---
title: "Earth's motion, solar constant and seasons"
subject: "Energy Resources"
chapter: 2
key: "semester_6/energy_resources:earth-sun-geometry-solar-constant"
source: https://www.bctengineer.com/q/semester_6/energy_resources/earth-sun-geometry-solar-constant
site: BCT Engineering
---

# Earth's motion, solar constant and seasons

Energy Resources · Chapter 2: Solar energy

- Asked in: year not given, 5 marks
- Video: [The Earth's Sun Angle](https://www.youtube.com/watch?v=av46WpG7xsc) — MS Meteorology
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/energy_resources/earth-sun-geometry-solar-constant
- Whole chapter: https://www.bctengineer.com/md/semester_6/energy_resources/chapter-2

## Question

Explain the movement of the earth around the sun and the cause of seasons. Define solar constant, air mass, beam, diffuse and global radiation.

## Short answer

Earth's rotation causes day/night; its tilted axis (23.45°) and yearly revolution cause seasons by varying sun angle and day length. Solar constant is the extraterrestrial irradiance at mean distance, 1367 W/m². Air mass is the ratio of atmospheric path length to the vertical. Beam radiation comes directly from the sun; diffuse is scattered skylight; global is their sum.

## Answer

#### Movement of the earth
The earth has two motions: **rotation** about its own axis once in 24 hours (which causes day and night) and **revolution** around the sun in an elliptical orbit once in 365.25 days. The axis is tilted by 23.45° from the normal to the orbital plane and keeps a fixed direction in space.

The sun-earth distance varies from 1.471×10¹¹ m (about 3 January) to 1.521×10¹¹ m (about 4 July), with a mean of 1.496×10¹¹ m (1 AU).

#### Cause of seasons
Because of the fixed tilt, the angle between the sun's rays and the surface at a place changes through the year. The **declination** $\delta$ (the angle of the sun north or south of the equator) varies from +23.45° on 21 June (summer solstice) to −23.45° on 22 December, and is zero at the equinoxes (21 March, 23 September). When the northern hemisphere leans towards the sun, it has longer days and more direct rays, i.e. summer. The distance from the sun is not the cause.

Declination (Cooper): $\delta = 23.45 \sin\left[\frac{360(284+n)}{365}\right]$, where $n$ = day of the year.

#### Definitions
- **Solar constant** $G_{sc}$: the energy from the sun per unit time on a unit area perpendicular to the rays, at the mean earth-sun distance, outside the atmosphere. Value = 1367 W/m² (WRC value; recent satellite measurements give about 1361 W/m²).
- **Air mass** $m$: the ratio of the path length of the rays through the atmosphere to the path length when the sun is overhead. $m \approx 1/\cos\theta_z$ (for $\theta_z < 70°$). Air mass zero (AM0) is outside the atmosphere; AM1.5 is the standard for testing solar cells.
- **Beam (direct) radiation:** radiation that reaches the surface directly from the sun without being scattered.
- **Diffuse radiation:** radiation scattered by air molecules, dust and clouds, arriving from all directions of the sky.
- **Global (total) radiation:** the sum of beam and diffuse radiation on a surface, $G = G_b + G_d$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What causes the seasons?
   A. Change in sun-earth distance
   B. Rotation of the earth about its axis
   C. Variation of the solar constant
   D. The fixed 23.45° tilt of the earth's axis, changing the sun's ray angle through the year
   Answer: D. The distance is least in January, yet the northern hemisphere has winter; tilt is the cause. (Key point: Cause of seasons)

2. What is the declination on 21 June (summer solstice)?
   A. -23.45°
   B. 0°
   C. +23.45°
   D. +90°
   Answer: C. Declination is +23.45° at the June solstice, -23.45° on 22 December and zero at the equinoxes. (Key point: Declination)

3. The solar constant is the energy per unit time per unit area...
   A. On a horizontal surface at sea level
   B. Perpendicular to the rays, at mean earth-sun distance, outside the atmosphere
   C. At the earth's surface on a clear day
   D. Averaged over a full day at the equator
   Answer: B. Its value is 1367 W/m². (Key point: Solar constant)

4. Global radiation on a surface is...
   A. Beam plus diffuse radiation
   B. Beam radiation only
   C. Diffuse radiation only
   D. Radiation outside the atmosphere
   Answer: A. G = Gb + Gd. (Key point: Global radiation)

## Related in Energy Resources

- [Solar radiation measuring instruments](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Apyranometer-pyrheliometer-sunshine-recorder) — Energy Resources, chapter 2
- [Calorific value and air from ultimate analysis](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Adulong-calorific-value-fuel-oil) — Energy Resources, chapter 1

## Related in other subjects

- [Beam, diffuse and global radiation](https://www.bctengineer.com/question.md?key=semester_7%2Fenergy_environment_and_society%3Abeam-diffuse-global-radiation) — Energy Environment and Society, chapter 3
- [Solar constant, insolation, irradiance, peak sun](https://www.bctengineer.com/question.md?key=semester_7%2Fenergy_environment_and_society%3Asolar-constant-insolation-definitions) — Energy Environment and Society, chapter 3, asked 3×
- [Solar panel and battery for a house (6 h sun)](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Apv-sizing-12v-6h-sun) — Power Plant Design, chapter 1, asked 2×
- [Solar panel and battery for a house (7 h sun)](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Apv-sizing-12v-7h-sun) — Power Plant Design, chapter 1, asked 2×