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Here is the ultimate, examiner-level Obsidian Markdown cheat sheet for 9702 A-Level Physics: Gravitational Fields.

Copy and paste this directly into your Obsidian vault. It is strictly structured around the 2025–2027 syllabus, packed with direct insights from the examiner reports, mark schemes, and common “fatal errors” to ensure maximum marks.

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🪐 The Holy Grail: 9702 A-Level Gravitational Fields

Overview

Gravitational Fields is a highly mechanical topic. Marks are heavily skewed towards precise definitions, mathematical derivations, and avoiding classic algebraic pitfalls (like forgetting to square a radius or confusing potential with potential energy).

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13.1 Gravitational Field

1. The Gravitational Field Concept

Syllabus: Understand that a gravitational field is an example of a field of force and define gravitational field as force per unit mass.

Formal Definition: Gravitational Field Strength ( $g$)

Gravitational field strength at a point is defined as the gravitational force exerted per unit mass on a small object placed at that point.

Examiner Catching Point

• DO NOT say “force on a unit mass” or “force on 1kg”. You must indicate the ratio by using the word “per” (or “force divided by mass”).
• DO NOT use units in definitions (e.g., “force per kg” scores 0).
• Field vs. Field Strength: The syllabus defines the field as a region of space where a mass experiences a force. The field strength ($g$) is the specific vector quantity ($F/m$).

2. Gravitational Field Lines

Syllabus: Represent a gravitational field by means of field lines.

• Field lines show the direction of the gravitational force acting on a (test) mass placed at that point.
• Around a point mass / uniform sphere: Lines must be strictly radial and pointing inwards towards the centre of mass.

Common Drawing Errors (Examiner Reports)

• Carelessly drawn lines that do not converge exactly at the centre of the sphere.
• Drawing concentric circles (these are equipotential lines, not field lines, and will lose you marks!).
• Forgetting to draw the arrows pointing towards the mass.

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13.2 Gravitational Force Between Point Masses

1. Uniform Spheres as Point Masses

Syllabus: Understand that, for a point outside a uniform sphere, the mass of the sphere may be considered to be a point mass at its centre.

• This is the core justification for applying Newton’s Law of Gravitation to planets and stars.

2. Newton’s Law of Gravitation

Syllabus: Recall and use Newton’s law of gravitation $F=G{m}_1{m}_2/r^2$

Formal Definition

The gravitational force of attraction between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation.

Fatal Omissions

You will lose marks if you forget to explicitly state the condition that this applies to point masses. Also, avoid the word “distance” without context; use “separation”.

3. Circular Orbits & Centripetal Acceleration

Syllabus: Analyse circular orbits in gravitational fields by relating the gravitational force to the centripetal acceleration it causes.

This is the most frequently tested derivation in the topic.

Golden Phrasing (Memorize This)

“The gravitational force provides the centripetal force.”

What NOT to say (Examiner Reports)

• “Gravitational force is equal and opposite to centripetal force” (This implies equilibrium, which is false—the object is accelerating!).
• “Gravitational force balances centripetal force” (Again, implies zero resultant force).
• Just writing $F_g=F_c$ without the explanatory text will often cost you the B1 (explanation) mark in “Explain your working” derivations.

Standard Derivation:

1. Stating the principle: “Gravitational force provides the centripetal force.”
2. $G\frac{Mm}{r^2}=\frac{m{v}^2}{r}$ OR $G\frac{Mm}{r^2}=mr{\omega }^2$
3. Use $\omega =\frac{2\pi }{T}$ or $v=\frac{2\pi r}{T}$ to link to time period $T$.
4. Arrive at Kepler’s Third Law: $T^2=(\frac{4{\pi }^2}{GM})r^3$

4. Geostationary Orbits

Syllabus: Understand that a satellite in a geostationary orbit remains at the same point above the Earth’s surface…

Required Conditions for Geostationary Orbit (B-marks)

1. Equatorial orbit (orbits directly above the Equator).
2. Period is exactly 24 hours.
3. Orbits from West to East (same direction as Earth’s rotation).

Calculation Pitfall

If asked to find the height of a geostationary satellite above the Earth’s surface, first calculate the orbital radius $r$ using the formulas above. Then, subtract the radius of the Earth ($h=r-R_E$).

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13.3 Gravitational Field of a Point Mass

1. Deriving $g$

Syllabus: Derive, from Newton’s law… the equation $g=GM/r^2$

1. Start with $F=\frac{GMm}{r^2}$
2. State definition of $g$: $g=\frac{F}{m}$
3. Substitute $F$: $g=\frac{GMm/r^2}{m}\Rightarrow g=\frac{GM}{r^2}$

2. Calculating $g$

Syllabus: Recall and use $g=GM/r^2$

Math Errors to Avoid

• Unit Conversions: Always convert km to m ($10^3$) before squaring.
• Inside vs Outside: If asked for $g$ at a height $h$ above a planet, remember $r=R_{planet}+h$. Do not just use $h$.
• Ratios: Questions often ask for ratios (e.g., $g_{Earth}/g_{Moon}$). Set up $\frac{g_1}{g_2}=\left(\frac{M_1}{M_2}\right)\times {\left(\frac{r_2}{r_1}\right)}^2$. Examiners noted many students forget to square the radii when calculating ratios!

3. $g$ near the Earth’s surface

Syllabus: Understand why $g$ is approximately constant for small changes in height near the Earth’s surface.

Standard Examiner Answer

For small changes in height ($h\ll R_E$), the change in distance from the Earth’s centre is negligible. Therefore, $r\approx R_E$, meaning $g$ remains effectively constant. Additionally, over a small area, the radial field lines are approximately parallel, indicating a uniform field.

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13.4 Gravitational Potential

1. Defining Gravitational Potential ($\varphi$)

Syllabus: Define gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to the point.

Formal Definition (Learn word-for-word)

The work done per unit mass in moving a small mass from infinity to that point.

"Why is gravitational potential always negative?" (Standard 2-mark question)

1. Gravitational potential is defined as zero at infinity.
2. Gravitational forces are strictly attractive.
3. Therefore, work is done by the mass (or work done on the mass is negative) as it moves from infinity to the point, meaning potential must be less than zero.

2. Using Potential ($\varphi$) and Potential Energy ($E_p$)

Syllabus: Use $\varphi =-GM/r$ and $E_p=-GMm/r$

The #1 Student Error Across All Papers

Students constantly mix up Gravitational Potential ($\varphi$) and Gravitational Potential Energy ($E_p$).

• Potential ($\varphi$) = Joules per kilogram ($J\cdot k{g}^{-1}$). Equation: $\varphi =-\frac{GM}{r}$
• Potential Energy ($E_p$) = Joules ($J$). Equation: $E_p=m\varphi =-\frac{GMm}{r}$

Calculating Changes in Potential Energy ($\Delta E_p$): When a mass moves from $r_1$ to $r_2$: $\Delta E_p=E_{p2}-E_{p1}=\left(-\frac{GMm}{r_2}\right)-\left(-\frac{GMm}{r_1}\right)=GMm\left(\frac{1}{r_1}-\frac{1}{r_2}\right)$ Examiners report that weak candidates try to write $GMm/(r_1-r_2)$, which is mathematically completely wrong.

Using $\Delta E_p=mg\Delta h$

Only use this formula if the change in height $\Delta h$ is very small compared to the radius of the planet (i.e., $g$ is constant). If a rocket travels into space, you MUST use $\Delta E_p=GMm(1/r_1-1/r_2)$.

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🚀 High-Yield Exam Scenarios & Tough Questions

Scenario A: Binary Star Systems

Two stars of masses $M_A$ and $M_B$ orbit a common centre of mass. Distance between them is $d$.

• The Trap: Students use the wrong radii in the equations.
• The Truth:
  • The Gravitational Force uses the total separation: $F_g=G\frac{M_A{M}_B}{d^2}$
  • The Centripetal Force uses the radius of the specific star’s orbit: $F_c=M_A{r}_A{\omega }^2$
  • Because they are locked in a binary orbit, they share the same angular velocity ($\omega$) and the same time period ($T$).
  • Equating them: $G\frac{M_A{M}_B}{d^2}=M_A{r}_A{\omega }^2$. (Notice $M_A$ cancels out!)

Scenario B: Changing Orbits (Energy Considerations)

A satellite moves from a higher orbit to a lower orbit (radius $r$ decreases).

• Potential Energy ($E_p$): Because $E_p=-GMm/r$, as $r$ decreases, the fraction $GMm/r$ gets larger, but because it is negative, the $E_p$ decreases (becomes more negative).
• Kinetic Energy ($E_k$): From circular motion, $E_k=\frac{GMm}{2r}$. As $r$ decreases, $E_k$ increases.
• Examiners Note: Do NOT just write “by conservation of energy, $E_k$ increases because $E_p$ decreases”. If there are resistive forces or thrusters fired, total energy is not conserved! Use the orbital equations to prove it.

Scenario C: Escape Velocity

A mass is projected from the surface of a planet to escape to infinity.

• Physics Principle: Loss in Kinetic Energy = Gain in Potential Energy.
• Equation: $\frac{1}{2}m{v}^2=\Delta E_p=\frac{GMm}{R_{planet}}-0$
• Catching Point: Remember that total energy at infinity is 0. So initial $E_k+E_p\ge 0$.

Scenario D: The Neutral Point (Null Point)

A point exactly between the Earth and the Moon where the resultant gravitational field strength is zero.

• Set up: $g_{Earth}=g_{Moon}\Rightarrow \frac{G{M}_E}{x^2}=\frac{G{M}_M}{(d-x{)}^2}$
• Pro Tip for Algebra: Do not expand the quadratic! Take the square root of both sides immediately: $\frac{\sqrt{M_E}}{x}=\frac{\sqrt{M_M}}{d-x}$. This saves massive amounts of time and prevents algebraic errors.

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🧮 A Checklist for Calculations (Don’t lose silly marks!)

• Did I convert km to m? ($10^3$)
• Did I convert days/hours to seconds? (e.g., $24\times 60\times 60$)
• Did I remember to square the radius in $g=GM/r^2$ and $F=GMm/r^2$?
• Did I remember NOT to square the radius in $\varphi =-GM/r$ and $E_p=-GMm/r$?
• Did I remember the negative sign for Potential and Potential Energy?
• Is my radius calculated from the centre of the planet, or did I mistakenly use just the height above the surface? ($r=R+h$)
• In “Show That” questions, did I substitute ALL numbers (including $G$) into the equation before writing the final answer? (Examiners give 0 marks if you just write the formula and then the final answer).