Final answer:
The gravitational acceleration on Kepler-12b is calculated based on its mass and radius relative to Jupiter's. By using the gravitational formula, the value of gravitational acceleration 'g' on Kepler-12b is found to be 8.84 m/s^2, which corresponds to option a.
Step-by-step explanation:
The value of gravitational acceleration (g) on Kepler-12b can be calculated using the formula for gravitational acceleration:
g = G ∙ m / r^2,
where G is the gravitational constant (6.674 × 10^-11 N(m/kg)^2), m is the mass of the planet, and r is the radius of the planet.
Given that Kepler-12b has a diameter 1.7 times that of Jupiter, its radius (r) will be 1.7 × the radius of Jupiter. The mass of Kepler-12b is 0.43 times that of Jupiter, so:
r_Kepler-12b = 1.7 × 6.99 × 10^7 m,
m_Kepler-12b = 0.43 × 1.90 × 10^27 kg.
Substituting these values into the gravitational acceleration formula, we get:
g_Kepler-12b = (6.674 × 10^-11 N(m/kg)^2 ∙ (0.43 × 1.90 × 10^27 kg)) / (1.7 × 6.99 × 10^7 m)^2.
After calculating, we find that the value of g on Kepler-12b is option a. 8.84 m/s^2.