Interactive physics simulator
Orbital Velocity
Orbital velocity is the exact speed needed to maintain a stable circular orbit around a massive central body. Learn how speed changes with altitude and planet mass.
Orbital Velocity Simulator
Animate satellites in stable circular orbits, study gravity fields, adjust launch altitudes, and trace speed vectors.
Live Telemetry
- Central Planet
- Earth
- Orbit Altitude
- 6,650 km
- Orbital Speed
- 7.67 km/s
- Escape Speed
- 10.85 km/s
- Orbital Period
- 92.7 min
- Centripetal Accel
- 8.70 m/s²
- Gravity Force
- Bound circular
- Launch Condition
- Stable circular
| Orbit Type | Altitude | Velocity | Period |
|---|---|---|---|
| LEO (Low Earth Orbit) | 400 km | 7.67 km/s | 92.7 min |
| MEO (Medium Earth Orbit) | 20,200 km | 3.87 km/s | 12.0 hours |
| GEO (Geostationary Orbit) | 35,786 km | 3.07 km/s | 24.0 hours |
What is Orbital Velocity?
Orbital velocity is the exact speed needed to maintain a stable circular orbit around a celestial body. Gravity acts as the centripetal force, pulling the satellite inward, while its forward inertia keeps it moving sideways. When these are perfectly balanced, the satellite falls in a circular path at a constant altitude.
Key Principles
Stable circular orbits rely on balanced forces:
- Gravitational force supplies the centripetal force.
- Speed does not depend on satellite mass.
- Higher orbits require lower speeds.
- Orbital speed is perpendicular to gravitational acceleration.
- A circle is a special orbit case where eccentricity is zero.
Orbital Velocity Formula
Variables:
- vorb = circular orbital speed (m/s)
- G = Gravitational Constant (6.6743 × 10-11 N·m²/kg²)
- M = Mass of the central attractor (kg)
- r = Orbit radius from center (R + altitude) (m)
Earth Orbit Regimes
| Regime | Altitude Range | Typical Speed | Orbital Period |
|---|---|---|---|
| LEO (Low) | 160 – 2,000 km | ~7.8 km/s | ~90 – 120 mins |
| MEO (Medium) | 2,000 – 35,786 km | ~3.9 km/s | ~2 – 12 hours |
| GEO (Geostationary) | 35,786 km | 3.07 km/s | exactly 24 hours |
Solved Examples
Calculate the circular orbital velocity of a satellite orbiting Earth at an altitude of 400 km (like the ISS). Earth mass M = 5.972 × 1024 kg and radius R = 6,371 km.
- Convert orbital radius to meters: r = R + altitude = 6,371 km + 400 km = 6,771 km = 6.771 × 106 m.
- Identify G: G = 6.6743 × 10-11 N·m²/kg².
- Use the circular orbital velocity formula: vorb = √(GM/r).
- Substitute values: vorb = √((6.6743 × 10-11 × 5.972 × 1024) / (6.771 × 106)).
- Calculate the term inside the root: GM/r ≈ 5.887 × 107 m²/s².
- Take the square root: vorb ≈ 7,673 m/s = 7.67 km/s.
Answer: vorb ≈ 7.67 km/s (approx. 27,600 km/h)
A satellite is orbiting Jupiter at an altitude equal to Jupiter’s radius. Find its orbital velocity. Jupiter mass M = 1.898 × 1027 kg and radius R = 69,911 km.
- Calculate orbital radius from the center: r = R + R = 2R = 2 × 69,911 km = 139,822 km = 1.39822 × 108 m.
- Use vorb = √(GM/r).
- Substitute values: vorb = √((6.6743 × 10-11 × 1.898 × 1027) / (1.39822 × 108)).
- Calculate GM/r ≈ 9.060 × 108 m²/s².
- Take the square root: vorb ≈ 30,100 m/s = 30.1 km/s.
Answer: vorb ≈ 30.1 km/s
Determine the orbital period of a weather satellite orbiting Earth at an altitude of 35,786 km (Geostationary orbit, radius r ≈ 42,164 km).
- Use the period formula: T = 2πr / vorb, or Kepler’s Third Law: T = 2π√(r³ / GM).
- First find orbital speed: vorb = √(GM / r) = √((3.986 × 1014) / (4.2164 × 107)) ≈ 3,075 m/s = 3.075 km/s.
- Calculate period: T = (2 × 3.14159 × 4.2164 × 107) / 3,075 ≈ 86,164 seconds.
- Convert to hours: 86,164 s / 3,600 ≈ 23.93 hours (which is exactly 1 sidereal day, matching Earth’s rotation).
Answer: T ≈ 24 hours
Common Misconceptions
- Thinking heavier satellites require higher circular orbit speeds (mass cancels out).
- Using altitude directly for the radius r instead of adding the planet's radius.
- Assuming there is no gravity in space (gravity keeps them in orbit; weightlessness is due to free fall).
- Confusing circular orbital velocity with escape velocity.
Kepler's Third Law
By equating gravity to circular acceleration, we find the orbital period T:
This shows that the square of the orbital period is proportional to the cube of the orbital radius, meaning outer satellites take significantly longer to complete an orbit.
Practice Questions
1. How does satellite mass affect circular orbital velocity?
Circular orbital velocity is completely independent of the satellite mass. The mass cancels out because gravitational force and required centripetal force are both directly proportional to the satellite mass.
2. If a satellite’s orbital radius is doubled, what happens to its speed?
Since vorb is proportional to 1/√r, doubling the radius reduces the speed by a factor of √2, meaning the new speed is about 70.7% of the original speed.
3. What keeps a satellite from falling down due to gravity?
The satellite is actually constantly falling toward Earth, but its forward tangential velocity is so high that as it falls, the Earth’s surface curves away at the same rate. Hence, it remains at a constant altitude.
4. How is circular orbital velocity related to escape velocity?
At any given radius, the escape velocity is exactly √2 times the circular orbital velocity: vesc = √2 × vorb ≈ 1.414 × vorb.
FAQ
Frequently Asked Questions
What is orbital velocity?
Orbital velocity is the minimum speed an object must maintain to stay in a stable circular orbit around a central body like a planet or star without falling or flying away.
What is the formula for circular orbital velocity?
The formula is vorb = √(GM/r), where G is the gravitational constant, M is the mass of the central attractor, and r is the orbital radius from the center of the body.
Does orbital velocity depend on the mass of the satellite?
No. In the orbital formula, the mass of the satellite cancels out because gravity and centripetal forces are both proportional to the satellite's mass. It depends only on the central attractor's mass and the orbit radius.
How does orbital velocity change with altitude?
Orbital velocity decreases as altitude increases. Since the orbital radius r is in the denominator of √(GM/r), a larger distance from the center of mass results in a lower speed needed to balance gravity.
What is the relationship between orbital velocity and escape velocity at the same radius?
At the same radius, the escape velocity is exactly √2 (about 1.414) times the circular orbital velocity: vesc = √2 * vorb. Thus, escape velocity requires 41.4% more speed than circular orbit speed.
What is the orbital speed of the International Space Station (ISS)?
The ISS orbits at an altitude of about 400 km. Substituting Earth's mass and its radius plus 400 km altitude into the formula gives an orbital velocity of approximately 7.67 km/s (about 27,600 km/h).
What happens if a satellite's speed is slightly less than circular orbital velocity?
If the speed is less than circular orbital velocity but still above a threshold, the orbit becomes elliptical, with the launch point as the highest point (apogee). If it is too low, the satellite falls into the atmosphere and crashes.
What happens if a satellite's speed is greater than circular orbital velocity?
If the speed is greater than circular orbital velocity but less than escape velocity, the satellite enters an elliptical orbit, with the launch point as the closest point (perigee).
Why do satellites in higher orbits take longer to complete one orbit?
Satellites in higher orbits take longer because they travel at a slower orbital velocity, and they have a much longer distance to cover. This is described by Kepler's Third Law (T² is proportional to r³).
Is a satellite in orbit in free fall?
Yes. A satellite is in a continuous state of free fall toward the Earth, but because of its high sideways orbital velocity, the Earth's surface curves away at the same rate the satellite falls, keeping it in orbit.
What is a geostationary orbital velocity?
A geostationary satellite orbits Earth at an altitude of 35,786 km (radius ~42,164 km) directly above the equator. At this distance, its orbital velocity is about 3.07 km/s, which matches Earth's rotation period of exactly 24 hours.
How does the orbital velocity simulator work?
The simulator calculates vorb = √(GM/r) based on the selected planet mass and altitude, and visualizes the circular path, velocity vector tangent to the path, and centripetal acceleration pointing inward.