Gravitational Field and Field Intensity Easy Explanation

Every mass fills the space around it with an invisible influence called the gravitational field. Place a test mass anywhere in that field and it feels a pull. The field intensity at a point is simply the gravitational force felt per kilogram of test mass there — the whole story of gravity rewritten as a property of space itself.

This matters because the field idea powers modern gravitational physics, from satellite orbits to underground oil mapping. Once you can draw the field around any object — a planet, a shell, a ring — you can find the force on anything inside it instantly, without re-deriving Newton's law each time.

Key Concepts

• Field intensity E = F/m: force per unit test mass. Units are N/kg, identical to m/s² — field intensity is the acceleration a mass would feel there.
• Field lines point toward the mass; their crowding shows strength. Around a sphere they are radial and E falls as 1/r².
• Shell theorem: outside a spherical shell it pulls as if all mass sat at the centre; inside a hollow shell the field is exactly zero — pulls from every direction cancel.
• Superposition: the total field is the vector sum of every mass's field.

Formulas

• Point mass or exterior of sphere: E = GM/r², directed toward the mass. At Earth's surface this gives g = 9.8 m/s².
• Inside a hollow spherical shell: E = 0 everywhere inside.
• Inside a solid uniform sphere (r < R): E = GMr/R³ — zero at the centre, rising linearly to GM/R² at the surface.
• Units: E in N/kg; G = 6.674 × 10⁻¹¹ N·m²/kg².

Worked Example

The space station orbits 400 km above Earth. What is the field intensity there?

1. Orbital radius: r = 6.371 × 10⁶ + 0.400 × 10⁶ = 6.771 × 10⁶ m.
2. E = GM/r² = (6.674 × 10⁻¹¹ × 5.972 × 10²⁴)/(6.771 × 10⁶)².
3. Numerator = 3.986 × 10¹⁴; denominator = 4.585 × 10¹³; E = 8.69 m/s².
4. Ratio to surface: 8.69/9.8 ≈ 0.89 — about 89% of surface gravity.

The field at the ISS is barely weaker than on the ground — astronauts float because they are falling around the Earth, not because the field is gone. The same formula says at one Earth-radius altitude (h = R) the field is exactly g/4 = 2.45 m/s².

Common Misconceptions

• "Field intensity and g are different things." They are the same quantity with the same units (N/kg = m/s²). E is just the name for g at any point in space.
• "Inside a hollow planet the field is strongest at the centre." It is zero everywhere inside a hollow shell — every pull cancels perfectly.
• "Field lines are real objects." They are a drawing tool, like contour lines on a map. The field is real; the lines are our picture of it.

Real-World Applications

• Mission design: every orbit calculation starts from E = GM/r² around Earth, the Moon or Mars.
• Gravity surveys: tiny field variations locate oil, ore and groundwater; GRACE satellites map Earth's field monthly.
• Planetary science: tracking field strength tells scientists whether a planet has a dense core.

The gravitational field turns "masses attract" into a map: E = GM/r² gives the pull per kilogram everywhere, zero inside hollow shells, rising linearly inside solid ones. Field intensity and g are the same thing in different words — and a weak field never means no field, as the floating astronauts prove.