Gravitational Fields Common Exam Traps

Overview

This page is a rapid revision sheet for common mistakes in Gravitational Fields.

Focus on avoiding:

• symbol confusion,
• sign errors,
• wrong radius usage,
• vector/scalar mistakes,
• orbital misconceptions,
• formula misuse.

Why It Matters

Gravitational-field questions are often lost through sign, symbol, and interpretation mistakes rather than hard algebra.

Definition

This note collects the most common exam traps in gravitational fields and gives the correct interpretation for each one.

Key Representations

$$\vec{g}=-\frac{GM}{r^2}\hat{r}$$ $$V=-\frac{GM}{r}$$ $$U=-\frac{GMm}{r}$$ $$v=\sqrt{\frac{GM}{r}}$$ $$v_e=\sqrt{\frac{2GM}{r}}$$

Trap 1: Confusing $G$ with $g$

Wrong Thinking

$G$ and $g$ are the same quantity.

Correct

$G$ = universal gravitational constant:

$$G=6.67\times 10^{-11}\mathrm{N}{\mathrm{m}}^2\mathrm{k}{\mathrm{g}}^{-2}$$

$g$ = gravitational field strength / free-fall acceleration:

$$g=\frac{GM}{r^2}$$

Near Earth:

$$g\approx 9.81\mathrm{m}{\mathrm{s}}^{-2}$$

Quick Reminder

• $G$ is constant everywhere.
• $g$ depends on location.

Trap 2: Confusing Gravitational Force with Gravitational Field Strength

Wrong Thinking

${\vec{F}}_G$ and $\vec{g}$ are interchangeable.

Correct

Gravitational force on a mass $m$:

$${\vec{F}}_G=m\vec{g}$$

Field strength $\vec{g}$ is a property of space.

Quick Reminder

• ${\vec{F}}_G$ depends on the test mass.
• $\vec{g}$ does not.

Trap 3: Confusing Gravitational Potential with Gravitational Potential Energy

Wrong Thinking

$V$ and $U$ are the same.

Correct

Gravitational potential:

$$V=-\frac{GM}{r}$$

Units:

$$\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}$$

Gravitational potential energy:

$$U=mV=-\frac{GMm}{r}$$

Units:

$$\mathrm{J}$$

Quick Reminder

Potential = per unit mass.

Trap 4: Forgetting That Gravitational Potential Is Negative

Wrong Thinking

Potential should always be positive.

Correct

With zero at infinity:

$$V=-\frac{GM}{r}$$

So potential near a mass is negative.

Quick Reminder

More negative = deeper gravitational well.

Trap 5: Using Height Above Surface Instead of Distance from Centre

Wrong Thinking

Use altitude $h$ directly in formulas.

Correct

Use centre-to-centre distance:

$$r=R+h$$

Then substitute into:

$$g=\frac{GM}{r^2}$$ $$V=-\frac{GM}{r}$$ $$v=\sqrt{\frac{GM}{r}}$$

Quick Reminder

Most gravitation formulas use $r$ from the centre.

Trap 6: Assuming Constant $g$ Everywhere

Wrong Thinking

$g=9.81\mathrm{m}{\mathrm{s}}^{-2}$ always.

Correct

Near Earth’s surface only:

$$g\approx 9.81\mathrm{m}{\mathrm{s}}^{-2}$$

At altitude:

$$g=\frac{GM}{r^2}$$

Quick Reminder

Use constant $g$ only when height change is small compared with Earth radius.

Trap 7: Thinking Objects in Orbit Feel No Gravity

Wrong Thinking

Astronauts float because gravity is zero.

Correct

Gravity provides the centripetal force for orbit:

$$\frac{GMm}{r^2}=\frac{m{v}^2}{r}$$

Astronauts feel weightless because they are in free fall.

Quick Reminder

Weightlessness $\ne$ no gravity.

See Orbital Motion in Gravity.

Trap 8: Thinking Higher Orbit Means Higher Orbital Speed

Wrong Thinking

Farther orbit means faster motion.

Correct

Circular orbital speed:

$$v=\sqrt{\frac{GM}{r}}$$

So as $r$ increases, $v$ decreases.

Quick Reminder

Higher orbit = slower speed, longer period.

Trap 9: Misusing Escape Velocity

Wrong Thinking

Escape velocity means rocket must instantly travel upward at $11.2\mathrm{km}{\mathrm{s}}^{-1}$.

Correct

Escape velocity is an energy benchmark:

$$v_e=\sqrt{\frac{2GM}{r}}$$

It is the minimum speed for total mechanical energy to become zero.

Real rockets use continuous thrust.

Quick Reminder

Escape velocity is not a launch procedure.

See Escape Velocity.

Trap 10: Forgetting Vector vs Scalar Distinctions

Wrong Thinking

All quantities add the same way.

Correct

Vectors:

• ${\vec{F}}_G$
• $\vec{g}$

Scalars:

• $V$
• $U$

Quick Reminder

• Fields add vectorially.
• Potentials add algebraically.

Trap 11: Wrong Sign for Force Direction

Wrong Thinking

Gravitational force points outward.

Correct

Gravity is attractive.

If $\hat{r}$ points outward:

$${\vec{F}}_G=-\frac{GMm}{r^2}\hat{r}$$

Quick Reminder

Negative sign indicates inward direction.

Trap 12: Forgetting Satellite Mass Cancels

Wrong Thinking

Heavier satellite needs greater orbital speed.

Correct

From:

$$\frac{GMm}{r^2}=\frac{m{v}^2}{r}$$

$m$ cancels:

$$v=\sqrt{\frac{GM}{r}}$$

Quick Reminder

Orbital speed does not depend on satellite mass.

Quick Checklist

Before final answer, check:

• Did I use $G$ or $g$ correctly?
• Did I use $r=R+h$ if needed?
• Is this quantity vector or scalar?
• Did I keep gravitational potential negative?
• Am I using constant $g$ appropriately?
• For orbit, did I set gravity = centripetal force?
• For escape, did I use energy logic?

Links

Related Links

• Gravitational Fields
• Orbital Motion in Gravity
• Escape Velocity
• Gravitational vs Electric Fields
• Circular Motion
• Electric Fields
• Work, Energy and Power