Trap 1: Escape Velocity Depends on Launch Mass

Wrong belief: Heavier objects need higher escape velocity. Correct: v_e is the same for ALL masses. Heavier objects need more energy (½mv_$e^{2}$) but the same speed threshold.

Trap 2: Confusing PE with Total Energy

Wrong: "Gravitational PE of satellite = −GMm/(2r)" Correct: PE = −GMm/r. The value −GMm/(2r) is the TOTAL energy E (not PE alone).

Memory aid:

• PE = −GMm/r (one r in denominator)
• E = −GMm/2r (one r in denominator, factor of 2 in numerator)
• KE = +GMm/2r (same magnitude as E but positive)

Trap 3: Using Approximate g Formula Outside Valid Range

Wrong: Using g' ≈ g(1 − 2h/R) when h = R/2 Correct: Use exact formula g' = $gR^{2}$/(R+h)^{2} for h comparable to R

Trap 4: Escape Velocity Is Direction-Dependent

Wrong: Must launch vertically to escape. Correct: Any direction works. Escape is an energy condition, not a trajectory condition.

Trap 5: g Is Zero Because of Distance from Surface at Centre

Wrong: "g = 0 at centre because it's farthest from the surface" Correct: g = 0 at the centre because gravitational forces from all directions cancel by symmetry (Shell Theorem), not because of any special distance.

Trap 6: All Satellites Have Same Energy at Same Orbit

Wrong: "Two satellites at the same orbital radius have the same total energy" Correct: E = −GMm/(2r); energy depends on satellite mass m. Heavier satellite has more negative (lower) energy.

Trap 7: Raising Orbit Increases Speed

Wrong: "Adding energy makes satellite go faster" Correct: Adding energy raises the orbit, which actually decreases orbital speed (v_{0} ∝ 1/√r). The satellite moves slower in the higher orbit.

Trap 8: Geostationary Satellite Can Be Anywhere

Wrong: "A geostationary satellite can hover over any location" Correct: Geostationary orbit is only possible in the equatorial plane. It can only appear stationary over equatorial locations. A geosynchronous satellite in an inclined orbit traces a figure-eight.