As a top astrophysicist, NASA wants your help with a found planet system. In the distant Stellaris system, planets orbit the star Lumina at different speeds creating interesting math relationships. For the basic info on that planet system, you need to work out the orbital periods of all the planets. You have some facts about orbital periods and you need to figure out the missing values for the other planets using relative time relationships.
Information We Know
Orbital Periods We Know:
- Planet Verdania: 360 days
- Planet Rubicon: 720 days
Relative Information:
- Planet Zephyr circles 3 times faster than Rubicon
- Planet Nexus takes half as long as Verdania to complete one orbit
- Planet Crimson’s orbital period lasts 4 times longer than Planet Zephyr’s
- Planet Astra completes 5 orbits in the same time in which Crimson finishes 2
The Science Behind It
The orbit time of planets depends on their distance from the star Lumina. This follows Kepler’s Third Law: planets farther away need more time to finish an orbit. The connection between a planet’s speed and its distance creates patterns we can predict using math. This allows us to work out unknown orbit times if we know other details.
Your Job
Using the information you have, figure out the orbital periods for Planets Zephyr, Nexus, Crimson, and Astra. Give your answers in days.
Questions to Answer:
What’s the orbital period of Planet Zephyr? What’s the orbital period of Planet Nexus? What’s the orbital period of Planet Crimson? What’s the orbital period of Planet Astra?
Let’s rank all the planets (including Verdania and Rubicon) based on their orbital periods, from shortest to longest.
View the answer
Here’s how we figure it out:
- Zephyr’s orbit: Rubicon takes 720 days, so Zephyr = 720 ÷ 3 = 240 days
- Nexus’s orbit: Half of Verdania’s time = 360 ÷ 2 = 180 days
- Crimson’s orbit: Four times Zephyr’s time = 240 × 4 = 960 days
- Astra’s orbit: Crimson goes around twice while Astra goes around five times so Astra = (960 × 2) ÷ 5 = 384 days
The final order (quickest to slowest):
- Planet Nexus: 180 days
- Planet Zephyr: 240 days
- Planet Verdania: 360 days
- Planet Astra: 384 days
- Planet Rubicon: 720 days
- Planet Crimson: 960 days
