Никола 2019, 28 септември · лист a — Задача 7. Antennae GMRT
28 септември 2019г.
Условие
A table with coordinates of the GMRT antennae as relative positions from the central antenna A14 is given below. The latitude and longitude of A14 are , .
7.1. Prepare the map of the GMRT antennae system. You need to mark the central square on the map (the 1 km × 1 km area, which you saw during your GMRT visit), mark antenna at the origin and plot all the antennae outside the central square. Write down the antenna number near its location on the graph paper.
Parallel beams of radio-waves come from distant objects and falls on the GMRT antenna. The signals will reach different antennas at slightly different times depending on the inclination of the source with respect to the Antenna. Let us assume that the four antennas listed below are observing Sun at noon 23 September: A1, A10, A14, A30.
7.2. Calculate the delay in signal arrival between A1 and the Antenna farthest from A1, assuming a flat Earth.
7.3. Assuming now the Earth is not flat, calculate the additional term in time lag due to curvature of the Earth.
| Number of Antenna / Номер антенны | x (to the East) (m) / (на восток) (м) | y (to the North) (m) / (на север) (м) | z (to zenith) (m) / (в зенит) (м) |
|---|---|---|---|
| A01 | -11245.6 | 9405.97 | -802.858 |
| A02 | -8103.19 | 8241.44 | -711.116 |
| A03 | -7039.01 | 5340.29 | -411.950 |
| A04 | 12073.2 | 4791.68 | -389.911 |
| A05 | 10199.8 | 3529.75 | -324.311 |
| A06 | 7780.52 | 3071.49 | -266.059 |
| A07 | -5199.93 | 3054.46 | -242.446 |
| A08 | 4575.99 | 2047.70 | -203.543 |
| A09 | -3099.40 | 1496.91 | -90.1932 |
| A10 | 2814.54 | 1012.49 | -73.9663 |
| A11 | -1591.91 | 625.657 | -15.1934 |
| A12 | -565.940 | 132.944 | -9.99081 |
| A13 | -372.720 | 142.908 | -7.13641 |
| A14 | 0.00000 | 0.00000 | 0.00000 |
| A15 | 67.8200 | -257.968 | 22.0312 |
| A16 | -31.4400 | -230.489 | 24.4676 |
| A17 | 326.430 | -39.7862 | 32.7314 |
| A18 | 687.870 | -18.0767 | 37.1877 |
| A19 | 280.670 | -419.343 | 38.2252 |
| A20 | 41.9400 | -156.320 | 40.3858 |
| A21 | -164.860 | -615.653 | 51.1638 |
| A22 | 174.850 | -666.922 | 53.1313 |
| A23 | -603.940 | -333.732 | 56.0502 |
| A24 | -474.670 | -658.490 | 70.3163 |
| A25 | -639.500 | -1171.08 | 119.326 |
| A26 | 633.920 | -2948.73 | 258.251 |
| A27 | -367.080 | -4503.71 | 371.735 |
| A28 | 333.120 | -6742.06 | 581.014 |
| A29 | 947.470 | -9458.39 | 782.898 |
| A30 | -369.050 | -14097.4 | 1202.39 |
Решение
Внимание: Непълно решение
В архива липсва файл с решения
Оригинал в Архива: 28092019a.pdf