How to test the equivalence principle in space? The Microscope mission

The goal of the Microscope mission is to test the equivalence principle to a precision two orders of magnitude better than is achieved on ground, more precisely 10-15 or one part in 1 000 000 000 000 000.

Members of the mission like to say that this is the difference of weight of a 500 000 ton tanker when a 0.5 milligram drosophilia fly lands on the deck.

coaxial_cylindersIn order to do so, one needs to compare the free
fall of two objects of different composition (see why here). But the two objects must feel exactly the same gravitational field, and thus be placed at the same point in space. In the Microscope set up, they are two coaxial cylinders of different material – one is made of titanium and the other one of a platinum-rhodium alloy- which have coinciding centers of mass (as shown on the figure to the right).





As a matter of fact, the Microscope mission has two devices (see on the left): one with two cylinders of the same material, and one with cylinders of different materials. This allows to make sure that any effect observed with the two different cylinders is not observed with the two identical cylinders!



Actually, the cylinders are not in strictly free fall. Remember that an object in orbit keeps falling, with horizontal velocity. The satellite, and the two coaxial cylinders, are in orbit but they have slightly different motions: the satellite is submitted to non-gravitational perturbations (inducing friction or drag) which are compensated by micro-thrusters. And, in case the equivalence principle is violated, the two cylindrical masses should have tiny differences of motion. In the Microscope experiment, they are forced to follow the same motion at the center of the satellite by applying on them electrostatic forces, or if you prefer external acceleration on them. If the applied accelerations need to be different on the two masses, this means their natural motion is different: there is a violation of the equivalence principle. In other words, different accelerations on the two cylindrical masses mean different gravitational motions. Another beautiful illustration of the equivalence between acceleration and gravitational field!

It is very important to make sure that the effect observed must be attributed to a violation of the equivalence principle, and not to the set up malfunctioning. In order to do so, the physicists have a clever way of modulating the signal, that is of making the potential violation signal vary with time at a given frequency. Here is the trick.


The satellite is following a quasi-circular orbit at an altitude of 710 km. The axis of the cylinders is pointing in a direction fixed with respect to the distant stars, and the acceleration measurement is made along this axis. As you can see in the figure above, there are positions along the orbit where the gravitational attraction is perpendicular to this axis, and thus not active along this axis. There are other positions where it is parallel or antiparallel, and thus the effect is maximal. In this way, one modulates the effect at a known frequency which is directly related to the frequency of rotation along the orbit. Any effect of violation of the principle of equivalence must have such a modulation.

In order to further check the results, the physicists of Microscope have decided also to spin the satellite around the axis perpendicular to the orbital plane with a period of 1000 seconds. In this way, they introduce a further modulation of the signal.

If you want to watch the launch of the Microscope mission from Kourou, see here.


Gravitational Wave Fiesta : course material

Following our Gravitational Wave Fiesta, below are the slides shown in the various presentations and a record of the last session, the ultimate quizz proposed by Pierre Binétruy to the learners of the Gravity!

Thanks to all for these fruitful and friendly couple of days!

fiesta16 001

Pierre Binétruy (Paris Centre for Cosmological Physics/APC)

Introduction to the Fiesta: physicists dreamed about them for 100 years English/French

Introducing the Fiesta

Eric Chassande-Mottin (Laboratoire APC)

The story of GW150914 discovery (English)


Matteo Barsuglia (APC)

The LIGO and Virgo detectors (English)


Eric Plagnol (APC)

LISAPathfinder news (English)



Antoine Petiteau (APC)

How will we analyze the LISAPathfinder data? (French)


Joël Bergé (ONERA)

The Microscope mission and the equivalence principle (English)


Pierre Binétruy and all the participants

A last quiz: questions and answers during the last session of the “Fiesta”

The teaser:

The full recording:


Pierre Binétruy at Livre Paris




This Saturday 19 March from 3pm to 4pm, Pierre Binétruy gives  a presentation at Livre Paris, the book fair that takes places at Porte de Versailles. The presentation is part of the programme “Rencontres de Sciences pour tous” which is held at booth P12 and the title of the conference (in French) is: In pursuit of gravitational waves.



Thanks for the picture to Jean-François Dars and Anne Papillaud who were passing by.

LISAPathfinder test masses released : a major step on the road

The gravitational skies seem to be auspicious these days. While the LIGO collaboration was announcing the discovery of gravitational waves, the LISAPathfinder team was going through a very delicate process : the release of the two test masses which was completed successfully this morning.


Behind the polished press release of ESA, let me explain what was at stake, and why everyone in the eLISA project is relieved and very joyful today. Indeed, you can see in the tweet below the reaction of Stefano Vitale, the scientist in charge of the mission, and César García, the project manager (we had met him in Kourou last November a few hours before launch, see the video of the hangout).


LISAPathfinder is testing the basic principle behind the eLISA mission which is to be able to measure variation of distances between two test masses which are only submitted to gravitation, in other words which are freely floating in the cosmos. These test masses are small cubes of gold-platinum of 46 mmm side.


Test mass ©CGS SpA

During the experimental phase, these masses are floating in a cage, called electrode housing. Thanks to these electrodes, the satellite is constantly monitoring the position of the test mass, and operates its external microthrusters in order to change its own position and reposition itself in such a way that the test mass stays at the centre of its cage. In this way, the satellite protects the test mass from external perturbations.

But there is one difficulty: whereas the test mass is floating once on site, it has to be tightly locked during launch: otherwise, the strong vibrations would shake it within its housing, which would provoke irreparable damage.


(c) University of Trento

Electrode housing © University of Trento



And here is the tricky engineering problem, which gave nightmares to ESA (and, in an earlier stage, NASA) teams: this was known to everyone in the mission as the “infamous caging mechanism”. How do you release the test mass once you have tightly locked it? The difficulty is that, once tightly pressed, the test mass sticks to the metal finger that presses on it. But one has to release the mass very softly, because only very small forces can be acted upon.


The solution that was finally adopted relies on a two-stage process.


Throughout LISAPathfinder’s launch, , and the six-week cruise to its work site, each cube was held firmly in place by eight ‘fingers’ pressing on its corners. On 3 February, the locking fingers were retracted and a valve was opened to allow any residual gas molecules around the cubes to vent to space. Each cube remained in the centre of its housing held by a pair of rods softly pushing on two opposite sides.



The rods were finally released from one test mass yesterday and from the other this morning, leaving the cubes floating freely, with no mechanical contact with the spacecraft.

Congratulations to the project manager, César García, and all the technical teams involved in this success !

It will be another week before the cubes are left completely at the mercy of gravity, with no other forces acting on them. Before then, minute electrostatic forces are being applied to move them around and make them follow the spacecraft as its flight through space is slightly perturbed by outside forces such as pressure from sunlight.


On 23 February, the team will switch LISA Pathfinder to science mode for the first time, and the opposite will become true: the cubes will be in free fall and the spacecraft will start sensing any motion towards them owing to external forces. Microthrusters will make minuscule shifts in order to keep the craft centred on one mass.


The final word to Stefano Vitale: “Releasing LISA Pathfinder’s test masses is another step forward in gravitational wave astronomy within this memorable month: the test masses are, for the first time, suspended in orbit and subject to measurements”.


Pierre Binétruy

Gravitational wave fiesta 29Feb/01Mar

This is the first of the Gravity! workshops for the learners of Gravity!, all their friends and all those interesting in getting a better understanding of the mysteries of our Universe.

The workshop will of course focus on the topic of gravitational waves, with the historic event of their discovery.
What is a gravitational wave? How were they observed? What have we learnt about black holes from their discovery? What comes next? What is the present status of  LISAPathfinder? So many questions to cover with specialists of the field, with a programme of lab visits in small groups, a social event and a hangout live with the rest of the world.


To reserve your participation, please go to this website  (we ask for a modest participation of 10€ in order not to cover the expenses but to have a better idea of the number of participants).

The event takes place from Monday February 29 at 9.30am till Tuesday March 1 at 4pm.

Language: English and French
Venue: University Paris Diderot, Amphitheater Buffon, 15, rue Hélène Brion (13th arrondissement)

Metro and RER stop: Bibliothèque François Mitterrand

Programme: see below

affiche_GW Fiesta_V3

A questionnaire has been distributed to all participants to stimulate their curiosity. You may have access to it here.

Monday 29 February/Lundi 29 février

Amphitéâtre Buffon

9h30-11h00 : Gravitational waves and their discovery, an overview/Les ondes gravitationnelles et leur découverte, une introduction (P. Binétruy)

11h00-11h30 : Coffee break/Pause café

11h30-12h30 : What do you expect from MOOCs, a discussion led by P. Binétruy

12h30-14h00 : Buffet lunch/Déjeuner buffet

  • Amphithéâtre Buffon (en français)

14h00-14h30 L’histoire de la découverte de GW150914 (E. Chassande-Mottin)

14h45-15h15 Les détecteurs LIGO et Virgo (M. Barsuglia)

15h30-15h50 Les nouvelles de LISAPathfinder (E. Plagnol)

16h00-16h20 Comment va-t-on analyser les données de LISAPathfinder (A. Petiteau)

  • Bâtiment Condorcet, Salle Luc Valentin (4th floor, 454A) (in English)

14h00-14h30 The LIGO and Virgo detectors (M. Barsuglia)

14h45-15h15 Story of GW150914 discovery (E. Chassande-Mottin)

15h30-15h50 How to analyze the LISAPathfinder data (A. Petiteau)

16h00-16h20 LISAPathfinder news (E. Plagnol)

  • Amphitéâtre Buffon

16h30-17h30 Coffee break/Pause café

17h30-18h30 Hangout with the whole Gravity! community (in English)


Tuesday 1 March/Mardi 1er mars

  • Bâtiment Condorcet

9h00-10h30 : Group visits/Visites par groupe

10h30-11h00 : Coffee break/Pause café (4th floor/4ème étage)

11h00-12h30 : Group visits/Visites par groupe

12h30-14h00 : Free time for lunch/Temps libre pour déjeuner

  • Amphithéâtre Buffon

14h00-14h40 : The Microscope mission and the equivalence principle/La mission Microscope et le principe d’équivalence (J. Bergé)

14h40-16h00 : Discussion session, future actions, wrap up/Session de discussion, actions futures, conclusions (P. Binétruy)

The curtain rises on the gravitational Universe

After a long wait, the rumour has been confirmed: gravitational waves have been detected in the LIGO interferometric antenna. This is a major scientific event, not only because it concludes a century long chase : Einstein predicted the existence of such waves in 1916, only a few months after his seminal series of papers on General Relativity in November 1915. But this is also the opening of a new era: the direct observation of the gravitational Universe.


Indeed, all the discoveries of the XXth century have confirmed Newton’s point of view that gravitation is running the Universe in its largest spatial dimensions as well as its evolution with time. But all detection until now was based on light, or more generally electromagnetic waves. Not so surprising from human beings equipped with a sensitive light detector, the eye. The discovery of today opens up the exciting possibility of exploring the Universe, and our space-time with waves of gravity. We will thus get first-hand information on the most gravitational of all astrophysical objects, the black holes, but also on many violent phenomena in the Universe, and ultimately the most violent of all, the Big Bang.


Today is clearly only a beginning. Ground detectors are now in a position to observe many more stellar events and do outstanding science. The space detector eLISA, as well as the observation of pulsar timing, will open the window onto the gravitational Universe at large. It is a beautiful symbol for the future that, at the time the discovery is announced, the LISAPathfinder satellite is waking up at the Lagrange point L1, ready to test the technology of the future eLISA mission.


It is time to rejoice and to congratulate the scientists of the LIGO collaboration, but also the GEO600 and Virgo European teams who joined in the analyses, for their commitment over many years to this search, and for their careful handling of this outstanding discovery, despite the pressure from the scientific community and the media. And its is also the occasion to stress that this is an incredible achievement in terms of ultra-precise measurements.


We hope that all the learners of Gravity! feel gratified to have spent weeks on understanding better the gravitational Universe, and thus that they better share the excitement of this discovery.


We propose on this website a series of posts, under the heading Gravitational wave discovery, which presents more details on gravitational waves, their detection, and the present discovery. They will be complemented in the future. Do not hesitate to comment and ask questions.


We had also said that we would organize the first Gravity! Workshop at the end of this month. The dates are nox fixed, February 29 and March 1, and the location is Paris. And the title: Gravitational wave fiesta. Surprised? All you want to know about gravitational waves and their discovery. Reserved to Gravity! learners… and all their friends. So it is time to visit Paris for the week-end, and make a short excursion into the gravitational Universe. And if you really cannot come and meet us, we will have a hangout on the evening of February 29.

We had promised exciting news for the forthcoming months and years. It only begins.

Pierre Binétruy and George Smoot

What is a gravitational wave?

According to Einstein’s theory of general relativity, a mass deforms space-time. This was spectacularly observed in 1919, only four years after the publication of the theory: thanks to a Sun eclipse, one could observe that light rays passing close to the Sun are following slightly curved trajectories.


Since mass induces curvature of space-time, mass in motion will induce propagation of curvature. If you throw a stone into a pond, you induce, on the water surface, wavelets that originate from the place where the stone fell. Similarly, if a mass suddenly moves in the Universe, this will induce waves of curvature, called gravitational waves, that propagate through space-time.



Which sources generate gravitational waves? Every mass in motion does generate such waves. But we will see that the effects of a passing gravitational wave are extremely tiny. We thus have to ask which are the most powerful sources of gravitational waves. They are energetic events like the rapid rotational motion of two nearby compact stars (like neutron stars or black holes) or explosions (for example supernova explosions, or even the Big Bang itself).


How do I know that a gravitational wave is passing through the lab? Because distances between objects vary in a periodic way (remember that a wave is a periodic phenomenon). Imagine masses which are arranged in a circle as on the left-hand side of the following Figure.


The two types of gravitational wave polarizations

The two types of gravitational wave polarizations

If a gravitational wave propagates perpendicularly to the screen, the distances between the masses will change and the circle will be deformed periodically into an ellipse. There are actually two different types of deformation, which correspond to what one calls the two polarizations of the gravitational waves.


The relative motion of the masses is largely exaggerated in the Figure above. It turns out that, for the most significant cosmic events, the relative variation of distance is smaller than 10-21, in other words 1/1000000000000000000000 meter for a circle of one meter diameter. It is thus not surprising that discovering gravitational waves is such a difficult task!


Why are gravitational waves so interesting?


The effect of gravitational waves is so tiny because gravity is a very weak force. But conversely, this means that gravitational waves are interacting very little with the environment, and are thus very little disturbed by the objects they encounter on their way: they keep intact all the information of the sources that produced them. They are thus ideal messengers of very distant cosmic events.


Moreover, we have known since Newton that the Universe in its largest dimensions is moved by gravity. With the discovery of gravitational waves, we will thus have the possibility to get first-hand information on gravity, through gravity itself turned into waves!

Detecting gravitational waves with interferometry

In order to detect gravitational waves, one must be able to measure exquisitely small (and periodic) variations of distances. There is no use to take the prototype metre bar out of the Bureau International des Poids et Mesures in Sèvres. One has known for a long time that precise metrology requires a more refined type of prototype, the wavelength of light.




Light is an electromagnetic wave. As any wave, it is an oscillation characterized by its wavelength, the distance between two crests. The wavelength of visible light is a fraction (0.4 to 0.7) of a micron (one millionth of a metre).


Diapositive2But how to turn light into a measuring device? It is the physicist Albert A. Michelson who taught us how to do this at the end of the XIXth century. He used the phenomenon of interference: when you shed coherent light (nowadays laser light) onto a board pierced with two slits, the light beams reemitted by the two slits on the other side of the board interfere. One observes on a screen placed further away zones (called “fringes”) which are alternatively luminous and dark. They are forming an interference pattern. The thickness of the fringes is directly related to the wavelength of the light.


Albert Michelson (1852-1931) counting interference fringes

Albert Michelson used this phenomenon to measure distances in a set up called an interferometer. In its modern version, a laser beam falls onto a beamsplitter which splits into two: each beam is then reflected on distant mirrors to return to the beamsplitter where they are recombined to interfere on a screen some distance away. The two arms of the interferometer are the trajectories of the two independent beams. The interference pattern on the final screen depends on the difference of length of the two arms.

A Michelson interferometer

A Michelson interferometer

If a gravitational wave goes through an interferometer, distances such as the arm lengths change periodically, which leads to a periodic change of the interference pattern. This allows to detect the gravitational wave.

Which kind of detectors for gravitational waves?


As for any wave, a gravitational wave is characterized by its velocity, its wavelength and its amplitude.


The velocity is predicted by general relativity to be the same as the velocity of light. This will have to be tested once gravitational waves are discovered.

The wavelength is directly related to the size of the cosmic site (binary system or explosion) which is the source. To understand this, note that, in the picture below, the size of the drop fixes the wavelength of the waves (the distance between crests). It is similar for gravitational waves. Now, the size of the detector has to be of the order of the wavelength, neither much larger, nor much smaller. Hence the size of the detector has to be of the order of the size of the cosmic site.


One thus have two main types of man-made detectors:

  • small cosmic sites i.e. wavelengths of a few thousand kilometres : ground interferometers
  • large cosmic sites i.e. wavelengths of a tens of million kilometres : space interferometers


Finally, the amplitude of the wave is related to the strength of the event, measured by the amount of mass that produces the propagating curvature. In large cosmic sites, there is usually much more mass available, hence the signals are much larger for space detectors. For ground detectors, they are much weaker and thus only events within a certain distance of the detector are accessible.


There are also two other ways of detecting gravitational waves.

One uses millisecond pulsars, that is cosmic sources in our own Galaxy that emit regularly electromagnetic pulses observed on Earth. When a gravitational wave passes between the source and us, this induces time distortions that can be measured. Using several of these sources, one obtains a detector of the size of our Galaxy (say tens of thousands of light-years).


One can also look at the effect of primordial gravitational waves, that is gravitational waves produced in the very early Universe, on the first light emitted 380 000 years after the Big Bang. They tend to polarize this cosmic background of light. In this case, because the background light fills the early Universe, one uses in a sense a detector of the size of the whole observable Universe at that early time. It is this polarisation that the BICEP2 experiment thought that they had detected some years ago.


To summarize, the following Figure shows the rich variety of scales over which one hopes to detect gravitational waves, and the science one would study with them:

The gravitational wave spectrum (NASA Goddard Space Flight Center)

The gravitational wave spectrum (NASA Goddard Space Flight Center)

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