We present the first example of binary microlensing for which the parameter measurements can be verified (or contradicted) by future Doppler observations. This test is made possible by a confluence of two relatively unusual circumstances. First, the binary lens is bright enough (I = 15.6) to permit Doppler measurements. Second, we measure not only the usual seven binary-lens parameters, but also the "microlens parallax" (which yields the binary mass) and two components of the instantaneous orbital velocity. Thus, we measure, effectively, six "Kepler+1" parameters (two instantaneous positions, two instantaneous velocities, the binary total mass, and the mass ratio). Since Doppler observations of the brighter binary component determine five Kepler parameters (period, velocity amplitude, eccentricity, phase, and position of periapsis), while the same spectroscopy yields the mass of the primary, the combined Doppler + microlensing observations would be overconstrained by 6 + (5 + 1) − (7 + 1) = 4 degrees of freedom. This makes possible an extremely strong test of the microlensing solution. We also introduce a uniform microlensing notation for single and binary lenses, define conventions, summarize all known microlensing degeneracies, and extend a set of parameters to describe full Keplerian motion of the binary lenses.

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Parallax is the most fundamental technique for measuring distances to astronomical objects. Although terrestrial parallax was pioneered over 2000 years ago by Hipparchus (ca. 140 B.C.E.) to measure the distance to the L147

We describe the development of a low cost, low resolution (R ∼ 350), high throughput, long slit spectrograph covering visible (4000-8000Å) wavelengths. The spectrograph has been developed for fully robotic operation with the Liverpool Telescope (La Palma). The primary aim is to provide rapid spectral classification of faint (V ∼ 20) transient objects detected by projects such as Gaia, iPTF (intermediate Palomar Transient Factory), LOFAR, and a variety of high energy satellites. The design employs a volume phase holographic (VPH) transmission grating as the dispersive element combined with a prism pair (grism) in a linear optical path. One of two peak spectral sensitivities are selectable by rotating the grism. The VPH and prism combination and entrance slit are deployable, and when removed from the beam allow the collimator/camera pair to re-image the target field onto the detector. This mode of operation provides automatic acquisition of the target onto the slit prior to spectrographic observation through World Coordinate System fitting. The selection and characterisation of optical components to maximise photon throughput is described together with performance predictions.

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