Orbital Velocity
v = √(GM/r) for a circular orbit
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Orbital Velocity is built for v = √(GM/r) for a circular orbit — fast, free, and private. Drop Central Mass (kg) and Altitude (km) into Orbital Velocity — the figure refreshes as you type. Every Orbital Velocity answer can be reproduced by hand. Anyone comparing options in Science can use Orbital Velocity to compare scenarios. No sign-up is needed for Orbital Velocity. The math runs on your device. Orbital Velocity handles orbital velocity calculator satellite earth the same way as free online orbital velocity calculator — one of the Science tools on CalcProMaster. Orbital Velocity goes from question to answer fast. Start with Orbital Velocity; the first number takes seconds.
What does the Orbital Velocity do?
Orbital Velocity works out the √(gm/r) from the Central Mass and Altitude, using Science conventions. With the defaults, orbital velocity gives a √(gm/r) of v = 7671.03 m/s.
- Inputs: Central Mass and Altitude.
- Output: the √(gm/r), with the working that produced it.
- Method: Science conventions applied in sequence, with the √(gm/r) produced by local arithmetic.
Quick answer
orbital velocity returns a √(gm/r) of v = 7671.03 m/s with the default inputs (central mass of 5,970,000,000,000,000,000,000,000, altitude of 400).
How does the Orbital Velocity work?
Orbital Velocity computes the √(gm/r) directly from your inputs — the Central Mass and Altitude feed the formula. All the work happens in your browser session and the √(gm/r) never leaves it.
How it works
Set the Central Mass and Altitude on Orbital Velocity to your own case and the √(gm/r) re-derives from scratch — no stored state and no cached figure from an earlier run.
How to use it
- Central Mass — read literally by the orbital velocity formula, so a placeholder produces a placeholder answer.
- Altitude — the field the rest of the orbital velocity case hangs on; revisit it to move the result.
- Read the last line first on the orbital velocity page — the √(gm/r) — then work upward until the number stops being surprising.
- Reopen Orbital Velocity with the share link and the same √(gm/r) returns, which is the easiest way to revisit a case later.
The formula behind the result
No coefficient in Orbital Velocity is tuned by guesswork: each term comes from the Science definition, and the steps name the term that produced each figure in the √(gm/r).
Worked example: with central mass of 5,970,000,000,000,000,000,000,000, altitude of 400, this orbital velocity calculation returns v = 7671.03 m/s. The same run reports Period: 1.54 hours.
The steps it follows:
- r = R_earth + altitude = 6.771e+6 m
- v = √(GM/r) = 7671.03 m/s
- Period = 2πr/v = 1.54 h
Understanding the result
If two result figures appear on the orbital velocity page, read the labels rather than assuming the bigger one is the headline.
Where it helps
The orbital velocity page comes up most for sizing a decision that cannot be undone, running a low case and a high case, and seeing whether a quoted number holds up — the recurring cases where a rough mental estimate tends to be off by enough to matter.
Common mistakes
Pasting a figure with a thousands separator or a currency symbol into Orbital Velocity is only harmless when the field expects it, so check the Central Mass and Altitude first.
Tip: Orbital Velocity returns v = 7671.03 m/s at its defaults; double the Central Mass (kg) and it returns v = 10848.48 m/s.
Assumptions and limitations
Inputs outside a reasonable range may produce a output from Orbital Velocity that is mathematically correct but practically implausible; the steps panel helps you spot that quickly.
Why use this calculator
Because a figure you cannot reproduce is a figure you cannot argue with, Orbital Velocity leaves the output standing on visible arithmetic.
Frequently Asked Questions
What does orbital velocity work out?
Use Orbital Velocity when the result needs to be right the first time: it evaluates your inputs against the standard Science method and shows the working, not just the answer. Because the Central Mass and Altitude never leave the tab, Orbital Velocity is safe to use with real figures rather than rounded ones.
How is the √(gm/r) worked out on this page?
The first steps are r = r_earth + altitude = 6.771e+6 m, then v = √(gm/r) = 7671.03 m/s. Change one input in the orbital velocity form and the formula re-runs from the start — there is no cached intermediate value that could carry a stale figure into the √(gm/r).
What has to be entered before Orbital Velocity produces a result?
The orbital velocity form needs Central Mass and Altitude, and computes the √(gm/r) from them.
How much does the Central Mass (kg) move the result?
At the defaults Orbital Velocity returns v = 7671.03 m/s; doubling Central Mass (kg) to 11,940,000,000,000,000,000,000,000 moves it to v = 10848.48 m/s.
What does the result from the Orbital Velocity represent?
The main number the orbital velocity returns is the √(gm/r) for your exact inputs. Rounding, regional convention, and local rules sit outside Orbital Velocity: the page applies the method as documented, and the √(gm/r) inherits whatever the inputs leave out.
What is the Orbital Velocity best used for?
Orbital Velocity earns its place in the Science toolkit wherever the √(gm/r) has to be explained, not just produced. Keep the Central Mass and Altitude in the order the steps list them when you re-run Orbital Velocity, so the step numbers line up with what you typed.
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