Earth Orbit Calculator
Calculate orbital period, velocity, and altitude for satellites orbiting Earth using Kepler's laws.
Earth Orbit Calculations
Satellites in circular low Earth orbit follow Kepler's laws. Given altitude above Earth's surface, you can find orbital period and velocity using the standard gravitational parameter for Earth.
Orbital Formulas
$$T = 2\pi\sqrt{\frac{a^3}{GM}}$$ $$v = \sqrt{\frac{GM}{r}}$$For a circular orbit, semi-major axis \(a\) equals orbital radius \(r = R_\text{Earth} + h\). We use \(GM = 3.986 \times 10^{14}\,\text{m}^3/\text{s}^2\) and \(R_\text{Earth} = 6{,}371\,\text{km}\).
Example: the ISS at 408 km altitude has \(r \approx 6{,}779\,\text{km}\), period about 92.6 minutes, and velocity near 7.67 km/s.
Low Earth Orbit Context
LEO typically spans 160–2,000 km altitude. Below about 160 km, atmospheric drag decays orbits quickly. Geostationary orbit sits near 35,786 km with a 24-hour period.
Frequently Asked Questions
What is GM for Earth?
The standard gravitational parameter is \(GM = 3.986 \times 10^{14}\,\text{m}^3/\text{s}^2\). It combines Earth's mass and the gravitational constant.
Why assume a circular orbit?
Circular orbit is the simplest case where \(a = r\). Elliptical orbits need eccentricity and perigee/apogee inputs.
How fast is the ISS?
At roughly 408 km altitude, orbital velocity is about 7.66 km/s (27,600 km/h) with a period near 92 minutes.
Does orbital speed depend on satellite mass?
No. For a given altitude, all satellites share the same orbital velocity — a consequence of Kepler's third law.
What altitude is geostationary orbit?
About 35,786 km above the equator, where the orbital period matches Earth's rotation (24 hours).
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