth.


Elliptic orbits
Johannes Kepler (1571 – 1630) was the first to realise that planetary orbits in general are ellipses. The circle we suggested above is just a special case of an ellipse with zero eccentricity. Kepler formulated his famous three laws (in about 1618) that describe orbital motion.
It was one of Newton’s great accomplishments that he could mathematically prove Kepler’s laws, what Kepler had never been able to do, because Kepler did not have access to the required mathematics, in particular Calculus.

Kepler second lawImage credit: Wikipedia When an object is moving in an elliptical orbit it has a velocity that is always directed along the tangent to the orbit at every point. It also has an acceleration in the direction of the focal point where the central mass is. This acceleration is due to the gravitational attraction between the object and the central mass.


Another animation
Now get a feeling for the elliptic orbit and Kepler’s Laws by spending some time with this great animation.
(Choose “Newtonian features” to switch on the v and a vectors). Show ellipse features, e.g. centre, focal points, semi-major and –minor axis, eccentricity, etc. Also note that the ellipse becomes a circle at zero eccentricity.





Getting a payload into Earth orbit requires a frustratingly large amount of energy. This has nothing to do with orbital motion, but is because we also need to launch a large amount of rocket fuel and a whole structure of a rocket to make it happen. Once we are in orbit and the spacecraft has the necessary velocity (speed and direction) it follows a freefall orbit which generally is elliptic as we saw. You do not need any further energy to maintain that orbit. The launch of a spacecraft is thus the propelled trajectory designed to bring the spacecraft into the required initial conditions of free fall. And the velocity (direction and speed) once in orbit determines where the spacecraft will go

Let us now go back to Newton’s animation of the canon at the mountain top. You may already have found that at the minimum speed of 6.84 km/s the cannon ball just falls around the entire Earth (it is actually closer to 7.9 km/s as we stated above). If you now stepwise increase the initial speed you will see that the orbit becomes a little more elliptical as it extends further at the opposite side of the Earth. However the cannon ball keeps coming back to the canon where it took off.

There is however a speed with which the cannon ball does not come back but disappears into space. The minimum speed with which this happens is called the Escape Velocity.

escape velocity



The shape of that orbit is no longer an ellipse but a related shape called parabola. Beyond escape velocity the orbit becomes a so-called hyperbola.

The diagram below shows the conditions for the various types of orbit. For Earth the escape velocity is just above 11 km/s.



newton cannon orbital types SeedsTo learn more about conic sections, circles and ellipses, etc. watch these Kahn Academy video lectures:

Introduction conic sections

Introduction ellipses

Introduction parabolas

Introduction hyperbolas

To get a feeling for the possible variations in orbit have a play with this animation that in particular shows how the initial velocity vector defines the orbit (you must drag your mouse to choose the initial vector).

Once the object is launched, it follows a freefall orbit that can either be an ellipse, a parabola (special case) or a hyperbola.

Before we go into deep space let us first look at spacecraft in Earth orbit.


Modifying Earth orbit

Hohmann transfer orbit copyHohmann transfer. Image source: Wikipedia For reasons of fuel efficiency actual space missions very often start with bringing the spacecraft a circular low Earth orbit (LEO) the blue circle in the diagram. Then we can increase the altitude in two steps with the so-called Hohmann Transfer.

At one point P we burn a booster rocket for a short time. The orbit then becomes an ellipse where the point we started from is the perigee, the closest point to Earth (and the radius of the original circular orbit is the perigee distance). At the furthest point A (apogee) in the new orbit, the yellow ellipse, we burn the booster again for a short time and if we do this precise the orbit becomes another circle (the red orbit) but now with radius equal to the distance to the apogee.


Note on apsides. In an ellipse the closest point to the central body’s focal point is called the periapsis and the furthest point the apoapsis. For Earth orbit these are called perigee and apogee and for a planetary orbit around the Sun perihelion and aphelion. More here.



The ∆V’s in the figure are the increments in the velocity that we apply by the boosters. Very little energy is needed for these manoeuvres and they are far more efficient than bringing the spacecraft directly into the higher circular orbit. At typical satellite altitude a 1m per second speed increase will raise the orbit by about 3 km. During these two short burns the spacecraft is being accelerated but otherwise it continues in a free fall around the Earth. The same technique but in opposite direction is used the bring a spacecraft back to Earth. The burns are then called retroburns.


Note: If we burn the boosters in a direction perpendicular to the velocity of the spacecraft we do not change the orbit itself, but we change the tilt of the orbit in space (its inclination). In contrast to the previous manoeuvers, a change in inclination requires a lot of energy.



Orbit maintenance
Over longer periods an Earth satellite will experience some orbital decay (loss of orbital energy) due to surface forces such as solar radiation pressure, atmospheric drag, etc. This results in a lowering of orbital altitude (and actually increase in orbital speed; see the formula for VC above). In the case of the ISS the ground crew initiates regular short booster buns to bring the orbit back to its nominal altitude. This video is an excellent illustration of such a manoeuver and in particular shows how the spacecraft temporarily goes from free fall to an accelerated motion, although everything that is loose inside wants to continue its free fall.

While we can now launch our spacecraft into pre-designed orbits, the second most important technique in space travel is the rendezvous. This is French for “getting together” or “meeting up”. In space travel it is the ability to let a spacecraft catch up and dock with another spacecraft that is already in orbit. Even in the early days of space travel, e.g. for the Apollo programme in the 1960’s and 1970’s, rendezvous manoeuvres have been absolutely essential both above Earth and in Lunar orbit.

figure08Image from First of all the orbits of the two spacecraft must have the same inclination (tilt with respect to the Earth’s equatorial plane) which sets critical conditions for the launch time and location of the visiting spacecraft.

You basically get only one chance to do it right and if you would miss the target, there is practically no way to try again from orbit, because of the impossible fuel requirements for such major orbit corrections.

Secondly for rendezvous with an object in Earth orbit, e.g. the ISS, the visitor is first brought into an intermediate orbit a few km below the target. Of course the timing needs to be right so that not only the orbits are close but that both objects themselves are also at the right position in their orbit.

The next stage of the rendezvous involve small ∆V’s to gradually bring the visitor higher up to the target. This generally requires several orbits to gradually reach the same orbit. Finally the two spacecraft, once in the same orbit, need to be brought together. This is quite counter-intuitive because when the visitor trails the target it will need to slow down to get closer after one orbit and when it leads the target it needs to speed up to meet after one orbit. Such “proximity operations” are calculated using appropriate software to determine the correct burns for a successful rendezvous.

Most Sci-Fi movies and TV series on space suggest that these manoeuvres can be carried out manually by pilots who have clear view of the target, but reality is a lot more complex.
For more on the space rendezvous technique go here or see astronaut Buzz Aldrin’s work.

Undocking and descent
Undocking from the ISS and controlled descent back to Earth is basically the same procedure in reverse. Nothing is done “manually” but this procedure is carefully prepared and carried out with support from both space and ground crews. A good explanation of this can be seen in the third of the ESA movies linked below.

As a conclusion of this section watch these three excellent ESA videos explaining

  1. Soyuz launch,
  2. Rendezvous and docking and
  3. Undocking, reentry and landing.






Once our spacecraft has exceeded escape velocity it is leaving Earth in a hyperbolic orbit as we saw above. But that is with respect to Earth’s gravity. Now we must look at the bigger picture and see that the gravity field of the Sun becomes important because the spacecraft is actually now in an elliptic orbit around the Sun just like Earth itself. Actually for precise calculations we must also include the gravity fields of most of the planets, in particular the largest planet Jupiter. But we will ignore these effects here for simplicity and continue to work with Kepler orbits about one central body.

The simplest way to get e.g. to Mars is similar to the Hohmann transfer technique we discussed above.

Curiositys orbit showNOriginal image: NASA. Edited and animated by Ngā Whetū Resources  

The diagram shows the actual trajectory of the Curiosity mission (Mars Science Laboratory, MSL) that was launched in October 2011. You can see that MSL was launched into an elliptic orbit around the Sun, that has its aphelion just touching the orbit of Mars. Once the MSL got to that position Mars obviously needed to be there too. This sets critical conditions on the time of the launch from Earth and requires a just favourable common configuration of Earth and Mars. Such configuration happens only once in about every 2.1 years.

Once MSL reaches Mars, its aphelion velocity is slower than Mars in its orbit so the spacecraft must speed up. Then in order to go into orbit around Mars it needs to slow down to be caught in Mars’ gravity field.

It must be noted that the gravity field of the Sun is dominant during most of the trajectory, but as the spacecraft approaches Mars, the gravity field of that planet has increasing effect on the spacecraft’s orbit. Hence this seemingly simple trajectory is already highly complex and requires careful planning and calculations as well as in-flight orbital corrections at critical points. An overriding issue always is the fuel economy of inter-planetary travel as it is prohibitively expensive, and from some point impossible, to take large amounts of propellant into space.



Tip: If you really want to “get your hands dirty” try this practical lesson in calculating launch windows for Mars.


Gravity Assist
Many missions that have been carried out would never have been possible without an important technique for saving propellant. This is the technique of gravity assist that could be referred to as “stealing a bit of orbital energy from a natural Solar system object”.

Compare this in its simplest form with an elastic ball that bounces off a wall. If the collision is elastic the ball will bounce off with the same speed but opposite direction as when it came in. Now assume that the wall itself is moving towards the incoming ball. The ball now bounces off the wall with the sum of the incoming speed plus twice the speed of the wall. If the wall is very massive in comparison to the mass of the ball, there will be no noticeable change in the speed of the wall. When we do this with spacecraft passing by (of course not bouncing off) say a planet, the spacecraft can gain a lot of speed that in effect is “stolen” from the planet. The image shows the principle of a spacecraft performing a gravity assist at Jupiter.


 cassini at jupiterImage from


This technique is also used to slow a spacecraft down, which is important when travelling to the inner part of the Solar system or when going into orbit around a planet or moon.

Read more about this important technique here and here.




The simplest way to describe the motion of a mass in a gravity field is the so-called two body problem as we have used above. This can be solved in a closed form (only for point masses) with the Kepler equations. Celestial bodies never are point masses so that gives one complication in the reality of space travel. Another even bigger complication is that there are always other masses in the vicinity that have a non-negligible effect on the motion that is studied.

The strength of gravity diminishes with the square of the distance as Newton taught us, but that means that theoretically the gravity effect of any mass in the Universe only completely vanishes at infinity. In practice we fortunately do not have to incorporate all masses in the Universe when we study e.g. the motion of one of Jupiter’s moons, or the orbit of the Earth around the Sun. But we do need to take into account those objects (in our examples within our Solar system) that do have measurable gravitational influence on the motion we study. This leads to at least a three-body problem and in general to an n-body problem in orbital mechanics.

Lagrange portraitGiuseppe Lodovico Lagrangia Even the three-body problem cannot be solved in closed form, except in special cases. Nowadays we have fast computers and advanced numerical techniques to solve complex motion problems, and the many successful space missions to date are witness to that. But in the 18th century mathematicians such as Euler and Lagrange were looking for special cases where calculations could be simplified in order to arrive at a solution.

Lagrange studied the three-body problem for the Earth, Sun and Moon and also Jupiter's moons. In 1772 he published a special case solution to this problem and formulated what are now known as Lagrangian points (or Lagrange points). If you add a relatively small mass to a two-body system, there are five locations in that system where the small mass will follow the larger masses in their relative motion.


The general definition of a Lagrange point is any location in a two-body system where gravity would cause a third (much smaller) object to stay at a constant distance with respect to the two main masses. Lagrange identified five such locations.

Another way Lagrange points are commonly defined is by stating that the combined gravity of the two main bodies produces the exact centripetal force required to follow the orbital motion of the two bodies. However some authors use the term centrifugal force, but it does in our view not seem a good practice to use an imaginary force in a definition. Our first definition closely follows the mathematical formulation and the condition of a constant distance between two points is easily defined in mathematical terms.

L pointsFive Lagrange points. Image: NASA

L1, L2 and L3 lie on a straight line connection the mass centres of the two masses M1 and M2.
In the Sun-Earth system, L1 and L2 are at a distance of about 1.5 million km from the Earth centre and L3 orbits the Sun at a slightly larger orbit than the Earth, e.g. a little more than 1AU (150 million km) from the Sun.

L4 and L5 are at the same distance from the two masses as the separation between M1 and M2 themselves and thus each form an equilateral triangle with the two masses. This means that L4 and L5 are in the same orbit as the second mass. In case of the Sun-Earth system this is the Earth’s orbit, although not precisely because of the slight eccentricity of Earth’s orbit.

The importance of these points lies in the fact that any mass (e.g. a spacecraft) located in any of these points will stay in the same position relative to the two masses. So a spacecraft in a Lagrange point of the Sun-Earth system will follow the Earth in its orbit around the Sun.

This is not obvious because Kepler’s third law says that an object closer to the central mass (e.g. the Sun) will move faster and objects further out will move slower. In the L1, L2 and L3 points this is certainly not true because objects there will move at the same orbital period as the Earth although they have a different distance to the Sun than Earth. The reason is that the combined gravity of Sun and Earth is “dragging” objects in these locations along with the Earth in its orbit. This is illustrated very well in this ESA website for L1 – L3.



Objects in L1 and L2 are unstable. This can best be compared with a marble sitting on top of a saddle. At one position the marble is in equilibrium, but the slightest deviation from that point will cause the object to move away. In the case of a mass in any of these Lagrange points the mass will move away exponentially with an e-folding time of about 23 days for the Sun-Earth system. Spacecraft in these locations require periodical position corrections within that frequency. For L3 this time about 150 years.

L4 and L5 are stable when the mass M1 is at least about 25 times that of M2.
For the Sun-Earth system the mass ratio is: 333,000
For the Earth-Moon system it is: 81

Mathematically L4 and L5 are in fact also unstable positions, but because a spacecraft there will essentially orbit the ideal Lagrange point it will thus stay in that region. Compare this with air mass in a hurricane revolving around a vortex which relates to conservation of angular momentum. This will keep the spacecraft close to the Lagrange point for a very long time.

Natural occupants of L-points
Because L4 and L5 are long-term stable (for a large enough mass ratio) asteroids and other natural material can collect at these locations. This is very clear for the Sun-Jupiter system where L4 and L5 are the locations of the Trojan asteroids, the Greek camp in L4 and the Trojan camp in L5. See e.g. this animation.

This could also happen for the Sun-Earth and Earth-Moon systems, although we mostly have only detected some dust concentrations at the Lagrange locations of these systems. In 2010 however the Trojan asteroid 2010 TK7 was detected in L4 of the Sun-Earth system.

For space missions, some of the Lagrange points are of great significance. Take the Sun-Earth system. The advantage of L1 is an uninterrupted view of the Sun and of L2 it is the fact that the Sun, Earth and the Moon are always “behind” when looking away. The latter is ideal for deep space research and for spacecraft that require to be cooled to low temperature with appropriate light and thermal shielding at the rear of the spacecraft.

The NASA/ESA SOHO spacecraft is in L1 and continuously observes the Sun. This is an early warning mission for Solar activity so continuity is essential. The WMAP and Planck spacecraft were in L2. In 2019 L2 will come again in the spotlight when the James Webb Space Telescope will be positioned there.

An example of use of the L1 point for space travel, is the GRAIL mission. These twin spacecraft were first taken to the Sun-Earth L1 point and from there continued towards the Moon. This was a complicated and time consuming trajectory, but it saved a large amount of fuel, because launching from a Lagrange point requires very little energy and arrival at the moon happened at low speed, saving a lot of fuel for orbit insertion. It took the Apollo astronauts 3 days to get to the Moon while it took the Grail spacecraft 3.5 months.

Some further reading






To illustrate the reality of inter-planetary space travel based on the principles we discussed above, we show here a few of the actual missions that have been carried out successfully.


CASSINI to Saturn



1776 Cassini interplanet trajectoryImage credit: Cassini, NASA


This trajectory shows multiple flyby’s requiring a favourable configuration of planets, in particular for the last gravity assist past Jupiter. Launch windows are usually quite specific when gravity assist manoeuvers are needed. It took Cassini 6.7 years to reach its destination Saturn. Since its arrival in 2004 most of Cassini’s manoeuvring has been done with further gravity assist at Saturn’s moon Titan.

Cassini speed related to Sun copyImage credit: Python eggs at English Wikipedia


The graph depicts the speed increases (∆V’s) during the trajectory towards and while at Saturn. After mid 2004 (arrival at Saturn) the frequent ∆V’s are due to flyby’s at Titan. This programme would not have been possible with Cassini’s own propellant. The highly successful mission continued until the end of 2017 when Cassini was steered into Saturn.



JUNO to Jupiter


The Juno trajectory took it initially beyond Mars’ orbit and then after a deep space manoeuvre back for an Earth flyby. Then it followed the outer cruise until Jupiter orbit insertion five years after launch.
After 20 months of science at Jupiter the mission is scheduled to end in February 2018 when Juno will be steered into the gas giant.

The insertion manoeuvre occurred at the spacecraft’s closest approach to Jupiter, and slowed it enough to be captured by Jupiter’s gravity into a 53.5-day orbit. In this way the spacecraft saved fuel as compared to going directly into the 14-day orbit required for the science mission.




juno trajectory 2016 6 1024x682Images credit: NASA


Juno is in a highly eccentric, polar orbit over Jupiter and passes very close to the planet at its closest approach (jovelion). Juno needs to get extremely close to Jupiter to make very precise measurements required by the mission. This orbital path carries the spacecraft repeatedly through hazardous radiation belts, which are similar but much stronger than the Earth’s Van Allen belts. See this animation.




NEW HORIZONS to the Kuiper Belt


Although there were backup launch opportunities in February 2006 and February 2007, only the first twenty-three days of the January 2006 window permitted a Jupiter flyby. Any launch outside that period would have forced the spacecraft to fly a slower trajectory directly to Pluto, delaying its encounter by 2–4 years. Fortunately, after some delays, the spacecraft could successfully launch on 19 January 2006 in a direct path towards the outer solar system with a heliocentric speed of 16.3 km/s, which is above solar escape velocity. It used the Atlas V551 rocket with five solid fuel rocket boosters and a third stage added to reach the necessary speed. This third stage is now also in a solar system escape trajectory and must have crossed Pluto’s orbit approximately in October 2015.

The only gravity assist of New Horizons was at Jupiter in February 2007 which increased its speed to 23 km/s. It flew past the Pluto-Charon system in July 2015. Data transmission of the Pluto encounter observations was finally completed in October 2016.


NewHorizonsnow copy


New Horizons is healthy and now on its way further through the Kuiper Belt as displayed in the diagram above (Credit: JHU, NASA). Its mission has been extended to 2021 with a close flyby of Kuiper Belt Object 2014 MU69 on 1 January 2019 and to perform more distant observations of another couple of dozen objects.




MESSENGER to Mercury



MESSENGER was the first spacecraft to go into orbit around Mercury in 2011. This is not because there was little interest in this planet, but primarily because it is so difficult to do this. A direct Kepler orbit to Mercury would be a heliocentric ellipse with perihelion in Mercury’s orbit. But the spacecraft’s speed at that point would be very much faster than Mercury itself and directly braking into an orbit insertion is impossible.


The actual 6.6 year trajectory has been one of the most complex ever flown, with six gravity assist flyby’s at Earth (1), Venus (2) and Mercury itself (3).


MESSENGER flybuys 


Notice the colour code in the diagram, indication the various phases. After each flyby the spacecraft gets into a narrower orbit around the Sun. In the final phase MESSENGER is almost in the same orbit as Mercury, and thus will have a small relative velocity with that planet.





GRAIL to the Moon - We can also make it really difficult to save energy.



The Apollo spacecraft took only three days to reach the Moon in a direct approach. The twin GRAIL mission launched in 2011 took a very indirect approach taking 3.5 months to save energy.




Grail trajectory to the Moon passed by the L1 Lagrangian point (see Chapter 5 above) between the Sun and Earth at low speed, before swinging back towards the Moon. The twin spacecraft arrived at low relative speed with respect to the Moon to also save energy with the slowing down.

Orbit insertion was performed separately for each of the two spacecraft. They needed to be in specific relative orbits around the Moon for their mission. The precise gravity mapping involved microwave ranging systems between the two spacecraft who therefore had to be in mutual visibility during the entire science phase at a very low 50 km orbit.






Above we discussed spacecraft that are essentially in a free fall motion in gravity. The only orbital corrections are performed by short bursts of on-board booster rockets or through flyby’s past planets for gravity assist.

Electric propulsion systems for spacecraft have been imagined for as long as rockets in general have been. But lifting a payload off the Earth into space can still only be done with chemical propulsion systems that work with the burning (oxidation) of solid or liquid fuel. We cannot give a full account in this article of non-chemical rocket propulsion systems, (find a good overview here) but want to emphasise that there are good options to use electrical systems while the spacecraft is in space.

The chief advantage of such systems is that they can provide a thrust over long periods of time and with very efficient use of propellant, although the thrust itself is far less than that of chemical systems. This means that such propulsion systems can provide extended periods of acceleration during the space flight, making it more complicated than non-propelled spaceflight, but also making it a lot more economical.


The DAWN mission was launched in September 2007 and visited the asteroid 4Vesta and subsequently went into orbit around the dwarf planet 1Ceres. This mission would have been impossible without the ion thrusters that DAWN had on board. This propulsion system also saved the mission a lot of propellant (fuel and oxidiser) that conventionally would have been used, as it only used a relatively small amount of Xenon gas as propellant.

Dawn trajectoryImage credit


The graph shows DAWN’s trajectory from launch, which included a gravity assist past Mars. It also shows the extended periods that the ion-thrusters were operating (thrusting). Watch an interview with Marc Rayman, Dawn Chief Engineer at JPL discussing the advantage of the Ion Thruster for the Dawn mission here.

A “traditional” trip to Mars such as the MSL mission discussed above takes about 9 months. Then you will have to stay on Mars for another three months before Earth is at the correct position relative to Mars to allow you to go home. An on-board propulsion system could shorten the flight time to Mars significantly (although it forces the system to stay longer on Mars for return missions). This would also have the important advantage that astronauts will not be exposed to harmful radiation and micro-meteorites while in space for too long. On-board propulsion systems are therefore much at the forefront of current research in space technology. An example of this on-going research is the Hall thruster.








No propellant at all?
Arguably the most interesting recent invention that has first been made by British engineer Roger Shawyer is the “impossible” EM Drive. Many scientists have claimed that this idea would violate conservation of momentum, but after years of study and experimentation by several research groups, the idea persists and claims are made that the Cannae drive, which is different but similar to Shawyer’s design, will soon be tested in orbit on a Cubesat. These drives do not require any propellant but only electric energy and in principle employ radiation pressure from microwave radiation leaving an antenna.








The New Horizons spacecraft that flew by the Pluto and Charon dwarf planet system is one of the fastest spacecraft ever launched. It continues to fly at a speed of about 13 km/s and will eventually leave the Solar system, just like the Voyager spacecraft are doing. If New Horizons would fly towards the closest star system Alpha Centauri (which it isn’t) it would take about 80,000 years to get there.
So if we ever want to stand a chance to travel to the nearest stars in a reasonable time (as compared to a human lifetime) we will need on-board propulsion systems with very long life time.


tothestarsImage credit:


A deep-space probe with a mass of 10,000 kg based on the Cannae drive discussed above, claims to reach a distance from Earth of 0.1 lightyears within 15 years and 0.5 lightyears within 33 years (ref here).


Alternatively cosmologist Stephen Hawking and others have suggested a fleet of mini spacecraft that could make the journey to Alpha Centauri in 20 years, using light sails that are laser powered from Earth orbit (project Stars shot).












It will be very interesting to see how space travel will evolve throughout this century but do not forget that gravity dictates the motion of all objects in the Universe and the gravitational freefall orbit will always be the primary principle of getting from A to B in space. Space based propulsion systems can provide an important add-on to make space travel more economical and/or time saving.


"The future is not there waiting for us. We create it by the power of imagination”
Vilayat Inayat Khan











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