Question

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

Answer 1

To determine Saturn's orbital period in Earth years, we can use the equation t² = (4π² / g * ms) * d³, where t is the orbital period, g is the gravitational constant, ms is the mass of the Sun, and d is the distance between Saturn and the Sun.

Step-by-step explanation:

To determine Saturn's orbital period in Earth years, we can use the equation t² = (4π² / g * ms) * d³, where t is the orbital period, g is the gravitational constant, ms is the mass of the Sun, and d is the distance between Saturn and the Sun. We are given the distance as 1.43 × 1012 m and the mass of the Sun as 1.99 × 1030 kg.

Substituting the values into the equation, we have t² = (4π² / (6.67 × 10-11 N·m2/kg2) * (1.99 × 1030 kg)) * (1.43 × 1012 m)3. We can solve for t by taking the square root of both sides of the equation.

t = √((4π² / (6.67 × 10-11 N·m2/kg2) * (1.99 × 1030 kg)) * (1.43 × 1012 m)3)

Calculating the expression gives us the orbital period of Saturn in Earth years.