Satellite Speed Calculator
Calculate the orbital speed of a satellite at any altitude above Earth. Enter values for instant results with step-by-step formulas.
Formula
v = sqrt(GM/r)
Orbital speed v equals the square root of the gravitational constant G times the central body mass M divided by the orbital radius r (center of body to satellite). The orbital period T = 2*pi*r/v. Escape velocity = sqrt(2) times the orbital speed.
Worked Examples
Example 1: International Space Station Orbital Speed
Problem: Calculate the orbital speed and period of the ISS at 408 km altitude above Earth.
Solution: G = 6.674 x 10^-11, M(Earth) = 5.972 x 10^24 kg\nr = 6,371,000 + 408,000 = 6,779,000 m\nv = sqrt(GM/r) = sqrt(6.674e-11 x 5.972e24 / 6,779,000)\nv = sqrt(5.878e7) = 7,667 m/s = 27,601 km/h\nPeriod = 2*pi*r/v = 2 x 3.14159 x 6,779,000 / 7,667\nT = 5,553 seconds = 92 minutes 33 seconds\nOrbits per day = 86,400 / 5,553 = 15.56
Result: Speed: 7,667 m/s (27,601 km/h) | Period: 92.5 min | 15.56 orbits/day
Example 2: Mars Reconnaissance Orbiter
Problem: Calculate the orbital speed of a satellite at 300 km altitude above Mars (M = 6.417 x 10^23 kg, R = 3,389.5 km).
Solution: r = 3,389,500 + 300,000 = 3,689,500 m\nv = sqrt(GM/r) = sqrt(6.674e-11 x 6.417e23 / 3,689,500)\nv = sqrt(1.160e7) = 3,406 m/s = 12,262 km/h\nPeriod = 2*pi*r/v = 2 x 3.14159 x 3,689,500 / 3,406\nT = 6,806 seconds = 113 minutes 26 seconds
Result: Speed: 3,406 m/s (12,262 km/h) | Period: 113.4 min | 12.7 orbits/day
Frequently Asked Questions
How is the orbital speed of a satellite calculated?
The orbital speed of a satellite is calculated using the vis-viva equation simplified for circular orbits: v = sqrt(GM/r), where G is the gravitational constant (6.674 x 10^-11 N m^2/kg^2), M is the mass of the central body (5.972 x 10^24 kg for Earth), and r is the orbital radius measured from the center of the body (Earth's radius plus altitude). For the International Space Station at 408 km altitude, r = 6,371 + 408 = 6,779 km = 6,779,000 m. This gives v = sqrt(6.674e-11 x 5.972e24 / 6,779,000) = 7,661 m/s or about 27,580 km/h. The key insight is that orbital speed depends only on altitude and the central body's mass, not on the satellite's own mass.
What is escape velocity and how does it relate to orbital speed?
Escape velocity is the minimum speed an object must reach to break free from a celestial body's gravitational pull without further propulsion. It is calculated as v_esc = sqrt(2GM/r), which is exactly sqrt(2) (approximately 1.414) times the circular orbital speed at the same altitude. For Earth's surface, escape velocity is about 11,186 m/s (40,270 km/h), while orbital speed at the surface would theoretically be 7,910 m/s. At the ISS altitude of 408 km, escape velocity drops to about 10,834 m/s. This means a satellite already in orbit needs to increase its speed by only about 41.4% to escape the planet entirely. This mathematical relationship holds true for any altitude around any gravitationally bound body.
How are satellite orbits classified?
Low Earth Orbit (LEO) is 200-2,000 km altitude with 90-minute periods and is used for the ISS and imaging satellites. Medium Earth Orbit (MEO) at 2,000-35,786 km is used for GPS. Geostationary Orbit (GEO) at 35,786 km matches Earth's rotation for communication satellites. Sun-synchronous orbits pass over areas at the same local time.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
Is Satellite Speed Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.
Does Satellite Speed Calculator work offline?
Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.