Formula used
For a circular orbit around a central body, the required orbital speed is: v = √(μ / r). Here, μ = G·M is the gravitational parameter and r is the distance from the body’s center.
- r = R + h when you enter altitude above the surface.
- Centripetal acceleration: a = μ / r².
- Orbital period: T = 2π √(r³ / μ).
- Specific orbital energy (circular): ε = −μ / (2r).
How to use this calculator
- Select a preset body to auto‑fill typical μ and radius values.
- Choose whether you will enter μ directly or provide mass and G.
- Pick altitude mode or radius‑from‑center mode for the orbit size.
- Select your preferred output unit and decimal precision.
- Click Calculate to show results above the form.
- Use the CSV or PDF buttons to export your computed results.
Example data table
| Central body | Input | Orbit size | Velocity (km/s) |
|---|---|---|---|
| Earth (approx.) | μ preset | Altitude 400 km | 7.669 |
| Earth (approx.) | μ preset | Altitude 35,786 km | 3.075 |
| Moon (approx.) | μ preset | Altitude 100 km | 1.634 |
| Mars (approx.) | μ preset | Altitude 250 km | 3.427 |
Circular orbit velocity: concepts and data
1) What this velocity represents
Circular orbit velocity is the steady speed that keeps orbital distance constant. Gravity continuously pulls inward, while the spacecraft’s sideways motion prevents impact. It is a practical baseline even when real orbits are only near-circular. It also helps benchmark simulation outputs.
2) The governing physics
The calculator applies v = √(μ / r). Here μ = GM is the gravitational parameter, and r is the center-to-orbit radius. For Earth, μ ≈ 3.986×1014 m³/s² is commonly used in mission math.
3) Radius versus altitude
Altitude is measured above the surface, but the equation needs center distance. When you enter altitude, the tool converts using r = R + h. For Earth, a representative mean radius is about 6371 km, so a 400 km orbit uses r ≈ 6771 km.
4) Units and conversions
To avoid unit slips, μ is treated in m³/s² and radius in meters internally. You can input km, m, miles, or feet, and display velocity in m/s, km/s, ft/s, or mi/s. Presets auto-fill μ and a typical radius for the selected body.
5) Typical numbers you can compare
Low Earth orbit near 400 km is roughly 7.7 km/s. Geostationary radius is about 42,164 km with speed near 3.07 km/s. A low lunar orbit is about 1.6 km/s. A 250 km Mars orbit is around 3.4 km/s, depending on the model.
6) Relationship to escape velocity
At the same radius, escape velocity is vesc = √(2μ / r). That means v = vesc / √2. This is a fast check: if your circular speed is close to escape speed, the orbit radius is likely too small.
7) Where the result is used
Circular speed supports quick estimates for orbital period and transfer planning. Many Δv methods compare circular speeds at two radii before applying transfer equations. It is also useful for comparing how “fast” low orbits are around different planets or moons. Use it when building orbit tables.
8) Assumptions and accuracy limits
The equation assumes two-body motion and a spherical central body. Real trajectories include atmosphere, oblateness, and third-body effects, plus finite burns. Even so, circular velocity remains a strong first-order estimate and a reliable sanity check for inputs.
FAQs
1) What is μ and why is it used?
μ is the gravitational parameter, equal to G×M. It bundles constants into one value, making orbit equations simpler and numerically stable. Many references publish μ directly for planets and moons.
2) Should I enter altitude or radius?
Use altitude when you know height above the surface. Use radius when you already have the center-to-orbit distance. If you enter altitude, the calculator adds the body radius automatically.
3) Why does velocity decrease for higher orbits?
Gravity is weaker at larger radii, so less sideways speed is needed to “fall around” the body. In the equation, v scales as 1/√r.
4) Is this valid for elliptical orbits?
This tool is for circular orbits. For an ellipse, speed changes around the orbit and depends on semi-major axis and current radius. Use the vis-viva equation for elliptical cases.
5) How can I sanity-check my result?
For Earth low orbits, expect about 7–8 km/s. Geostationary speed is near 3.1 km/s. Also, circular speed should be about escape speed divided by √2 at the same radius.
6) What if I use a different μ value?
The result scales with √μ. If μ is 1% higher, velocity is about 0.5% higher. Small parameter differences are normal between reference models.
7) Does atmospheric drag change this speed?
Drag does not change the ideal circular speed for a given radius, but it removes energy, causing orbital decay. Maintaining altitude requires periodic thrust to counteract drag losses.