Integrated Laser Doppler Method for Measuring Planetary Gravity Fields

Abstract

Four main approaches have been applied to, or studied extensively for use in, high-resolution determination of the global gravity fields of the Earth, other planets, or the Moon. These approaches are the following: laser or microwave tracking of spacecraft orbiting the Earth; microwave tracking from the Earth of spacecraft orbiting other planets or the Moon; satellite-to-satellite microwave tracking; and gravity gradiometry from an orbiting spacecraft. This paper will discuss another possibility which has been studied much less extensively. It is the use of integrated laser Doppler measurements between two spacecraft in essentially the same nearly polar orbit. In this case, the shot noise in the measurement system can be extremely low, even for 5 cm diameter transmit and receive apertures and 1 milliwatt of laser power. For the highest accuracy, it is assumed that a Disturbance Reduction System would be used to strongly reduce the disturbing forces on a freely floating and carefully shielded test mass inside each spacecraft. As one example, we take 50 km spacecraft separation and a spurious acceleration level of 5 × 10⁻¹⁰ m/s²/Hz^0.5 from 0.005 to 0.1 Hz. The achievable accuracy with laser Doppler measurements is then expected to be 10⁻⁵ Eötvös/Hz^0.5 in this frequency range for the difference of the line-of-sight test mass accelerations divided by the spacecraft separation. The error budget includes an allowance for laser frequency noise ranging from 4 × 10⁻¹²/Hz^0.5 at 0.005 Hz to 1 × 10⁻¹⁴/Hz^0.5 at 0.1 Hz. High stability for the laser in each spacecraft would be achieved by tightly locking the laser wavelength to the length of an isolated and temperature-stabilized Fabry-Perot interferometer. For a spacecraft altitude of 200 km, the expected spatial resolution for mapping the Earth’s gravity field is 50 km. A second example has 1000 km spacecraft separation and 600 to 700 km altitude. The objective for such a mission would be to measure time variations in the low degree part of the Earth’s gravity field. For the other inner planets and the Moon, a considerably simple approach would be required. In this case, Disturbance Reduction Systems would not be included, the laser frequency stability would be somewhat lower, and perhaps only one spacecraft would have a laser.