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To achieve a circular orbit rather than an elliptical one, the launch velocity must match the orbital velocity for a circular orbit at the desired altitude. This velocity is known as the *circular orbit velocity* or *orbital velocity*, and it is given by:

\[
v = \sqrt{\frac{GM}{r}}
\]

where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the central object (e.g., Earth),
- \( r \) is the distance from the center of the central object to the object in orbit.

In this context:
- If the launch velocity is less than this calculated velocity, the orbit will be elliptical with the launch point as the closest approach (perigee).
- If the launch velocity exceeds this orbital speed, the object will either enter a hyperbolic trajectory (if it's above escape velocity) or an elliptical orbit.

Do you want more details on the calculations, or have any specific questions?

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Here are five related questions:
1. What is the formula to calculate the escape velocity from Earth?
2. How does altitude affect the circular orbit velocity?
3. What role does gravitational constant \( G \) play in orbital mechanics?
4. How would orbital shape change if velocity is slightly less than the circular orbit velocity?
5. Can the circular orbit velocity vary if orbiting different planets?

**Tip:** For circular orbits, always match velocity to the gravitational pull for a balanced orbital path.

Which launch velocity will create a circular (rather than elliptical) orbit? (Adjust the launch velocity slider to achieve the desired result.)

Discover how to calculate the required launch velocity to achieve a circular orbit. This involves using the orbital velocity formula, v = √(GM/r), and understanding key concepts in orbital mechanics. Ideal for high school physics students.

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