Abstract

A method for the high resolution spectroscopy of rotating planets is discussed which in principle (1) uses all the light from the planet, (2) is not limited in its resolution by the rotation of the planet, (3) can produce spectra in which the only sharp lines present must be of planetary origin, (4) retains spatial resolution in latitude, and (5) uses only conventional coudé spectrograph equipment. Although it is not possible to take full advantage of all these gains with presently available gratings, a significant improvement over present techniques is still possible.

© 1971 Optical Society of America

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References

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  1. J. Connes, P. Connes, J. P. Maillard, Near Infrared Spectra of Venus, Mars, Jupiter, and Saturn (Centre National de la Recherche Scientifique, Paris, 1969).

Connes, J.

J. Connes, P. Connes, J. P. Maillard, Near Infrared Spectra of Venus, Mars, Jupiter, and Saturn (Centre National de la Recherche Scientifique, Paris, 1969).

Connes, P.

J. Connes, P. Connes, J. P. Maillard, Near Infrared Spectra of Venus, Mars, Jupiter, and Saturn (Centre National de la Recherche Scientifique, Paris, 1969).

Maillard, J. P.

J. Connes, P. Connes, J. P. Maillard, Near Infrared Spectra of Venus, Mars, Jupiter, and Saturn (Centre National de la Recherche Scientifique, Paris, 1969).

Other (1)

J. Connes, P. Connes, J. P. Maillard, Near Infrared Spectra of Venus, Mars, Jupiter, and Saturn (Centre National de la Recherche Scientifique, Paris, 1969).

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Figures (4)

Fig. 1
Fig. 1

Principle of matching dispersion to rotation. In the absence of a radial velocity difference, two points, A, B on the surface of a planet are imaged onto A′, B′ in monochromatic radiation by a suitable image forming and dispersing device (e.g., telescope plus spectrograph). A radial velocity difference v causes a doppler wavelength shift Δλ = v/c, resulting in an image of B at B″, which can coincide with A′ if the parameters of the telescope and spectrograph are correctly chosen. Under these conditions one can obtain a high resolution spectrum without using an entrance slit.

Fig. 2
Fig. 2

The relation between the angles of incidence (i) and diffraction (θ) and the angles γ and α discussed in the text.

Fig. 3
Fig. 3

Angles of incidence (i) as a function of γ and a = (2fcoll/ftel) (v/), required to give a match of dispersion and rotation.

Fig. 4
Fig. 4

The reflected Fraunhofer spectrum from Jupiter with the orientation of the rotation axis changed through 180° between the two spectra. The wavelength range is 4730–4775 Å.

Tables (1)

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Table I Planetary Equatorial Rotational Velocities (v), Opposition Semidiameters (ϕ), Limb-to-Limb Doppler Shifts (Δλ), and Required Angles of Incidence (i) for Matching Rotation to Dispersion with the McDonald Observatory 272-cm Coudé Spectrograph

Equations (9)

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ϕ s ( λ ) f tel = ( λ v / c ) [ 1 / K ( λ ) ]
K ( λ ) f tel s ( λ ) = λ v / c ϕ .
d ( sin i + sin θ ) = n λ ,
2 d cos γ sin α = n λ ,
s ( λ ) = f cam f coll d θ d i = f cam f coll cos i cos θ = f cam f coll cotan α - tan γ cotan α + tan γ ,
K ( λ ) = 1 f cam d λ d θ = d cos θ n f cam = λ 2 f cam ( cotan α + tan γ ) .
( λ f tel / 2 f coll ) ( cotan α - tan γ ) = λ v / c ϕ ,
cotan α = tan γ + [ 2 ( f coll / f tel ) ] ( v / c ϕ ) .
i = α + γ , cotan α = tan γ + a ,

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