Limitations to testing the equivalence principle with satellite laser ranging

Abstract We consider the possibility of testing the equivalence principle (EP) in the gravitational field of the Earth from the orbits of LAGEOS and LAGEOS II satellites, which are very accurately tracked from ground by laser ranging. The orbital elements that are affected by an EP violation and can be used to measure the corresponding dimensionless parameter ? are semimajor axis and argument of pericenter. We show that the best result is obtained from the semimajor axis, and it is limited-with all available ranging data to LAGEOS and LAGEOS II-to ? = 2 × 10-9, more than 3 orders of magnitude worse than experimental results provided by torsion balances. The experiment is limited because of the non uniformity of the gravitational field of the Earth and the error in the measurement of semimajor axis, precisely in the same way as they limit the measurement of the product GM of the Earth. A better use of the pericenter of LAGEOS II can be made if the data are analyzed searching for a new Yukawa-like interaction with a distance scale of one Earth radius. It is found that the pericenter of LAGEOS II is 3 orders of magnitude more sensitive to a composition dependent new interaction with this particular scale than it is to a composition dependent effect expressed by the ? parameter only. Nevertheless, the result is still a factor 500 worse than EP tests with torsion balances in the gravitational field of the Earth (i.e. at comparable distance), though a detailed data analysis has yet to be performed. While EP tests with satellite laser ranging are not competitive, laser ranging to the Moon has been able to provide a test of the EP almost 1 order of magnitude better than torsion balances. We show that this is due to the much greater distance of the test masses (the Earth and the Moon) from the primary body (the Sun) and the correspondingly smaller gradients of its gravity field. We therefore consider a similar new experiment involving the orbit of LAGEOS: testing LAGEOS and the Earth for an EP violation in the gravitational field of the Sun. We show that this test may be of interest, though it is a factor 300 less sensitive than in the case of the Moon due to the fact that LAGEOS is closer to the Earth than theMoon and consequently its orbit is less affected by the Sun. The limitations we have pointed out for laser ranging can be overcome by flying in low Earth orbit a spacecraft carrying concentric test masses of different composition with the capability, already demonstrated in ground laboratories, to accurately sense in situ any differential effects between them

EXPERIMENTAL VALIDATION OF A HIGH ACCURACY TEST OF THE EQUIVALENCE PRINCIPLE WITH THE SMALL SATELLITE "GALILEO GALILEI"

The small satellite "Galileo Galilei" (GG) has been designed to test the equivalence principle (EP) to 10-17 with a total mass at launch of 250 kg. The key instrument is a differential accelerometer made up of weakly coupled coaxial, concentric test cylinders rapidly spinning around the symmetry axis and sensitive in the plane perpendicular to it, lying at a small inclination from the orbit plane. The whole spacecraft spins around the same symmetry axis so as to be passively stabilized. The test masses are large (10 kg each, to reduce thermal noise), their coupling is very weak (for high sensitivity to differential effects), and rotation is fast (for high frequency modulation of the signal). A 1 g version of the accelerometer ("Galileo Galilei on the Ground" — GGG) has been built to the full scale — except for coupling, which cannot be as weak as in the absence of weight, and a motor to maintain rotation (not needed in space due to angular momentum conservation). GGG has proved: (i) high Q; (ii) auto-centering and long term stability; (iii) a sensitivity to EP testing which is close to the target sensitivity of the GG experiment provided that the physical properties of the experiment in space are going to be fully exploited

Experimental Validation of a High Accuracy Test of the Equivalence Principle with the Small Satellite "GALILEO GALILEI"

The small satellite "Galileo Galilei" (GG) has been designed to test the equivalence principle (EP) to 10-17 with a total mass at launch of 250 kg. The key instrument is a differential accelerometer made up of weakly coupled coaxial, concentric test cylinders rapidly spinning around the symmetry axis and sensitive in the plane perpendicular to it, lying at a small inclination from the orbit plane. The whole spacecraft spins around the same symmetry axis so as to be passively stabilized. The test masses are large (10 kg each, to reduce thermal noise), their coupling is very weak (for high sensitivity to differential effects), and rotation is fast (for high frequency modulation of the signal). A 1 g version of the accelerometer ("Galileo Galilei on the Ground" — GGG) has been built to the full scale — except for coupling, which cannot be as weak as in the absence of weight, and a motor to maintain rotation (not needed in space due to angular momentum conservation). GGG has proved: (i) high Q; (ii) auto-centering and long term stability; (iii) a sensitivity to EP testing which is close to the target sensitivity of the GG experiment provided that the physical properties of the experiment in space are going to be fully exploited

"Galileo Galilei" (GG) a small satellite to test the equivalence principle of Galileo, Newton and Einstein

"Galileo Galilei" (GG) is a small satellite designed to fly in low Earth orbit with the goal of testing the Equivalence Principle-which is at the basis of the General Theory of Relativity-to 1 part in 1017. If successful, it would improve current laboratory results by 4 orders of magnitude. A confirmation would strongly constrain theories; proof of violation is believed to lead to a scientific revolution. The experiment design allows it to be carried out at ambient temperature inside a small 1-axis stabilized satellite (250 kg total mass). GG is under investigation at Phase A-2 level by ASI (Agenzia Spaziale Italiana) at Thales Alenia Space in Torino, while a laboratory prototype (known as GGG) is operational at INFN laboratories in Pisa, supported by INFN (Istituto Nazionale di fisica Nucleare) and ASI. A final study report will be published in 2009