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The formula calculates the radius of the first spherical body (R1) given the center-to-center distance (z), the distance between surfaces (r), and the radius of the second spherical body (R2). This is commonly used in physics and geometry problems involving spherical objects.
The calculator uses the formula:
Where:
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.
Details: Accurate radius calculation is crucial for determining the size and position of spherical objects in various applications, including astronomy, physics experiments, and engineering designs involving spherical components.
Tips: Enter all distances in meters. Ensure values are positive and physically meaningful (z > R1 + R2 + r). The calculator supports very small values (nanometer scale) for precision calculations.
Q1: What if the calculated R1 is negative?
A: A negative result indicates that the input values are inconsistent with the geometric constraints of two separate spheres. Verify that z > r + R2.
Q2: Can this formula be used for overlapping spheres?
A: No, this formula assumes the spheres are separate and not overlapping. For overlapping spheres, different geometric relationships apply.
Q3: What units should I use?
A: The calculator uses meters, but you can use any consistent unit system as long as all inputs are in the same units.
Q4: How precise are the calculations?
A: The calculator provides results with 9 decimal places precision, suitable for most scientific and engineering applications.
Q5: Can this be used for non-spherical objects?
A: No, this formula is specifically designed for perfect spherical bodies. For other shapes, different geometric formulas must be used.