Gravitational field lines are a visual way to show how a mass creates a gravitational field in the space around it. They help students see both the direction and relative strength of gravity without drawing a force vector at every point. Around a planet, the lines point inward because gravity attracts objects toward the planet's center.
This idea matters in orbital motion, falling objects, satellite paths, and understanding why weight changes with location.
The gravitational field strength g tells the force per unit mass on a small test object placed in the field. For a spherical planet, the field outside the planet acts as if all the mass were concentrated at its center, so g = GM/r^2. Field lines are closer together where the field is stronger and farther apart where the field is weaker.
Near Earth's surface, the lines are nearly parallel and g is approximately constant at 9.8 N/kg over small height changes.
Key Facts
- Gravitational field lines point in the direction of the force on a small test mass.
- Around an isolated spherical mass, gravitational field lines point radially inward toward the center.
- Gravitational field strength is force per unit mass: g = F/m.
- For a spherical mass outside its surface: g = GM/r^2.
- Gravitational force between two masses is F = Gm1m2/r^2.
- Near Earth's surface, g ≈ 9.8 N/kg, which is the same as 9.8 m/s^2 for free fall.
Vocabulary
- Gravitational field
- A gravitational field is the region around a mass where another mass experiences a gravitational force.
- Field line
- A field line is an imaginary line that shows the direction a small test mass would be pulled by gravity.
- Gravitational field strength
- Gravitational field strength is the gravitational force on each kilogram of mass at a point, measured in N/kg.
- Inverse-square law
- The inverse-square law means gravitational field strength decreases in proportion to 1/r^2 as distance from the mass increases.
- Test mass
- A test mass is a small object used to probe a gravitational field without significantly changing the field itself.
Common Mistakes to Avoid
- Drawing gravitational field lines pointing away from a planet is wrong because gravity is attractive, so the force on a test mass points toward the planet's center.
- Spacing field lines evenly at all distances is wrong because the field weakens with distance, so the lines should spread farther apart as r increases.
- Using g = GM/r instead of g = GM/r^2 is wrong because gravitational field strength follows an inverse-square relationship outside a spherical mass.
- Treating g as exactly 9.8 N/kg everywhere is wrong because that value is only a useful approximation near Earth's surface and changes with altitude and planet mass.
Practice Questions
- 1 A 4.0 kg object is near Earth's surface where g = 9.8 N/kg. What gravitational force acts on it?
- 2 A planet has mass 6.0 x 10^24 kg. Find the gravitational field strength at a distance of 7.0 x 10^6 m from its center using G = 6.67 x 10^-11 N m^2/kg^2.
- 3 Explain why gravitational field lines around Earth are nearly parallel close to the ground but radial when viewed from far away.