Jupiter's equatorial radius \(\left(R_{\text {Jup }}\right)\) is \(71,500 \mathrm{km}\), and its oblateness is \(0.065 .\) What is Jupiter's polar radius \(\left(R_{\text {Polar }}\right) ?\) (Oblateness is given by \(\left[R_{\text {Jup }}-R_{\text {Polar }}\right] / R_{\text {Jup }}\).)

Jupiter's shape is not a perfect sphere; it bulges at the equator due to its rapid rotation. This difference in shape is called *oblateness*. Oblateness is a measure of how much a planet's shape differs from a perfect sphere.

The formula to calculate oblateness is:
\[ \text{Oblateness} = \frac{R_{\text{Jup}} - R_{\text{Polar}}}{R_{\text{Jup}}} \] Where \( R_{\text{Jup}}\) is the equatorial radius, and \( R_{\text{Polar}}\) is the polar radius. This tells us how much wider the planet is at the equator compared to the poles. On Jupiter, the equatorial radius is clearly larger because of this bulging effect.

Understanding oblateness helps scientists learn about a planet's rotation and internal structure, which is crucial for understanding its overall behavior and formation.

A planet's radii include the equatorial and polar radii, which can be different for some planets. The equatorial radius \( R_{\text{Jup}} \) refers to the radius measured around the planet's equator, while the polar radius \( R_{\text{Polar}} \) is measured from the center to the poles.

For Jupiter, the equatorial radius is \( 71,500 \text{ km} \). This is the starting point for our calculation. If we're given the oblateness (like in our example, \( 0.065 \)), we can use it to find the polar radius through the mentioned mathematical relationship.

It's important to understand that due to the planet's rotation, the equatorial radius will often be larger because the planet is 'flattened' at the poles and 'bulged' at the equator.

Using mathematical formulas is essential in planetary science to derive one parameter from another. In our example, we needed to rearrange the oblateness formula to solve for the polar radius.

Starting with the oblateness formula: \[ \text{Oblateness} = \frac{R_{\text{Jup}} - R_{\text{Polar}}}{R_{\text{Jup}}} \] we rearranged it to isolate \( R_{\text{Polar}} \):
\[ R_{\text{Polar}} = R_{\text{Jup}} - (\text{Oblateness} \times R_{\text{Jup}}) \]
This step-by-step approach makes it easier to substitute the given values and make the calculations.

• We first compute the term involving oblateness.
• Then, subtract it from the equatorial radius to find the polar radius.

For Jupiter, the result was significant: \[ R_{\text{Polar}} = 71,500 \text{ km} - 4,647.5 \text{ km} = 66,852.5 \text{ km} \] This method ensures accuracy and systematic problem-solving.