Rosetta and Philae

Philae, the robot carried by the Rosetta probe landed on the comet 67P/Churyumov-Gerasimenko November 12, 2014. Dropped at 9:35 pm Paris time, at a distance of 22.5 km from the center of the comet, the robot without propulsion, hit the sandy soil of the comet, 7 hours later at a speed of about 1 m/s. The site on which landed Philae called Agilkia (see nota).
This is the first comet landing ever attempted by man. To achieve on Earth, the signal confirming this historic landing took about 40 minutes and arrived at 4:03 p.m. UTC. The confirmation was relayed by the orbiter and captured simultaneously by the ground station ESA Malargüe, Argentina and NASA station in Madrid, Spain. The first data from the lander instruments were sent to the navigation center of the space agency in Toulouse, France. Landing on a comet so small is a remarkable feat, given the extremely low gravity of the object. Philae, the lander robot of 100 kg weighs only a few grams on the surface of "chury."
For ten years, from March 2, 2004, Rosetta and Philae traveled together to reach their destination. Since August 6, 2014, Rosetta rotates around the comet, analyzing its surface to select a landing site for Philae.
The landing site is located on the head of the object with both lobes, it was chosen according the images and data collected at distances of 30-100 km from the comet, just six weeks after arrival. After a very long journey of 6.4 billion km, 12 November 2014, Rosetta and Philae separated. The main objective of the mission was to reach the periodic comet Churyumov-Gerasimenko (1 pass every 6.59 years), and then put the robot lander Philae of 100 kg on its surface. Rosetta ESA spent a lot of time (the second half of October 2014) in orbit around the comet, to less than 10 km from its surface. Beautiful and original images taken by the navigation camera from Rosetta, we have received during this period.

They show us this disturbing and mysterious world that has imprisoned Philae to the dawn of time. In fact, the comet is very dark, much darker than the picture, blacker than coal, but the camera has accentuated the light and shadows of this ancient remnant of our solar system. These first images revealed a world littered with rocks, cliffs and pits and precipices impressive.
"In the coming hours we will learn exactly how and where we landed, and we'll start to get as much scientific data as we can from the surface of this fascinating world." said Stephan Ulamec, Director of the German Aerospace Center DLR.
The comet will reach its closest distance from the Sun August 13, 2015 at about 185 million km between the orbits of Earth and Mars. Rosetta will follow the comet and will monitor Philae throughout 2015, moving away from the Sun, then Rosetta and Philae will sleep in the cold area of our solar system.

NB: The Rosetta Stone discovered in 1799, is an engraved stone from ancient Egypt which is inscribed on three versions of the same text that allowed the deciphering of hieroglyphics in the early 19th century. Top of the stone, the text is in Egyptian hieroglyphs, the middle, the same text in Demotic and down in ancient Greek. The Rosetta Stone measure 112.3 cm high, 75.7 cm wide and 28.4 cm thick and weighs ≈760 kg.
Philae was an ancient Egyptian city on the Nile, which housed a temple of Isis, one of the best preserved. Since the commissioning of the Aswan High Dam in 1970, Philae is no longer a rock emerging from the lake. All the constructions placed on the granite soil of Philae, stone by stone, were transported to another block of granite, Aguilkia. Philae is a mythical site whose ancient beliefs and messages we have received.

Luck is with Philae, despite the dysfunction of the attachment system, it remained on the floor of the comet. The Philae robot landed on the comet Churyumov-Gerasimenko in the place provided by scientists, but the harpooning which was fix Philae to the ground, went wrong, the harpoons were supposed to be projected using an explosive system. So Philae under the pressure shock absorbers, a "bounced".
This dysfunction, which could have, forever eject the robot out the comet, was not catastrophic because Philae landed on soft ground.
According to astrophysicist Francis Rocard, if the ground was hard, Philae would have suffered a severe kickback, in fact the system plunged only 4 cm, while the maximum amplitude of the shock absorber is 20 cm. Then, according to Ulamec Stephan, head of the lander, Philae was "a huge leap", about a kilometer away. Because of the low gravity that leap took place at idle and it has lasted nearly two hours. Fortunately, it ended well but Philae finished his race in an uncomfortable position in the dark and with one leg in a vacuum, which will pose a problem to recharge its solar batteries.
 
NB: We must not confuse mass and weight although on Earth, mass and weight are used as synonyms. The weight of the body is a force exerted by the ambient gravitational field, the weight varies depending on location. The mass does not change depending on the location, it corresponds to an amount of material, it is the same throughout the universe. The weight is measured in Newton, mass in kg.

But what is the weight of Philae on the comet?
To calculate the weight of Philae on Churyumov-Gerasimenko, i.e. the force of gravity on the comet, we must use several parameters, the gravitational constant G, the gravitational acceleration g, the mass of the comet M, the mass of Philae m and the radius R of the comet, or rather R min and R max because it is not a spherical object.
G = 6,67384 10⁻¹¹ N.m².kg^-2 
g = G (M/R2) en m/s²
M = 1×10¹³ kg
m = 100 kg
R min and max = ≈0,65 km et ≈2,05 km, (dimensions of the lobes of the comet) (4,1×3,2×1,3 km) + (2,5×2,5×2,0 km).
It only remains to calculate the gravitational force exerted by the comet on Philae, where F=G ((Mm)/R²) newton or m·kg·s^-2
The gravitational force is ≈0,01588 N farthest from the center of the comet and 0.1579 N closer.
The weight of Philae is to ≈1,5 gram farther from the center of the comet and ≈15,7 grams closer.
Scientists need to be very delicately to control the instruments of Philae. A very small uncontrolled thrust, would be sufficient to orbit the robot and lost forever.