Predicting Orbits
Aligned to HS-ESS1-4 — Next Generation Science Standards.
What this lesson teaches
Gravity keeps planets and moons in orbit, and Kepler's laws let us predict their motion mathematically. A planet's orbital period depends only on its average distance from the sun: the farther out, the slower it moves and the longer its year.
Worked examples
Example 1
Kepler's third law says the period squared equals the distance cubed (in Earth units). Mars orbits at about 1.52 AU, so its period is the square root of 1.52 cubed, roughly 1.88 Earth years, which matches what astronomers observe.
Example 2
The law works for anything orbiting the same body. Jupiter's moons obey it around Jupiter with their own constant.
Example 3
It gives the period from the distance but says nothing about why. Newton supplied the why a lifetime later.
Practice questions
- Observe: Distant planets take longer to circle the sun than close ones. What relationship does that hint at between distance and orbital period?
- Model: Use period squared equals distance cubed to predict the orbital period of a dwarf planet at 4 AU.
- Explain: Two satellites orbit Earth at different altitudes. Predict which one moves faster and justify your answer using gravity and orbital distance.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Predecir órbitas
La gravedad mantiene a planetas y lunas en órbita, y las leyes de Kepler nos permiten predecir su movimiento matemáticamente. El período orbital de un planeta depende solo de su distancia media al Sol: cuanto más lejos, más lento se mueve y más largo es su año.
Ejemplo 1: La tercera ley de Kepler dice que el período al cuadrado es igual a la distancia al cubo (en unidades de la Tierra). Marte orbita a unas 1.52 UA, así que su período es la raíz cuadrada de 1.52 al cubo, unos 1.88 años terrestres, lo que coincide con lo que observan los astrónomos.
Ejemplo 2: La ley funciona para cualquier cosa que orbite el mismo cuerpo. Las lunas de Júpiter la cumplen alrededor de Júpiter con su propia constante.
Ejemplo 3: Da el periodo a partir de la distancia pero no dice por qué. Newton aportó el porqué una vida después.
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