Gravitational field obtained from orbital determination of explorers
On the Earth, we can measure gravity at various points with a gravity meter. For the Moon or other planets, we estimate gravitational fields based on perturbation to orbits of explorers that circulate celestial bodies. Left in Fig. 3 shows common and conventional measurement methods for gravitational field. Radio waves, such as microwaves transmitted from parabola antenna on the ground control station, are returned to the Earth via transponders on the explorer. The distance between the explorer and the ground station is given by its lapsed time, while relative velocity in the line-of-sight direction is given by the Doppler effect of returned radio frequency. This is called two-way ranging and ranging rate (RARR) measurement. With measurement at various points in orbit, we can calculate the accurate orbit and, then, orbital perturbation caused by the gravity anomaly.
We cannot, however, measure orbit directly when explorers are on the reverse side of celestial bodies because microwave transmission cannot reach there. Also, when explorers are on the rim side of celestial bodies, sensitivity becomes poor since the perturbation direction caused by gravity crosses the line-of-sight. Accordingly, measurement error increases. Since the period of lunar rotation is the same as that of the lunar revolution around the Earth, the near and far sides of the Moon are always fixed to the Earth and, thus, we cannot directly measure the reverse side. The gravitational field is therefore estimated by the constraint called Kaula’s law based on perturbation accumulated in orbit when explorers return to the near side. Look at Fig. 2 again. You can see an unnatural distribution of gravitational field expressed by vertical or lateral chains in the lunar far side. Since measurement accuracy is poor there, we cannot know accurately to what degree the distribution is real. Meanwhile, gravitational-field accuracy on the obverse side can be gradually improved as data increase with more explorer flights. Individual observation accuracy, however, depends on the accuracy of the time system. Therefore, as long as we use the same measurement method, a drastic improvement in accuracy is not expected. In this context, the SELENE mission using micro satellites comes up.
SELENE’s micro satellite mission: RSAT and VRAD
SELENE is Japan’s first large-scale science explorer to elucidate the origin and evolution of the Moon by global observations made by 15 observation missions (Fig. 1). SELENE is now under development to launch in 2007 by H-IIA launcher. SELENE will carry two micro satellites, “Relay Satellite (Rstar)” and “VRAD Satellite (Vstar),” which will be released from the main satellite. These satellites are designed to measure the lunar gravitational field.
Their missions are as follows:
(1) Four-way Doppler measurement by RSAT
“Relay Satellite Transponder (RSAT)” is a relay system which will be onboard the Rstar and main satellites, and will be used for four-way Doppler measurement (center in Fig. 3). When the SELENE main satellite flies on the lunar far side, radio waves transmitted from the 64m antenna at JAXA’s Usuda station are relayed via <1>→<2>→<3>→<4> as indicated in the Figure. We then measure the Doppler effect accumulated in the received radio frequency returned to the Usuda station. This is called the four-way Doppler measurement. Since the orbit of Rstar itself is measured by two-way RARR, this identifies the relative orbit of the main satellite against Rstar. In this way, the orbit on the lunar far side can be measured directly for the first time in the world. In the past, the four-way relay was conducted only for communications between geosynchronous satellites and earth orbiting satellites. It is RSAT’s excellent ability that it can relay the radio, the frequencies of which vary to each other for the Doppler effect, with the low power system. The available time to conduct the four-way measurement will be limited by various conditions, such as interactive sight on communication route and saving of power. Nonetheless, our provisional estimate shows that we can obtain better data up to the 70th degree of the gravitational field expansion coefficient than previous gravitational-field models without using Kaula’s law.
For the lunar topography, dichotomization (different features of near and far sides) is known. For example, plane terrains called seas widely exist only on the obverse side. We have no decisive evidence in previous gravitational-field data, however, that the absence of prominent mascon shows actual distribution in the reverse side. It is expected that RAST will look into the dichotomization of the gravitational field in detail and clarify it for the first time. As a result, we will be able to clear up various lunar issues including the interaction of its rotation period and crust thickness, and the relation between physical phenomena in the Moon’s early revolutionary phase and its internal structure.
(2) Multi-frequency differential VLBI observation by VRAD
“VLBI Radio Source (VRAD)” is radio sources installed on Rstar and Vstar to be used for multi-frequency differential VLBI (Very Long Baseline Interferometry) observation (right in Fig. 3). VLBI was originally a method to conduct precise measurement of position of telescopes or detailed structure of radio stars by simultaneously receiving radio signals emitted from radio stars such as quasars or maser sources at multiple radio telescopes located far away from each other. Today, this method is also used for trajectory determination of explorers such as NOZOMI and HAYABUSA. The differential VLBI method, which alternately observes radio signals from Rstar and Vstar to correct errors by the Earth’s ionosphere, is introduced in SELENE to improve accuracy.
The VRAD mission’s other ingenuity is a multi-frequency phase-delay VLBI, which uses three frequencies in S band (2GHz) and one frequency in X band (8GHz). The phase-delay VLBI directly identifies geometric delay time from phase differences of radios. With this new technique, high-accuracy estimation with low power becomes possible compared to the conventional method, group-delay VLBI method, which was used in the past explorers and is based on inclination of fringe phase against observed frequency. However, if the phase-delay amount exceeds 2π, the solution is underspecified. In this case, we have to use multiple radio signals with different frequencies. By using low-frequency signals synthesized from multiple frequencies, it becomes possible for us to perform vague to precise positioning. With VRAD, we can measure the orbit around the Moon at an accuracy of 20cm, which is two orders of magnitude better than with two-way RARR.
Since active altitude and attitude control will not be employed for the two micro satellites carrying VRAD, we can observe the long-term components of the gravity anomaly in particular. Compared to previous gravitational-field models, accuracy improvement by 1 to 1.5 orders of magnitude is expected up to 10th degree of the gravity-field expansion coefficient. In addition, since VLBI has sensitivity for the plane crossing the sight line, observation accuracy is improved for the rim side of the Moon where the huge crater, South Pole-Aitken Basin, exists. By combining RSAT data, a detailed gravitational-field map of the entire Moon will be created.