The mass of the Sun is 2 times 10 to the 30th power kilograms , and the mass of Saturn is 5 point 6 8 times 10 to the 26th power kilograms The distance between Saturn and the Sun is 9 point 5 8 AU Veronica is solving the equation to calculate the orbital period of Saturn, but there is an error in the equation. cap t is equal to square root of open paren the fraction with numerator 4 mathrm pi squared and denominator open paren 6 point 6 7 times 10 to the negative 11 power mathrm the fraction with numerator Nm squared and denominator kg squared close paren times open paren 2 times 10 to the 30th power mathrm kg close paren close paren times open paren 9 point 5 8 mathrm AU close paren cubed end root What should Veronica change to correct the equation?
Answer
A
change the position of 2 times 10 to the 30th power kilograms and 9 point 5 8 AU
B
change 9 point 5 8 AU to the distance in meters
C
change 2 times 10 to the 30th power kilograms to 5 point 6 8 times 10 to the 26th power kilograms
D
change the square root to a cube root
Explanation
The orbital-period formula is T = √(4π²r³/GM), where r must be measured in meters when using G = 6.67 × 10⁻¹¹ N·m²/kg². The equation uses Saturn’s distance as 9.58 AU, so Veronica should convert that distance to meters before substituting it. The Sun’s mass belongs in the formula, and the square root is correct.
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