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)$\frac{360° * (3*365 + 366)}{365\ldotp 24\;\textrm{days}}\;$

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"