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The Webfooted Astronomer - March 2002


Apolo? Oh No!

By Greg Donohue

RECENTLY, headlines across the country blazed with the news: ìApolo, Oh No!î as Seattle speed skating hero Apolo Ohno took silver instead of gold in the 1,000 meter short track, the victim of a sprawling crash in the last lap. Dr. Tom Murphy, our speaker for the February meeting, discussed APOLLO as well. But was his talk about the speed skater Apolo? Oh, no! And he wasnít talking about the program of manned Moon landings either.

Instead, this APOLLO stands for Apache Point Observatory Lunar Laser-ranging Operation. (As Tom puts it, ìHouston, we have an acronym!î) Tom got his Ph.D. from Caltech. He has come to the UW as a postdoctoral scholar to work on the APOLLO project, which will test the Strong Equivalence Principle (SEP) that underpins Einsteinís theory of General Relativity.

Simply put, gravitational mass is that property of an object that causes it to attract other massive objects. An objectís inertial mass is its resistance to changes in motion. There is no a priori reason we know of why a given object should have equivalent quantities of both gravitational and inertial mass. But General Relativity grew out of positing that all forms of mass and energy have equivalent quantities of gravitational and inertial mass.

APOLLO aims for the most sensitive test of SEP to date by, in effect, ìweighingî gravity. This will be accomplished by bouncing a laser beam off retro-reflectors on the Moon to determine the Earth-Moon distance to unprecedented millimeter accuracy.

How does knowing the Earth-Moon distance to such precision test the Equivalence Principle? First, recall that mass can be converted to energy (E=mc2). The reverse is also true: energy is equivalent to an appropriate amount of mass (m=E/c2). Using this formula, the energy stored in the Earthís gravitational field equates to a mass equivalent to 4.6x10-10 of the Earthís total mass. If SEP holds true, then this gravitational self-energy should have equivalent quantities of gravitational and inertial mass. To put it another way, the energy of its gravitational field makes the Earth ìweighî more, and also makes it more resistant to changes in motion (inertia).

Now assume that the Earthís gravitational self-energy does not obey SEP. That is, the quantity of gravitational mass associated with the energy of our planetís gravitational field differs from the inertial mass associated with that same field. How the distance between the Earth and Moon is affected by such a violation of SEP depends on how much the gravitational and inertial masses differ. But we can bound the problem by looking at the two most extreme possibilities: 1) The energy has the expected amount of gravitational mass, but no component of inertial mass; 2) the opposite condition, with the expected amount of inertial mass, but lacking any gravitational mass constituent.

In the first case, the extra gravitational mass would result in a slightly stronger attraction between the Earth and Sun. In the absence of any additional inertial mass, this would cause a net increase in the Earthís acceleration toward the Sun. Due to its much smaller mass, the Moonís gravitational field energy produces no significant extra gravitational or inertial mass, so our natural satellite would not share in this additional acceleration. The Earth would then feel an extra pull toward the Sun while the Moon would not, and this would manifest itself as a displacement of the Moonís orbit away from the Sun by about 13 meters.

In the second case, the opposite would be true, with the Moonís orbit being displaced 13 meters towards the Sun. If the discrepancy between the inertial and gravitational masses lies somewhere between these two extreme cases, then the displacement in the Earth-Moon distance would be correspondingly smaller.

Current LLR (Lunar Laser Ranging) can determine the Earth-Moon distance to within 2-3 cm, so we already know that SEP holds down to a level of about 5 parts in 104. APOLLO expects to push that down another order of magnitude, giving us the ability to detect SEP violations as small as a few parts in 105.

Each 115mJ, 120ps pulse of APOLLOís Nd:YAG 532nm laser contains about 1018 photons. Even if perfectly collimated at the surface, this beam will be spread to at least 1 arc second by the Earthís atmosphere. Consequently, the beam will be about 2 km wide upon reaching the Moon. Effects from the retro-reflectors will result in the beam being about 18 km wide when it returns to Apache Point. Due to this beam spreading and other factors, such as telescope and CCD inefficiencies, APOLLO expects to only capture about 5-10 of the original photons from each pulse. But that is a vast improvement over other LLRís, which experience something like a return of 1 photon per every 100 pulses.

The returning laser beam appears to be about 19th magnitude. So how does one ìseeî this weak signal against the -13 magnitude glare of the Moon? A combination of spatial, wavelength, and temporal filtering of the light reduces the Moonís effective brightness down to magnitude 23. The result? The laser appears about 40 times brighter than the Moon. APOLLO is really seeking to measure the distance between the Moonís center of mass and the Earthís center of mass. Many factors resulting in both real and apparent changes to this distance must be taken into account if the precise distance is to be determined. Changes to local loading factors such as ground water levels, atmospheric pressure, and ocean water piling up on coastlines due to tides, can deform the Earthís crust by many millimeters. Tidal forces between the Earth and Moon changes the local level of the Earthís crust by more than a foot every 12 hours. Additionally, changes in atmospheric pressure change the time it takes the laser pulses to traverse Earthís atmosphere.

Accurate measurement, modeling, or both must account for all of these effects and more. APOLLO will employ a gravimeter at the site to help measure some of the effects that are only modeled in other LLR projects. Itís important to note that any change in the Earth-Moon distance due to SEP violation will have a period of 29.5 days (the lunar synodic period). The other effects are either random, or have periods that differ from 29.5 days, making them easier to recognize and eliminate.

But doesnít all this seem like a lot of hard work just to get a little more accuracy on something we already know holds to a few parts in 10,000? Well, we already know that General Relativity cannot be the ultimate answer, since it breaks down in the extreme conditions of black holes and the instant of the big bang. Other competing models of physics (e.g., string theory) predict violations of SEP to one degree or another. Placing bounds on SEP violation may thus help discriminate between these models, and ultimately point towards that elusive ìtheory of everything.î

What if this program ultimately finds a discrepancy between inertial and gravitational mass? Tom jokingly says that maybe the new law might be named ìMurphyís Law,î and for once his last name would be associated with something positive! But Iím thinking maybe there is another possibility, with headlines around the globe screaming: ìAPOLLO: Oh No! Einstein was Wrong!î

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