Optical Clock and Drag-Free Requirements for a Shapiro Time-Delay Mission

The principle of equivalence states that an inertial reference frame at rest in a region of a uniform gravitational field is equivalent to a noninertial reference frame undergoing a constant acceleration relative to the fixed stars. Thus, the principle of equivalence can be combined with the special relativity in order to provide information on the behavior of light in a gravitational field1. Einstein predicted2 a change in the energy of photons in the proximity of a gravitational field, the change being directly proportional with the distance from the gravitational source. In the early 60’s Pound and Rebka3,4 have set to verify Einstein’s prediction. The experiment was reprised with even higher precision by Pound and Snider5 and later on by Vessot et. al6,7. The Vessot experiment yielded a precision of about 10-4. In the present we attempt to answer the question as to what happens if we attempt to reprise the Pound-Rebka experiment by replacing the two atomic oscillators with light clocks placed at different depths in the gravitational well of a gravitating body. We attempt to answer the question: if the speed of light is the same for both light clocks and if the distance between the mirrors is the same, how come that the periods of the two clocks are different? We will concentrate specifically on the limits for testing the local position invariance (LPI)22 and we will show that such limits can be pushed to attain a practical limit consistent with the precision of measuring the gravitational acceleration.

International Journal of Modern Physics D, 2013

ASTROD I is the first planned space mission in a series of ASTROD missions for testing relativity in space using optical devices. The main aims are: (i) to test General Relativity with an improvement of three orders of magnitude compared to current results, (ii) to measure solar and solar system parameters with improved accuracy, (iii) to test the constancy of the gravitational constant and in general to get a deeper understanding of gravity. The first ideas for the ASTROD missions go back to the last century when new technologies in the area of laser physics and time measurement began to appear on the horizon. ASTROD is a mission concept that is supported by a broad international community covering the areas of space technology, fundamental physics, high performance laser and clock technology and drag free control. While ASTROD I is a single-spacecraft concept that performes measurements with pulsed laser ranging between the spacecraft and earthbound laser ranging stations, ASTROD-GW is planned to be a three spacecraft mission with inter-spacecraft laser ranging. ASTROD-GW would be able to detect gravitational waves at frequencies below the eLISA/NGO bandwidth. As a third step Super-ASTROD with larger orbits could even probe primordial gravitational waves. This article gives an overview on the basic principles especially for ASTROD I.

Nuclear Physics B ( …

The performance of optical clocks has strongly progressed in recent years, and accuracies and instabilities of 1 part in 10 18 are expected in the near future. The operation of optical clocks in space provides new scientific and technological opportunities. In particular, an earth- ...

Motivated by the benefits of improving our knowledge of Newton's constant G, Feldman et al have recently proposed a new measurement involving a gravitational clock launched into deep space. The clock's mechanism is supposed to be the linear oscillation of a test mass falling back and forth along the length of a hole through the center of a spherical source mass. Similar devices—ones that would have remained in orbit around Earth—were proposed about 50 years ago for the same purpose. None of these proposals were ever carried out. Further back, in 1632 Galileo proposed the thought experiment of a cannonball falling into a hole through the center of Earth. Curiously, no one has yet observed the gravity-induced radial motion of a test object through the center of a massive body. Also known as a gravity-train, not a one has yet reached its antipodal destination. From this kind of gravitational clock, humans have not yet recorded a single tick. The well known reliability of Newton's and Einstein's theories of gravity may give confidence that the device will work as planned. Nevertheless, it is argued here that a less expensive apparatus—an Earth-based Small Low-Energy Non-Collider—ought to be built first, simply to prove that the operating principle is sound. Certain peculiar facts about Schwarzschild's interior solution are discussed here; and a novel way of interpreting gravitational effects will be presented in Part II, together adding support for the cautious advice to more thoroughly look before we leap to the outskirts of the Solar System.

American Journal of Physics

General relativity predicts that clocks run more slowly near massive objects. The effect is small-a clock at sea level lags behind one 1000 m above sea level by only 9.4 ns/day. Here, we demonstrate that a measurement of this effect can be done by undergraduate students. Our paper describes an experiment conducted by undergraduate researchers at Colorado College and the United States Air Force Academy to measure gravitational time dilation. The measurement was done by comparing the signals generated by a GPS frequency standard (sea-level time) to a Cs-beam frequency standard at seven different altitudes above sea level. We found that our measurements are consistent with the predictions of general relativity.

Monthly Notices of The Royal Astronomical Society, 2001

We present the radio light curves of lensed images of the gravitational lens B1422+231. The observations have been carried out using the VLA at 8.4 and 15 GHz over a period of 197 days. We describe a method to estimate the time delay from the observed light curves. Using this method, our cross-correlation analysis shows that the time delay between images B and A is 1.5$\pm$1.4d, between A and C is 7.6$\pm$2.5d, between B and C is 8.2$\pm$2.0d. When applied to other lensed systems with measured time delays our new method gives comparable results.

Experimental Astronomy, 2012

This paper on ASTROD I is based on our 2010 proposal submitted for the ESA call for class-M mission proposals, and is a sequel and an update to our previous paper [Experimental Astronomy 23 (2009) 491-527; designated as Paper I] which was based on our last proposal submitted for the 2007 ESA call. In this paper, we present our orbit selection with one Venus swing-by together with orbit simulation. In Paper I, our orbit choice is with two Venus swing-bys. The present choice takes shorter time (about 250 days) to reach the opposite side of the Sun. We also present a preliminary design of the optical bench, and elaborate on the solar physics goals with the radiation monitor payload. We discuss telescope size, trade-offs of drag-free sensitivities, thermal issues and present an outlook. ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test General Relativity with an improvement in sensitivity of over 3 orders of magnitude, improving our understanding of gravity and aiding the development of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system; and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals. For this mission, accurate pulse timing with an ultra-stable clock, and a drag-free spacecraft with reliable inertial sensor are required. T2L2 has demonstrated the required accurate pulse timing; rubidium clock on board Galileo has mostly demonstrated the required clock stability; the accelerometer on board GOCE has paved the way for achieving the reliable inertial sensor; the demonstration of LISA Pathfinder will provide an excellent platform for the implementation of the ASTROD I drag-free spacecraft. These European activities comprise the pillars for building up the mission and make the technologies needed ready. A second mission, ASTROD or ASTROD-GW (depending on the results of ASTROD I), is envisaged as a three-spacecraft mission which, in the case of ASTROD, would test General Relativity to one part per billion, enable detection of solar g-modes, measure the solar Lense-Thirring effect to 10 parts per million, and probe gravitational waves at frequencies below the LISA bandwidth, or in the case of ASTROD-GW, would be dedicated to probe gravitational waves at frequencies below the LISA bandwidth to 100 nHz and to detect solar g-mode oscillations. In the third phase (Super-ASTROD), larger orbits could be implemented to map the outer solar system and to probe primordial gravitational-waves at frequencies below the ASTROD bandwidth.

Journal of the Korean Physical Society, 2004

ASTROD-I is a mission concept under study to realize the general concept of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices). This mission concept has one spacecraft carrying a payload of a telescope, five lasers, and a clock together with ground stations (ODSN: Optical Deep Space Network) to test the optical scheme of interferometric and pulse ranging and yet give important scientific results. The scientific goals include a better measurement of the relativistic parameters, a better sensitivity in using optical Doppler tracking method for detecting gravitational waves, and measurement of many solar system parameters more precisely. The weight of this spacecraft is estimated to be about 300-350 kg with a payload of about 100-120 kg. The spacecraft is to be launched with initial period about 290 days and to pass by Venus twice to receive gravity-assistance for achieving shorter periods. With good orbit design, after about 370 days from launch, the spacecraft wil...

Space Science Reviews, 2017

Time measured by an ideal clock crucially depends on the gravitational potential and velocity of the clock according to general relativity. Technological advances in manufacturing high-precision atomic clocks have rapidly improved their accuracy and stability over the last decade that approached the level of 10 -18 . This notable achievement along with the direct sensitivity of clocks to the strength of the gravitational field make them practically important for various geodetic applications that are addressed in the present paper. Based on a fully relativistic description of the background gravitational physics, we discuss the impact of those highly-precise clocks on the realization of reference frames and time scales used in geodesy. We discuss the current definitions of basic The research of J.

viXra, 2016

Motivated by the benefits of improving our knowledge of Newton's constant G, Feldman et al have recently proposed a new measurement involving a gravitational clock launched into deep space. The clock's mechanism is supposed to be the linear oscillation of a test mass falling back and forth along the length of a hole through the center of a spherical source mass. Similar devices — ones that would have remained in orbit around Earth — were proposed about 50 years ago for the same purpose. None of these proposals were ever carried out. Further back, in 1632 Galileo proposed the thought experiment of a cannonball falling into a hole through the center of Earth. Curiously, no one has yet observed the gravity-induced radial motion of a test object through the center of a massive body. Also known as a gravity-train, not a one has yet reached its antipodal destination. From this kind of gravitational clock, humans have not yet recorded a single tick. The well known reliability of Ne...