Question

Saturn orbits the sun at a distance of 1.43 × 10¹² m. The mass of the sun is 1.99 × 10³⁰ kg. Use the equation t² = (4π²/G)(Ms)(d³) to determine Saturn's orbital period in Earth years.

Answer 1

By substituting the given values into the equation for orbital period, the orbital period can be determined and then converted into Earth years to find out how long it takes for Saturn to orbit the Sun.

Step-by-step explanation:

Calculating Saturn's orbital period in Earth years using the given equation t² = (4π²/G)(Ms)(d³) requires substituting the values for G (the gravitational constant), Ms (the mass of the Sun), and d (the distance of Saturn from the Sun). The given values are Ms = 1.99 × 10³° kg and d = 1.43 × 10¹² m. Using these, we can solve for t, which represents the orbital period. Although not provided directly in the question, G is a known constant (6.674× 10⁻¹¹ m³ kg⁻¹ s⁻¹). By calculating the value of t and converting it into Earth years, we can determine Saturn's orbital period around the Sun.