2016年IOAA理论第5题-穿过GMRT波束

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英文题目

(T5) GMRT beam transit

Giant Metrewave Radio Telescope (GMRT), one of the world's largest radio telescopes at metre wavelengths, is located in western India (latitude: 19°6′ N, longitude: 74°3′ E). GMRT consists of 30 dish antennas, each with a diameter of 45.0 m. A single dish of GMRT was held fixed with its axis pointing at a zenith angle of 39°42′ along the northern meridian such that a radio point source would pass along a diameter of the beam, when it is transiting the meridian.

What is the duration 𝑇_transit for which this source would be within the FWHM (full width at half maximum) of the beam of a single GMRT dish observing at 200 MHz?

Hint: The FWHM size of the beam of a radio dish operating at a given frequency corresponds to the angular resolution of the dish. Assume uniform illumination.

中文翻译

(T5) 穿越GMRT波束

巨米波射电望远镜（GMRT）位于印度西部（北纬19°6′，东经74°3′），是世界上最大的米波射电望远镜之一。GMRT由30个望远镜组成，每个望远镜的直径为$$45.0\rm m$$。GMRT的单个望远镜固定在其轴上，轴线指向天顶距39°42′的北子午线，这样当点状无线源通过子午线时，它将沿着波束的直径通过。

在$$200\rm {MHz}$$下，单个GMRT望远镜能观察到的半峰全宽范围内，该信号源的渡越持续时间$$T_{\rm transit}$$是多少？

提示：在给定频率下工作的无线电望远镜波束的半峰全宽与望远镜的角分辨率有关。假设均匀照明。