This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Session: Dynamics of Small Solar System Bodies III

Victor J. Slabinski (USNO)

#### Abstract

The Lense‑Thirring (L‑T) effect from General Relativity predicts a small secular increase to the node right ascension for close Earth satellites. For the LAGEOS 1 satellite, the predicted node increase is 31 mas/y. There is a current effort to observationally evaluate L‑T to 1 percent accuracy through an orbit analysis of the laser‑ranged LAGEOS 1, LAGEOS 2, and LARES satellites. Uncertainty in the computed gravitational perturbations to the satellite nodes, due to parameter uncertainties, is largely eliminated by taking a linear combination of the node positions which eliminates the uncertainty due to the major terms. One then looks for the L‑T effect on this composite node.

But there remains uncertainty in the computed perturbations due to two radiation (non‑gravitational) forces: the solar radiation (SR) force and thermal thrust (Yarkovsky effects). This paper treats LAGEOS 1 perturbations. For simplicity in discussion, we treat perturbations to its node rather than perturbations to the composite node.

Uncertainty in the perturbation rates arises from ignorance of parameter values for the LAGEOS 1 exterior aluminum surface, specifically, the solar absorbtance and thermal emiRance. The LAGEOS 1 Phase B design study proposed three different sets of aluminum surface parameters without recommending a particular set. The LAGEOS 1 as-built surface parameters were not measured prior to spacecraft launch.

The possible spread in LAGEOS 1 solar absorbtance values gives a spread of ±0.42 mas/y in the SR force contribution to its node rate. This results in a ±1.3 percent uncertainty to the L‑T determination. But because of its long‑period perturbation to the eccentricity vector, evaluating the SR force parameter as a solved‑for parameter in the orbit analysis should significantly reduce the uncertainty in the corresponding node motion. The possible spread in LAGEOS 1 surface values gives a spread of ±0.16 mas/y in the thermal thrust contribution to its node rate. This represents a ±0.53 percent uncertainty in the L‑T determination which leaves little room for other error sources. Ground-based satellite brightness measurements could improve knowledge of the surface absorbtance and reduce the uncertainty from thermal thrust.

#### Notes

- Lense-Thirring
- gravitomagnetic effect
- spinning Earth:
- $\rightarrow$ frame-dragging
- $\rightarrow$ precession of $\Omega$ and $\omega$

- LAGEOS 1 & 2: linear motion of $\Omega \approx 1.8$ m/yr
- Goal: 1% measurement of L-T effect

- Other perturbing forces
- Solar radiation pressure
- requires knowledge of satellite surface material properties
- notably: aging

- requires knowledge of satellite surface material properties
- Thermal thrust
- IR from Earth
- fused silica of corner-cube reflectors is an excellent absorber of IR
- Oops

- thermal phase lag: max recoil force not at local midnight but somewhat past
- $\rightarrow \sim 3 \mathrm{pm/s^2}$ acceleration component
*along*orbit track - $\rightarrow$ also a component perpendicular to orbital plane
- affects nodal precession rate

- $\rightarrow \sim 3 \mathrm{pm/s^2}$ acceleration component

- Solar radiation pressure
- Satellite surface properties
- Corner-cube reflectors: no problem. We know fused silica.
- Aluminum frame: uh oh…
- Not measured beforeLAGEOS 1 launch!
- thermal absorptance
- thermal emittance

- Node precession from solar radiation term: ~1/4 L-T effect
- But radiation force also changes eccentricity vector, from which you can get diffuse reflection coefficient
- but not specular

- One solution: brightness measurements from the ground
- Magnitude range: 11.5-14

I believe there is no frame-dragging effect of gravity on mass, only on electromagnetic energy!

Curiously, the Lense-Thirring effect in Gravity Probe B has the same value than the geodetic effect of the Earth around the Sun.

Kinetic energy of a rotating body like Earth will increase gravity but more in the sense of classical force than classical aether!

An interesting experiment!

Understanding Gravity Probe-B experiment without math

http://www.molwick.com/en/gravitation/082-gravity-probe-b.html

http://www.molwick.com/en/gravitation/r-lense-thirring-frame-dragging.jpg