Practice question

Given: A planet orbits the Sun with a period of 7 years. If Earth’s orbital radius is 1.5 × 10¹¹m, what is its semi-major axis? These values define the system as per NCERT data. Formula: Kepler’s third law: T_p²/T_E² = a_p³/a_E³. This is standard NCERT relation. Substitution & Calculation: T_E = 1 year, T_p = 7 years, a_E = 1.5 × 10¹¹m . 7²/1² = fraca_p³(1.5 × 10¹¹)³ . 49 = fraca_p³³.375 × 10³³. a_p³ = 49 × 3.375 × 10³³= 1.65375 × 10³⁵. a_p = (1.65375 × 10³⁵)^{1/3 approx 5.49 × 10¹¹m . Result: The computed value matches expected outcome and confirms correct choice as per NCERT.