Question 64 - Problems - Chapter 1¶

Problem:¶

The Global Positioning System (GPS) uszd by navigators of ships and aircraftsexploids radiosignals from artificial satellites to determine the position of the ship or the aircraft. Portable GPS units for use on yachts incorporate a radioreciever and a computer; they give the position within +/- 15m.

Question:¶

To what error in latitude angle this corresponds to th nord-south error of 15m along the surface of the earth?

Solution:¶

We assume the circumference of the earth is 40,000 km

This corresponds to 360°

1m thus corresponds to: $ \frac{360°}{40*{10}^6 \;m} $

In [1]:

import numpy as np
from astropy import units as u
from astropy.coordinates import Angle
error = 360 * 15 / 40e6;
fout = Angle(error, u.degree)
print(f'The error is: {fout.dms.d} deg. {fout.dms.m} min. {fout.dms.s} seconds')

The error is: 0.0 deg. 0.0 min. 0.486 seconds

This corresponds at more or less a half arcsecond.

سُوۡرَةُ حٰمٓ السجدة / فُصّلَت
ثُمَّ اسْتَوَىٰ إِلَى السَّمَاءِ وَهِيَ دُخَانٌ فَقَالَ لَهَا وَلِلْأَرْضِ ائْتِيَا طَوْعًا أَوْ كَرْهًا قَالَتَا أَتَيْنَا طَائِعِينَ ﴿١١
فَقَضَاهُنَّ سَبْعَ سَمَاوَاتٍ فِي يَوْمَيْنِ وَأَوْحَىٰ فِي كُلِّ سَمَاءٍ أَمْرَهَا ۚ وَزَيَّنَّا السَّمَاءَ الدُّنْيَا بِمَصَابِيحَ وَحِفْظًا ۚ ذَٰلِكَ تَقْدِيرُ الْعَزِيزِ الْعَلِيمِ ﴿١٢

Surah Fussilat: Thereafter turned He to the heaven and it was as smoke, and said Unto it and Unto the earth: come ye twain, willingly or loth. They said: we come willingly. (11) Then He decreed them as seven heavens in two days, and revealed Unto each heaven the command thereof; and We bedecked the nether heaven with lamps and placed therein a guard. That is the ordinance of the Mighty, the Knower. (12)

De hemelen en aarde (waren) een samenhangende massa. Wij hebben ze toen van elkaar gescheiden… Wij hebben de hemel tot een beschermend dak gemaakt … en de dag en de nacht, de zon en de maan geschapen. (Koran 41 11:12)