Formula and Method for Earth Orbit Calculations
A satellite, moon, or spacecraft in a stable circular orbit around Earth is held on its path by the balance between Earth's gravitational pull and the centripetal force needed to keep it moving in a circle. Setting Newton's law of gravitation equal to the centripetal force equation and solving for velocity gives the orbital speed required at any given distance from Earth's center. Combining that speed with the orbit's circumference gives the orbital period — the time for one full revolution. This calculator uses those two relationships, plus Earth's radius, to convert an altitude above the surface into orbital radius, orbital velocity, orbital period, and revolutions per day.
Deriving orbital velocity and period
For an object of mass m orbiting at radius r from Earth's center (mass M⊕), gravity supplies the centripetal force: GM⊕m / r² = mv² / r. The orbiting object's mass cancels out, leaving the circular orbital velocity v = √(GM⊕ / r). Since the orbit's circumference is 2πr, the orbital period is T = 2πr / v, which simplifies to T = 2π√(r³ / GM⊕) — a special case of Kepler's third law for a circular orbit. Here GM⊕ = 398,600.4418 km³/s² is Earth's standard gravitational parameter, and r is the orbital radius (altitude plus Earth's radius), not the altitude alone.
Working with altitude, radius, and units
- Always add Earth's radius to the altitude before computing velocity or period — using the altitude alone as "r" is the most common mistake and gives badly wrong results.
- Earth is not a perfect sphere: use the equatorial radius (6,378.137 km) for orbits referenced from the equator, the polar radius (6,356.752 km) for polar orbits, or the mean radius (6,371 km) for a general-purpose estimate.
- This calculator assumes a circular orbit. For an elliptical orbit, replace r with the semi-major axis a to get the period (Kepler's third law still holds), but the instantaneous velocity varies with position and requires the vis-viva equation instead of v = √(GM⊕/r).
Real-world orbit examples
Low Earth Orbit (LEO) satellites, including the International Space Station near 400 km altitude, complete an orbit in roughly 90 minutes. GPS satellites fly in medium Earth orbit (MEO) near 20,200 km altitude with a period close to 12 hours. Geostationary satellites sit near 35,786 km altitude, where the orbital period matches Earth's 23-hour-56-minute sidereal rotation, so the satellite appears to hang fixed over one point on the equator.
Frequently Asked Questions
What formula does the Earth Orbit Calculator use?
Why does the calculator add Earth's radius to the altitude?
Does this calculator work for elliptical orbits, like the Moon's?
How high does the ISS orbit, and how long does one orbit take?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |