Orbital Motion — Flashcards & Quiz

Q1: Derive the orbital velocity formula for a satellite.

For a circular orbit, gravity provides centripetal force: GMm/r² = mv²/r. Cancel m and solve: v = √(GM/r). Orbital velocity depends only on the central mass M and orbital radius r, NOT on the satellite's mass. Closer orbits are faster.

Q2: What is a geostationary orbit?

A geostationary orbit has period T = 24 hours (same as Earth's rotation), orbits above the equator, and moves in the same direction as Earth's rotation (west to east). The satellite appears stationary from the ground. Altitude ≈ 35,786 km. Used for communications and weather satellites.

Q3: What is orbital decay and why does it occur?

Orbital decay is the gradual decrease of a satellite's orbital altitude due to atmospheric drag (even thin upper atmosphere). As the orbit lowers, the satellite speeds up (lower orbit = higher velocity), drag increases further, creating a positive feedback loop leading to re-entry.

Q4: Compare low Earth orbits (LEO) and geostationary orbits.

LEO: altitude 200-2000 km, period ~90 min, used for imaging/ISS, orbital velocity ~7.7 km/s, covers different areas as Earth rotates beneath. Geostationary: altitude ~36,000 km, period 24 h, appears fixed above one point, orbital velocity ~3.1 km/s, used for communications/weather.

Q1: A satellite in a higher orbit travels faster than one in a lower orbit.

Answer: FALSE

v = √(GM/r). As r increases, v decreases. Higher orbit = slower speed. This is why geostationary satellites (r ≈ 42,000 km) travel at ~3.1 km/s while LEO satellites (r ≈ 6,700 km) travel at ~7.7 km/s.

Q2: A geostationary satellite must orbit above the equator.

Answer: TRUE

To appear stationary from Earth, the satellite must orbit in the equatorial plane (inclination 0°), move west to east with T = 24 h. Any other inclination would cause it to appear to move north-south during the day.

Q3: As a satellite loses energy due to atmospheric drag, it speeds up.

Answer: TRUE

Counter-intuitively, drag causes the satellite to drop to a lower orbit where orbital velocity is higher (v = √(GM/r)). The satellite loses total energy and potential energy, but gains kinetic energy as r decreases.