Two small satellites have circular orbits around the same planet. B's radius is four times A's. How does B's speed compare with A's?

• It is twice A's speed.
• It is four times A's speed.
• It is half A's speed.

Which set of conditions makes an Earth satellite geostationary?

• Circular, equatorial, eastward; period equals Earth's sidereal day.
• Circular, equatorial, westward; period equals Earth's sidereal day.
• Circular, polar, northward at the equator; period equals Earth's sidereal day.

For small satellites in circular orbits around the same central mass, plotting T² vertically against r³ horizontally gives a straight line through the origin.

For a small satellite in a circular orbit, which equation sets gravity equal to the required centripetal force?

• GMm/r² = mv²/r²
• GMm/r² = mv²/r
• GMm/r² = mv/r

Two small satellites have circular orbits around the same planet. B's orbital radius is nine times A's. By what factor is B's period longer?

A small satellite has circular orbital period T around a body of mass M. Which expression gives its orbital radius r?

• r = √(GMT²/(4π²))
• r = ∛(4π²T²/(GM))
• r = ∛(GMT²/(4π²))

Nina says a satellite with twice the mass needs twice the speed in the same circular orbit. Which step in the force equation corrects her claim?

• The factor m cancels from both sides of GMm/r² = mv²/r.
• The central mass M cancels from both sides of GMm/r² = mv²/r.
• The radius r cancels completely, so the speed is independent of orbital radius.

Calculate a geostationary satellite's height in km, to the nearest 100 km. Use GM = 3.986 × 10^14 m³/s², T = 86,164 s and Earth's radius R = 6,370 km. Use the small-satellite circular-orbit model.