Field lines and equipotentials
Far from a planet the field lines are radial, pointing to the centre, non-uniform with spacing widening outwards. Near the surface they are parallel, equally spaced and uniform. Line density represents field strength, and equipotentials are perpendicular to field lines with no work done moving along one.
What this actually means
Two diagrams, two descriptions, and examiners want the words as much as the picture. For the point-mass case say radial, directed towards the centre, and getting further apart as r increases. For the surface case say parallel, equally spaced, uniform, directed vertically downwards.
These are the same picture at different zoom. Zoom right in on a small patch of a radial field and the curvature becomes invisible, which is exactly why a uniform field is a fair model near the ground.
The spacing rule is the whole point of drawing field lines: closer lines mean a stronger field. Arrows are compulsory, since a line without an arrow does not say whether the field points in or out. Gravitational field lines always point IN, because gravity only attracts.
Equipotentials are surfaces of constant φ. Around a point mass they are concentric spheres, near the ground they are horizontal planes. They cut the field lines at right angles everywhere, and they are NOT equally spaced for equal steps in φ: they bunch up close to the planet where the field is strong.
No work is done moving a mass along an equipotential, because ΔU = mΔφ and Δφ = 0. That is the cleanest one-line answer to 'a satellite in a circular orbit does no work against gravity, explain', since a circular orbit follows an equipotential.
Drawing field lines without arrows, or spacing equipotentials evenly when they should crowd near the planet.
Prove it — watch it be true
- Load the Earth preset and look at the 3D field vectors far from the planet, noting they are radial and spread out with distance.
- Zoom the view down to a small patch just above the surface and see the arrows become effectively parallel and equal in length.
- Move the test mass probe around a circle at fixed r and confirm the g magnitude readout never changes, which is what an equipotential means.