Radius Of Spherical Body 2 Given Center-To-Center Distance Calculator

Formula Used:

\[ R2 = z - r - R1 \]

Center-to-center Distance (z):

Distance Between Surfaces (r):

Radius of Spherical Body 1 (R1):

Radius of Spherical Body 2 (R2):

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1. What is the Radius of Spherical Body 2 Formula?

The formula calculates the radius of a second spherical body (R2) given the center-to-center distance (z), the distance between surfaces (r), and the radius of the first spherical body (R1). This is commonly used in physics and geometry problems involving spherical objects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R2 = z - r - R1 \]

Where:

\( z \) — Center-to-center distance between the two spherical bodies (m)
\( r \) — Distance between the surfaces of the two spherical bodies (m)
\( R1 \) — Radius of the first spherical body (m)
\( R2 \) — Radius of the second spherical body (m)

Explanation: The formula derives from the geometric relationship between two spheres, where the center-to-center distance equals the sum of both radii plus the distance between their surfaces.

3. Importance of Radius Calculation

Details: Calculating the radius of spherical bodies is crucial in various scientific and engineering applications, including astronomy, particle physics, material science, and mechanical design where spherical objects interact.

4. Using the Calculator

Tips: Enter all distances in meters. Ensure values are positive and physically meaningful (z must be greater than or equal to R1 + r).

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: The calculator uses meters (m) for all distance measurements. Convert other units to meters before calculation.

Q2: Can this formula be used for non-spherical objects?
A: No, this formula specifically applies to perfect spherical bodies. For other shapes, different geometric relationships apply.

Q3: What if the calculated R2 is negative?
A: A negative result indicates invalid input values where z is less than the sum of R1 and r, which is physically impossible for separate spheres.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect spheres. Accuracy depends on the precision of your input measurements.

Q5: Can this be used for astronomical calculations?
A: Yes, this formula can be applied to celestial bodies, though astronomical distances are typically much larger and may require scientific notation.