use the equation $t = a^{3/2}$ to compute an unknown orbital period or distance

you used a telescope and other mathematics to discover that jupiter is 5.20 au from the sun. use the equation to find its orbital period. round to the nearest tenth of a year.

jupiters orbit: years

Question

use the equation $t = a^{3/2}$ to compute an unknown orbital period or distance

you used a telescope and other mathematics to discover that jupiter is 5.20 au from the sun. use the equation to find its orbital period. round to the nearest tenth of a year.

jupiters orbit:   years

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Keplers Third Law", "Rational Exponents" ], "new_concepts": [], "current_concepts": [ "Keplers Third Law", "Rational Exponents" ] } ## Identify given values and formula Using the *Keplers Third Law* and *Rational Exponents* knowledge points $$ \begin{aligned} &A = 5.20\text{ au}\ &T = A^{3/2} \end{aligned} $$ ## Calculate the orbital period Using the *Rational Exponents* knowledge point $$ \begin{aligned} &T = (5.20)^{3/2}\ &T = \sqrt{(5.20)^3}\ &T = \sqrt{140.608}\ &T \approx 11.8578 \end{aligned} $$ ## Round to the nearest tenth Using the *Rational Exponents* knowledge point $$ T \approx 11.9\text{ years} $$ You used a telescope and other mathematics to discover that Jupiter is 5.20 au from the sun. Use the equation to find its orbital period. Round to the nearest tenth of a year. Jupiter's Orbit: 11.9 years { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Keplers Third Law" ] }

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Question

Explanation:

Identify given values and formula

Calculate the orbital period

Round to the nearest tenth

Answer: