Q000 - Physics For Engineers And Scientists - Solutions

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Question 67 - Problems - Chapter 1

Problem:

In one astronomical year (or tropical year) of 365.24 days, the Earth moves once around the Sun. That is, it moves 360° along its orbit and returns to the same point of its orbit.

Question:

a) How far around the sun, in degrees, does the earth move in one calendar year (of 365 days)?

b) How far dous the Earth move in 4 consecutive years (one of which is a leap year of 366 days)?

Solution:

On one day the Earth travels $\frac{360°}{365\ldotp 24\;\textrm{days}}\;$

So on a calendar year the Earth travels $\frac{360° * 365}{365\ldotp 24\;\textrm{days}}\;$

On 4 consecutive years (one of which is a leap year)$\frac{360° * (3*365 + 366)}{365\ldotp 24\;\textrm{days}}\;$

In [1]:
import numpy as np
from astropy import units as u
from astropy.coordinates import Angle
angle_day = Angle((360  / 365.24),u.degree)
angle_year = angle_day * 365
angle_4_year = angle_day * (3*365 + 366 )
print(f'One day corresponds with: {angle_day.dms.d:.0f}° {angle_day.dms.m:.0f}\' {angle_day.dms.s:.2f}\"')
print(f'One year corresponds with: {angle_year.dms.d:.0f}° {angle_year.dms.m:.0f}\' {angle_year.dms.s:.2f}\"')
print(f'One day corresponds with: {angle_4_year.dms.d:.0f}° {angle_4_year.dms.m:.0f}\' {angle_4_year.dms.s:.2f}\"')
One day corresponds with: 0° 59' 8.35"
One year corresponds with: 359° 45' 48.40"
One day corresponds with: 1440° 2' 21.93"

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)


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