The planet has an orbital period of 130 days and the star has a mass of 1.1 x 1030 kg. What is the
semi-major axis of the planet’s orbit?

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.

The planet has an orbital period of 130 days and the star has a mass of 1.1 x 10^30 kg. What is the semi-major axis of the planet’s orbit?

Learn how to calculate the semi-major axis of a planet's orbit using Kepler's Third Law. This astrophysics problem involves the orbital period of 130 days and a star's mass of 1.1 x 10^30 kg. Step-by-step solution provided for students in Grades 10-12 or college-level physics courses.

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