Define average orbital speed from the equation v = 2 π r / T where r is the average radius of the orbit and T is the orbital period; recall and use this equation

6.1.1 The Earth – Orbital Speed

Objective: Define average orbital speed from the equation \$v = \frac{2\pi r}{T}\$ where \$r\$ is the average radius of the orbit and \$T\$ is the orbital period; recall and use this equation. 🚀

What is Orbital Speed?

Think of Earth as a runner on a giant circular track around the Sun. The orbital speed is how fast the runner (Earth) moves along that track. It’s the distance travelled divided by the time taken to complete one lap.

Key Formula

The average speed \$v\$ is calculated with:

\$v = \dfrac{2\pi r}{T}\$

  • \$r\$ – average radius of Earth’s orbit (≈ 1 AU = 149.6 million km)

  • \$T\$ – orbital period (≈ 365.25 days = 31 557 600 s)

  • \$v\$ – average orbital speed (≈ 29.78 km/s)

Step‑by‑Step Example

  1. Convert the orbital period to seconds: \$T = 365.25 \times 24 \times 3600 = 31\,557\,600\ \text{s}\$

  2. Insert \$r\$ and \$T\$ into the formula:

    \$v = \dfrac{2\pi \times 149.6\times10^6}{31\,557\,600}\$

  3. Calculate: \$v \approx 29.78\ \text{km/s}\$

Quick Reference Table

ParameterValueUnits
Average radius (\$r\$)149.6 millionkm
Orbital period (\$T\$)31 557 600s
Average speed (\$v\$)29.78km/s

Exam Tip: When you see a question about Earth’s orbital speed, remember:

  1. Identify the given values for \$r\$ and \$T\$.

  2. Check units – convert days to seconds if needed.

  3. Plug into \$v = \dfrac{2\pi r}{T}\$ and simplify.

Keep your answer in km/s unless the question asks otherwise. 🌍