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PhysicsMechanicsIntermediateStarter track

Concept module

Circular Orbits and Orbital Speed

See why a circular orbit needs the right sideways speed, how gravity supplies the centripetal acceleration, and how source mass and radius together set orbital speed and period on one bounded live model.

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Starter track

Step 3 of 50 / 5 complete

Gravity and Orbits

Earlier steps still set up Circular Orbits and Orbital Speed.

1. Gravitational Fields2. Gravitational Potential and Potential Energy3. Circular Orbits and Orbital Speed4. Kepler's Third Law and Orbital Periods+1 more steps

Previous step: Gravitational Potential and Potential Energy.

Start from track beginning

Why it behaves this way

Explanation

A circular orbit is not a place where gravity turns off. It is a special free-fall case where gravity already points inward and the sideways speed is exactly the value that keeps the radius from shrinking or growing.

This bounded lab keeps one source mass, one chosen reference radius, one speed factor, one live path, and the linked radius, speed, and acceleration-balance graphs on the same state. That makes the orbit condition honest: gravity supplies the centripetal acceleration, and the circular speed changes whenever you change source mass or radius.

Key ideas

01For a circular orbit at radius r, gravity itself is the centripetal acceleration: M/r^2 = v^2/r in the displayed units with G = 1.
02At one chosen radius, a speed below the circular value lets gravity bend the path inward, while a speed above the circular value lets the path open outward.
03The circular-orbit speed grows with source mass and falls with larger radius, while the circular period grows strongly with radius and shortens for heavier source mass.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
Use the same source mass, reference radius, speed factor, and current orbit state already on screen. The examples stay tied to the live bench instead of swapping to a detached answer key.

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View plans
Frozen valuesUsing frozen parameters

For the current source mass and chosen reference orbit radius, what circular speed keeps the orbit circular?

Source mass

4 kg

Reference orbit radius

1.6 m

1. Start from the circular-orbit balance

Set gravity equal to the needed centripetal acceleration: .

2. Solve for the circular speed

That gives in the displayed units.

3. Compute the live circular speed

So the circular-orbit speed is , with and for that same reference circle.

Required circular speed

The circular speed here comes from the shared gravity-and-turning balance rather than from a separate orbit rule.

Orbit-balance checkpoint

Start from the right side of the dashed reference circle. If the speed factor is set below 1, should the next part of the path stay on the circle, drift outside it, or bend inside it?

Make a prediction before you reveal the next step.

Answer before you press the too-slow preset: is gravity now too weak, too strong, or just right for the turning requirement?

Check your reasoning against the live bench.

It bends inside the dashed circle because the chosen speed is too small for a circular orbit at that radius.
At fixed radius, lowering the speed lowers . Gravity is then stronger than the inward acceleration needed for a circular turn, so the path curves inward.

Common misconception

A satellite in orbit is floating because gravity is basically absent there.

Orbit still needs gravity. The gravitational pull is the inward acceleration that keeps the path curved instead of straight.

What changes is not whether gravity exists, but whether the sideways speed matches the circular-orbit requirement at that radius.

Quick test

Reasoning

Question 1 of 4

Answer from the linked orbit state, not from detached formulas. Each question checks whether you can read circular-orbit balance honestly from the bench.

At one chosen circular-orbit radius, the actual speed is lower than the circular value. What should happen first?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows one fixed source mass at the center of the stage, a moving satellite launched from the right side of a chosen reference radius, and optional overlays for the dashed reference orbit, the live radius line, the tangent velocity vector, the inward gravity vector, and the trajectory trail.

Changing source mass, reference orbit radius, or speed factor updates the same orbit path, live readouts, and linked graphs together. Compare mode overlays a second setup without switching to a separate orbit model.

The displayed units use a bounded one-source gravity model with G = 1. A minimum sample radius keeps the stage and graphs finite and readable while preserving the correct inward and inverse-square trends.

Graph summary

The radius-history graph compares the live radius with the chosen circular reference radius over time. Hovering or scrubbing the graph previews the same instant on the orbit stage.

The speed-history graph compares the live speed with the circular speed required at the current radius, and the acceleration-balance graph compares gravity with the turning requirement v squared over r on that same live path.