Belgacem Jaroux

Energy-Optimal Solution to the Lambert Problem

T HE Lambert problem offers a substantial way of determining theminimumenergy transfer between twoknownpoints along a Keplerian orbit. Most of the analysis for this problem relies on a geometrical approach, since the problem’s definition is attuned to the geometry [1,2]. The main idea of the Lambert minimum-energy problem starts by defining the length between two position vectors. Consequently, it states geometrically that the semimajor axis of the minimum-energy orbit is related to the chord length and length of the position vectors [1]. Currently, there is no other analytical approach besides the geometric analysis for solving the problem. In this note, however, an alternative analytical method for solving the Lambert minimum-energy problem is proposed. Theminimum velocity at the initial position is obtained by applying a constrained optimization tool. As the initial position vector in the problem is fixed, it is apparent that determining theminimum initial velocity is the same as obtaining theminimum-energy orbit. Using the alternative technique could give us new insight into solving various orbital problems.

Ground testing and flight demonstration of charge management of insulated test masses using UV-LED electron photoemission

The UV LED mission demonstrates the precise control of the potential of electrically isolated test masses that is essential for the operation of space accelerometers and drag free sensors. Accelerometers and drag free sensors were and remain at the core of geodesy, aeronomy, and precision navigation missions as well as gravitational science experiments and gravitational wave observatories. Charge management using photoelectrons generated by the 254 nm UV line of Hg was first demonstrated on Gravity Probe B and is presently part of the LISA Pathfinder technology demonstration. The UV LED mission and prior ground testing demonstrates that AlGaN UV LEDs operating at 255 nm are superior to Mercury vapor lamps because of their smaller size, lower draw, higher dynamic range, and higher control authority. We show flight data from a small satellite mission on a Saudi Satellite that demonstrates AC charge control (UV LEDs and bias are AC modulated with adjustable relative phase) between a spherical test mass and its housing. The result of the mission is to bring the UV LED device Technology Readiness Level (TRL) to TRL 9 and the charge management system to TRL 7. We demonstrate the ability to control the test mass potential on an 89 mm diameter spherical test mass over a 20 mm gap in a drag free system configuration. The test mass potential was measured with an ultra high impedance contact probe. Finally, the key electrical and optical characteristics of the UV LEDs showed less than 7.5 percent change in performance after 12 months in orbit.

mSTAR: Testing special relativity in space using high performance optical frequency references

The proposed space mission mini Space-Time Asymmetry Research (mSTAR) aims at a test of special relativity by performing a clock-clock comparison experiment in a low-Earth orbit. Using clocks with instabilies at or below the 1·10-15 level at orbit time, the Kennedy-Thorndike coefficient will be measured with an up to two orders of magnitude higher accuracy than the current limit set by ground-based experiments. In the current baseline design, mSTAR utilizes an optical absolute frequency reference based on molecular iodine and a length-reference based on a high-finesse optical cavity. Current efforts aim at a space compatible design of the two clocks and improving the long-term stability of the cavity reference. In an ongoing Phase A study, the feasibility of accommodating the experiment on a SaudiSat 4 bus is investigated.

mSTAR: Testing Lorentz invariance in a low Earth orbit with high performance optical frequency standards

fundamental physics test, Kennedy-Thorndike, clocks, ultra-stable cavities, iodine spectroscopy, space instrumentation