To find the semi-major axis of the planet’s orbit, we can use Kepler's Third Law in its general form, which relates the orbital period of a planet to the mass of the star it orbits:

$T^2 = \frac{4 \pi^2 a^3}{G M}$

Where:

• $T$ is the orbital period of the planet (130 days, which we'll convert to seconds),
• $a$ is the semi-major axis (what we're solving for),
• $G$ is the gravitational constant ($6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}$),
• $M$ is the mass of the star ($1.1 \times 10^{30} \, \text{kg}$).

Steps:

1. Convert the orbital period $T$ from days to seconds.
2. Rearrange the equation to solve for the semi-major axis $a$.
3. Plug in the values and solve for $a$.

Let’s go through the calculations.The semi-major axis of the planet’s orbit is approximately $6.17 \times 10^{10}$ meters, or 61.7 million kilometers.

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:

1. How does Kepler’s Third Law change for planets orbiting different stars?
2. What is the significance of the semi-major axis in orbital mechanics?
3. How do you convert the semi-major axis from meters to astronomical units (AU)?
4. What factors influence the orbital period of a planet?
5. How would the semi-major axis change if the mass of the star were larger?

Tip: Kepler's Third Law is highly useful in astrophysics to estimate distances in space when the orbital period is known.