Circular Orbits: Speed and Period

Aeronautics and Aerospace · CHAPTER 5 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Estimate orbital speed from central-body gravity.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

In a two-body circular orbit, gravity provides the centripetal acceleration. Radius is measured from the central body’s centre, not its surface. The model neglects atmospheric drag, oblateness and other bodies. Real trajectories require higher-fidelity modelling.

2. Write the model

v = √(μ/r); T = 2π√(r³/μ)

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

Using Earth μ=3.986×10¹⁴ m³/s² and illustrative radius 7.0×10⁶ m, speed is about 7546 m/s and period about 5829 s, or 97.1 min.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Radius from centre (km)	Speed (m/s)	Period (min)
7000	7546.05	97.14
8000	7058.68	118.69
9000	6654.99	141.62

Increase radius in the circular model. Speed falls while period rises.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

Can altitude in metres be substituted directly for r?

Reveal the answer and check your work

No. Add the central body’s radius first.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

A circular two-body calculation is not a mission trajectory solution.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.