In the far-off Stellaris system, planets circle the star Lumina at varying rates, which creates interesting math connections. You have some details about orbital periods and need to figure out the missing values using relative time relationships.
Information We Know
Orbital Periods We Know:
Planet Verdania: 360 days
Planet Rubicon: 720 days
Relative Information:
Planet Zephyr goes around 3 times quicker than Rubicon
Planet Nexus takes half the time of Verdania to go around once
Planet Crimson’s orbit time is 4 times longer than Planet Zephyr
Planet Astra finishes 5 orbits in the same time Crimson finishes 2 orbits
The Science Behind It
The time it takes planets to orbit depends on how far they are from the star Lumina. This follows Kepler’s Third Law: planets that are further away take more time to complete an orbit. The link between how fast a planet moves and its distance creates patterns we can predict with math. This lets us figure out unknown orbit times if we know some other details.
Your Job
With the info you have, work out how long it takes Planets Zephyr, Nexus, Crimson, and Astra to orbit. Give your answers in days.
Problems to Work Out:
How long does it take Planet Zephyr to orbit?
How long does it take Planet Nexus to orbit?
How long does it take Planet Crimson to orbit?
How long does it take Planet Astra to orbit?
Let’s put all the planets (Verdania and Rubicon included) in order based on how long they take to orbit, from quickest to slowest.
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