Satellite Motion Calculator

How it works

1. 1Choose the central body (Earth, Mars, Moon, or Jupiter) and the altitude above its surface in kilometres.
2. 2The calculator adds the body’s mean radius to your altitude to get the orbital radius r, then evaluates v = √(GM ÷ r) and T = 2π√(r³ ÷ GM).
3. 3Results show orbital velocity in m/s and km/s, and the period in minutes and hours.

Use cases

• Verifying the speed and period of a planned orbit — a 400 km LEO gives ≈ 7.7 km/s and ~93 minutes.
• Comparing orbital parameters across planetary bodies for coursework or mission concepts.
• Exploring how higher orbits trade velocity for a longer period.

Frequently asked questions

How is the orbital radius found from the altitude?

The calculator adds the body’s mean radius to your altitude: r = R_body + altitude. For Earth at 400 km, r = 6,371,000 + 400,000 = 6,771,000 m.

What formulas are used?

Orbital velocity v = √(GM ÷ r) and period T = 2π√(r³ ÷ GM), where G = 6.6743×10⁻¹¹ N·m²/kg² and M is the central body’s mass.

What is a worked example for a 400 km low Earth orbit?

With Earth’s mass 5.972×10²⁴ kg and r = 6,771,000 m: v ≈ 7,672 m/s ≈ 7.7 km/s, and T ≈ 5,543 s ≈ 92.4 min — the International Space Station’s orbit.