Reading the picture

The large sphere is the planet and the small sphere is the satellite on its orbit.
The stacked bars (flat slabs, one per energy) are the three energies — kinetic, potential and total — drawn to the same scale so you can see the total stay negative.

What to do

Drag the orbit radius r outward.
Watch v drop and the period T grow — and watch the energy ledger: KE falls, PE rises toward zero, total E rises but stays negative.
Predict first: does a higher satellite move faster or slower?

What to observe

Orbital speed v = √(GM/r): higher orbits are SLOWER, with longer periods (Kepler's third law).
The brown arrow F = GMm/r² always points at Earth and provides exactly the centripetal force.
KE = +GMm/2r, PE = −GMm/r, and total E = −GMm/2r — negative because the satellite is BOUND.

What it means

Because E = −GMm/2r, raising an orbit needs energy input even though the satellite ends up moving slower — and drag, by removing energy, paradoxically speeds a satellite up as it spirals in.

Why this matters

The total energy is negative, and that is not bookkeeping: a bound orbit must have E < 0, because reaching infinity costs at least zero energy. The moment E reaches zero the satellite escapes, which is why escape speed is exactly the speed that makes the total vanish.
A higher orbit is a SLOWER orbit but a more energetic one, which sounds contradictory until you notice that the potential energy rises twice as fast as the kinetic energy falls. So raising a satellite costs energy even though it ends up moving more slowly.
Kinetic energy is exactly half the magnitude of the potential energy for any circular orbit. That is the virial theorem, and it is the reason the total comes out as exactly half the potential energy.

🛰️ Energy of a Satellite — E = −GMm/2r