Orbital Mechanics

Use this for “On an orbit from 6778 to 42,164 km, how fast is the craft 20,000 km from Earth’s center?”

Use this for “What orbit radius and altitude give a period of one sidereal day, 86,164 s, and how fast does that satellite move?”

Use this for “An orbit has a = 24,471 km and e = 0.723. How far from Earth’s centre is the satellite at true anomaly 90°?”

Use this for “An orbit has a = 24,471 km and e = 0.723. Where is the satellite 1.684 h after perigee?”

Use this for “In which plane is the right ascension of the ascending node measured, and from where?”

Use this for “A satellite circles at 3.075 km/s. What Δv turns its orbit plane through 28.5°? What turn does 1 km/s buy?”

Use this for “At apogee of a transfer orbit a craft moves at 1.618 km/s. One burn reaches a 3.075 km/s circle and turns the plane 28.5°. Find Δv.”

Use this for “Earth circles the Sun in 365.25 days and Mars in 687 days. How often does a Hohmann launch window to Mars open?”

Use this for “Earth orbits 1.496 × 10⁸ km from the Sun and has 3.003 × 10⁻⁶ of its mass. How far out does Earth’s pull take over from the Sun’s?”

Use this for “A satellite at 500 km has Iz = 1200 and Iᵧ = 800 kg·m², its z axis tilted 10° from the local vertical. Find the gravity-gradient torque.”

Use this for “A reaction wheel gives 0.1 N·m to a craft with I = 800 kg·m². How long does a 30° rest-to-rest slew take, and what momentum must the wheel hold?”