NARAYANKAR NOTES

🌞 Imagine the Sun is in the center of a playground. Two planets – Earth and Jupiter – are running in circles around it, like two kids on a race track. Let’s see how far they are and how long they take to go around the Sun once. 🌍 EARTH Distance from Sun: About 150 million km Time to go around the Sun (1 revolution): 1 year --- 🪐 JUPITER Distance from Sun: About 778 million km Time to go around the Sun (1 revolution): 11.86 years (almost 12 years) --- 🧮 Now let’s do Kepler’s Third Law Step-by-Step: Step 1: Take the time and square it (Time × Time) Earth: Time = 1 year 1 × 1 = 1 Jupiter: Time = 11.86 years 11.86 × 11.86 = about 140.7 --- Step 2: Take the distance and cube it (Distance × Distance × Distance) Let’s use Astronomical Units (AU) instead of kilometers to make it easier. 1 AU = distance from Earth to the Sun = 150 million km Earth: Distance = 1 AU 1 × 1 × 1 = 1 Jupiter: Distance = 5.2 AU 5.2 × 5.2 × 5.2 = about 140.6 --- 🧩 Now compare: Planet Square of Time (Years²) Cube o...

🌞 Imagine the Sun is in the center of a playground. Two planets – Earth and Jupiter – are running in circles around it, like two kids on a race track. Let’s see how far they are and how long they take to go around the Sun once. 🌍 EARTH Distance from Sun : About 150 million km Time to go around the Sun (1 revolution) : 1 year 🪐 JUPITER Distance from Sun : About 778 million km Time to go around the Sun (1 revolution) : 11.86 years (almost 12 years ) 🧮 Now let’s do Kepler’s Third Law Step-by-Step: Step 1: Take the time and square it (Time × Time) Earth : Time = 1 year 1 × 1 = 1 Jupiter : Time = 11.86 years 11.86 × 11.86 = about 140.7 Step 2: Take the distance and cube it (Distance × Distance × Distance) Let’s use Astronomical Units (AU) instead of kilometers to make it easier. 1 AU = distance from Earth to the Sun = 150 million km Earth : Distance = 1 AU 1 × 1 × 1 = 1 Jupiter : Distance = 5.2 AU 5.2 × 5.2 × 5.2 = about 140.6 🧩 Now comp...