# Motion in the universe

> Physics · Edexcel IGCSE 4PH1
> Source: https://www.owlsprep.com/study/edexcel-igcse-physics-s8-motion-in-the-universe/

This guide covers all core content for Edexcel IGCSE Physics Section 8.2-8.6: cosmic structure, gravitational field variation, orbit types, and orbital speed calculations, aligned to the 2017 4PH1 specification.

**Prerequisites:** [Weight = mg calculations (Forces and Motion S1_T02)](https://www.owlsprep.com/study/edexcel-igcse-physics-s1-force-motion-weight/); Unit conversion and standard form arithmetic skills

## Learning objectives

- Describe the hierarchical structure of the universe, Milky Way galaxy, and solar system
- Explain variations in gravitational field strength (g) across celestial bodies
- Relate gravitational force to orbital motion of moons, planets, satellites, and comets
- Compare orbit shapes and speed patterns of comets, moons, and planets
- Calculate orbital speed using v = 2πr/T, including correct unit conversions for astronomical values

## 1. Cosmic Structure and Gravitational Field Strength

The universe is a large collection of billions of galaxies. Each galaxy is a large collection of billions of stars held together by gravity. Our solar system (Sun, planets, moons, comets, asteroids) is located in the Milky Way galaxy.

**Gravitational field strength (g)** — The force per unit mass acting on an object in a gravitational field, measured in N/kg, which is numerically equal to free fall acceleration in m/s².

*Notation:* g

*Example:* g on Earth is 10 N/kg, while g on the Moon is 1.6 N/kg.

Gravitational field strength at the surface of a celestial body depends on two factors: the total mass of the body, and its radius. A larger mass or smaller surface radius leads to a higher g value. You will be given g values for other planets or moons in exam questions.

> **info**
>
> Assume g = 10 N/kg for all Earth-based calculations unless a question explicitly gives a different value.

**Worked example:** A Mars rover has a mass of 185 kg. The gravitational field strength on Mars is 3.7 N/kg. Calculate the rover's weight on Mars, using weight = mass × g.

1. Step 1: Identify given values: mass m = 185 kg, g on Mars = 3.7 N/kg
2. Step 2: Substitute values into the weight formula: W = m × g
3. $$W = 185 \times 3.7 = 684.5 N$$
4. Step 3: Round to 2 significant figures (matching the given g value): 680 N

## 2. Gravitational Force and Orbital Motion

Gravitational attraction between two bodies provides the centripetal force that keeps objects moving in stable orbits, preventing them from moving in a straight line away from the central body. This force explains all orbital motion in our solar system.

- Moons orbiting planets: gravitational pull of the planet on the moon maintains its orbit
- Planets orbiting the Sun: gravitational pull of the Sun on planets keeps them on their orbital path
- Artificial satellites orbiting Earth: Earth's gravity pulls satellites to keep them circling the planet for communication, weather, or navigation use
- Comets orbiting the Sun: the Sun's gravity pulls comets back towards the inner solar system even when they are very far away at the edge of their orbit

**Worked example:** Explain why a geostationary satellite stays in a fixed position above Earth's equator.

1. Step 1: Identify the force causing orbital motion: Earth's gravitational attraction to the satellite
2. Step 2: Link force to motion: This gravitational force acts as a centripetal force, pulling the satellite towards Earth's centre to stop it moving in a straight line away from the planet
3. Step 3: Add geostationary context: The satellite's orbital period matches Earth's 24 hour rotation, so it appears stationary relative to a fixed point on the equator

## 3. Comparing Orbits of Comets, Moons and Planets

Not all orbits are the same shape, and orbital speed varies depending on distance from the central body, due to changes in gravitational pull strength.

**Orbital eccentricity** — A measure of how much an orbit deviates from a perfect circle; higher eccentricity means a more stretched, elliptical orbit.

| Orbiting body | Orbit shape | Orbit speed pattern |
| --- | --- | --- |
| Planet | Nearly circular (very low eccentricity) | Almost constant speed, as orbital radius is almost uniform |
| Moon | Nearly circular (very low eccentricity, orbiting a planet) | Almost constant speed, similar to planets |
| Comet | Highly elliptical (very high eccentricity, stretches far from and close to the Sun) | Fastest when closest to the Sun (smaller orbital radius, stronger gravitational pull), slowest when farthest away |

> **warning**
>
> Exam questions frequently ask for orbit comparisons, so make sure you can clearly state the shape and speed differences for all three body types.

**Worked example:** A comet travels at 50 km/s when near the Sun, and 2 km/s when at the farthest point of its orbit. Explain this difference in speed.

1. Step 1: Recall comet orbit shape: Comets have highly elliptical orbits
2. Step 2: Link distance to gravitational force: When the comet is close to the Sun, the Sun's gravitational pull on it is much stronger than when it is far away
3. Step 3: Link force to speed: The stronger gravitational pull accelerates the comet, so it travels much faster at its closest approach to the Sun

## 4. Orbital Speed Calculations

You must recall the orbital speed formula for exams, as it is not provided on any formula sheet. The formula calculates the average speed of an object in a circular orbit as the circumference of the orbit divided by the time taken to complete one full orbit (orbital period).

**Orbital speed (v)** — Average speed of an object moving in a circular orbit, where r is orbital radius (m) and T is orbital period (s).

*Notation:* v = \frac{2\pi r}{T}

*Example:* A satellite orbiting Earth at radius 42,000 km with a 24 hour period has an orbital speed of ~3100 m/s.

> **tip**
>
> Always convert units first: convert km to m (× 1000) and days/hours/minutes to seconds before substituting values into the formula. Use standard form for large astronomical values to avoid arithmetic errors.

**Worked example:** The Moon orbits Earth at an average orbital radius of 384,000 km. It takes 27.3 days to complete one full orbit. Calculate the average orbital speed of the Moon in m/s, to 2 significant figures.

1. Step 1: Convert units to SI units: radius r = 384,000 km = 3.84 × 10⁸ m; period T = 27.3 days = 27.3 × 24 × 60 × 60 = 2.35872 × 10⁶ s
2. Step 2: Substitute into the orbital speed formula: v = 2πr / T
3. $$v = \frac{2 \times \pi \times 3.84 \times 10^8}{2.35872 \times 10^6} \approx 1022 m/s$$
4. Step 3: Round to 2 significant figures: 1.0 × 10³ m/s (or 1000 m/s)

**Check your understanding**

1. What is the correct unit for orbital period when using v = 2πr/T to calculate speed in m/s?

   - Hours
   - Days
   - Seconds
   - Years

   *Why:* All values must be in SI units for the speed to be calculated in m/s. Convert other time units to seconds first.

2. A planet orbits the Sun with a radius of 1.5 × 10¹¹ m, and a period of 3.15 × 10⁷ s. What is its orbital speed?

   - ~30 km/s
   - ~10 km/s
   - ~50 km/s
   - ~3 km/s

   *Why:* Calculation: v = (2 × π × 1.5e11) / 3.15e7 ≈ 30,000 m/s = 30 km/s

*Calculator:* allowed

## Common pitfalls

- **Wrong:** Forgetting to convert km to m or hours/days to seconds in orbital speed calculations.
  - Why it fails: The formula requires SI units to give speed in m/s, the unit required for exam marks. Incorrect units lead to wildly wrong answers.
  - Correct: Always convert radius to metres and time period to seconds before substituting into v = 2πr/T. Use standard form for large values to reduce errors.
- **Wrong:** Stating that comets have circular orbits, or that planets have highly elliptical orbits.
  - Why it fails: Exam questions regularly test orbit shape differences, and mixing this up loses easy marks.
  - Correct: Remember: planets/moons = nearly circular, comets = highly elliptical.
- **Wrong:** Using out-of-scope formulas like F = Gm₁m₂/r² or centripetal force equations for orbit questions.
  - Why it fails: These concepts are not part of the IGCSE specification, and using them will not gain extra marks, and may lead to mistakes.
  - Correct: Only use qualitative descriptions of gravitational force causing orbits, and the v = 2πr/T formula for calculations.
- **Wrong:** Using g = 9.81 m/s² for Earth calculations when not specified.
  - Why it fails: The exam board explicitly states you should use g = 10 N/kg for all Earth-based questions unless told otherwise.
  - Correct: Write g = 10 N/kg at the start of any weight or free fall calculation unless the question gives a different g value.
- **Wrong:** Stating that comets travel slowest when closest to the Sun.
  - Why it fails: Questions about comet speed changes are common, and reversing the relationship loses marking points.
  - Correct: Smaller orbital radius = stronger gravitational pull = higher orbital speed, especially for comets with elliptical orbits.

## Cheatsheet

| Concept | Key Facts / Formula |
| --- | --- |
| Cosmic structure | Universe → billions of galaxies; each galaxy → billions of stars; Solar System is in the Milky Way |
| g variation | Higher mass or smaller radius of a body → higher surface g; Earth g = 10 N/kg (default) |
| Gravitational force role | Causes orbits of moons, planets, artificial satellites, comets |
| Orbit shapes | Planets/moons: nearly circular; Comets: highly elliptical, fastest near Sun |
| Orbital speed formula | v = 2πr/T (must recall for exams); r in m, T in s, v in m/s |

## What's next

Now you have mastered the core content for Motion in the Universe, you are ready to progress to the remaining topics in Edexcel IGCSE Physics Astrophysics. Next, you will learn about stellar evolution, including the life cycle of stars like our Sun, and how astronomers classify stars using the Hertzsprung-Russell (HR) diagram. Following that, you will cover cosmology, including the Big Bang theory, red-shift evidence, and the evolution of the universe. Make sure you practice past paper questions focused on orbital speed calculations and orbit comparison questions to reinforce your understanding, and confirm you can recall the orbital speed formula without a prompt, as it is not provided in exams. Pay close attention to unit conversion steps to avoid losing easy marks in calculations.

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