Why a satellite meeting air resistance speeds up
Drag does negative work, so total energy decreases (more negative). Since TE = −GMm/2r, a more negative TE means r decreases. But KE = +GMm/2r, so as r falls KE increases and the satellite speeds up.
What this actually means
Counterintuitive and heavily examined, so learn the chain as four linked statements rather than trying to reason it out under pressure.
Step one: air resistance opposes motion, so it does negative work, so total energy decreases and becomes more negative. Step two: TE = −GMm/2r, and TE more negative forces r smaller, so the satellite spirals inwards. Step three: KE = +GMm/2r, and r smaller makes KE larger. Step four: therefore the satellite speeds up.
Energy is still conserved, which is the part markers want addressed. As the satellite drops, the GPE released is −GMm/r, twice as sensitive to r as the KE term. That GPE loss pays for BOTH the KE gain and the energy dumped into the atmosphere as heat.
Language matters here. Say 'total energy becomes more negative' rather than 'total energy is lost', and never say 'the satellite loses speed because of friction'. The friction is real and does slow it momentarily, but the orbit adjusts and the net effect over many orbits is a faster satellite.
This is also the mechanism behind orbital decay and re-entry: lower orbit, denser air, more drag, faster spiral. It runs away, which is why low satellites need periodic reboosts.
Concluding the satellite slows down because friction opposes motion, without arguing through the energy equations.
Prove it — watch it be true
- Use the orbit radius slider to step the orbit inwards, mimicking a satellite losing total energy.
- Watch the Total energy bar go more negative while the KE bar grows.
- Read the speed value at each step and confirm the smaller orbit is the faster one.