ما هي قوانين التسارع المركزي والجاذبية الكونية؟ What are centripetal acceleration and gravity formulas?

التسارع المركزي: a_c = v²/r والقوة المركزية: F_c = mv²/r. وقانون الجذب الكوني لنيوتن: F = G(m₁m₂)/r² حيث G ثابت الجذب العام (6.67 × 10⁻¹¹ N·m²/kg²). [الصيغة الرمزية الموزونة: a_c = v² / r | F_c = (m × v²) / r | F_g = G × (m₁ × m₂) / r² | v_orbit = √(G×M / r)]

Theme D — Fields

D.1.2 Gravitational Field Strength — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 4 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision

Curriculum Equation Key Circular Motion & Gravitation LawsFast Exam Solution

a_c = v² / r  |  F_c = (m × v²) / r  |  F_g = G × (m₁ × m₂) / r²  |  v_orbit = √(G×M / r)

0%read

Lesson summary

D.1.2 Gravitational Field Strength — IB PHYSICS SL notes: Define gravitational field strength and calculate g for point masses and spherical bodies at any distance.Gravitational field — a region of space where a test mass experiences a force due to the gravitational attraction of…

Source size
Gravitational field strength (g)
What the symbols mean
Dependence
Surface factors
Distance example

Part 1 of 7Gravitational field

Gravitational field

Gravitational field a region of space where a test mass experiences a force due to the gravitational attraction of another mass
A planet creates a field in the space around it, and any mass placed there feels it.
This avoids action at a distance and lets us describe the field at a point even when nothing is there.

Direction

Direction the field acts towards the centre of the mass producing it, because gravity is always attractive

Range

Range gravity has infinite range

Source size

Source size the force is greater around objects of large mass such as planets and almost negligible for atoms

Part 2 of 7Definition of field strength

1Gravitational field strength (g)

Gravitational field strength (g) the force per unit mass experienced by a small test mass at a point
g = F / m

Symbols

g is in N kg⁻¹, which equals m s⁻².
F is the gravitational force on the test mass in N.
m is the test mass in kg, small enough not to disturb the source.

3Vector

Vector g points in the direction of the force on the test mass, towards the source

4Free fall

Free fall because F = mg, g is also the free-fall acceleration at that point
At the Earth's surface it is 9.8 N kg⁻¹ or 9.8 m s⁻².

Part 3 of 7Field of a point or spherical mass

Equation

Equation g = GM / r²
What the symbols mean: g = gravitational field strength (N kg⁻¹) · G = 6.67 × 10⁻¹¹ N m² kg⁻² · M = mass of the body (kg) · r = distance from its centre (m)
Equate mg with GMm/r² and cancel the test mass.
M is the mass producing the field and r is the distance from its centre.

Dependence

Dependence g depends only on the source mass and position, and falls with the inverse square of distance
Objects of any mass in the field feel the same g.

Surface factors

Surface factors g at a planet's surface depends on the planet's mass (or density) and radius

Distance example

Distance example at the surface r = R, and at r = 2R the field is a quarter of the surface value

Graphs

Graphs g against r outside a body is a falling curve, and g against 1/r² is a straight line with gradient GM

Validity

Validity the formula holds for any point outside a spherical body

Part 4 of 7Combining fields

Superposition

Superposition the net field at a point is the vector sum of the fields due to each mass

Neutral point

Neutral point along the line joining two masses the fields point in opposite directions, so a point exists where they cancel
It lies closer to the smaller mass, where GM₁/r₁² = GM₂/r₂².

Uniform field

Uniform field near a planet's surface, over heights small compared with the radius, g hardly varies
This justifies constant-acceleration equations and E_p = mgh for ordinary projectiles.

Part 5 of 7Field strength versus weight

Weight

W = mg, where g is the local field strength
Weight is a force that changes from place to place.
Mass is a fixed property of the object.

Moon

Moon an astronaut has the same mass but a weight about one sixth as large, since the Moon's surface g is about 1.6 N kg⁻¹

Jupiter

Jupiter a very large g gives a large weight, so a human could hardly stand up

Two views of g

Two views of g a force per unit mass (N kg⁻¹) or an acceleration (m s⁻²), so use whichever is convenient and keep units consistent

Part 6 of 7Comparing planets

Ratio method

Ratio method write g ∝ M/r² and substitute ratios of mass and radius

With density

M = ρ × (4/3)πr³, so g ∝ ρr

Data booklet

Data booklet it gives g = GM/r², and the volume of a sphere

Part 7 of 7More from the specification

Key terms

Term	Meaning
Gravitational field	Region where a mass experiences a gravitational force.
Field strength g	Force per unit mass at a point; unit N kg⁻¹.
Test mass	A small mass used to probe a field without disturbing it.
Superposition	The net field is the vector sum of the individual fields.
Neutral point	A position where the net gravitational field is zero.
Uniform field	A field with the same magnitude and direction everywhere, as near a planet's surface.

Avoid these mistakes

Confusing g with G — g is field strength and G is the gravitational constant.

Writing g = F/m as a scalar — it is a vector pointing towards the source.

Using the height above the surface as r in GM/r^{2}.

Believing g = 0 for astronauts in orbit — g is nearly the same as on the ground.

Saying g depends on the test mass — the mass cancels.

Last updated: 18 October 2026