Question

1. The asteroid 128 Nemesis has an orbital radius of 2.751 AU. What is the orbital period of 128 Nemesis in years? 

   2. The asteroid 372 Palma has an orbital period of 5.585 years. How far away from the Sun is 372 Palma in astronomical units? 

Answer 1

1. To calculate the orbital period of an asteroid, you can use Kepler's third law, which relates the orbital period (T) to the semi-major axis of the orbit (a) using the following formula:

${�}^2={�}^3$

Where:

• $�$ is the orbital period in years.

• $�$ is the semi-major axis in astronomical units (AU).

For asteroid 128 Nemesis with an orbital radius of 2.751 AU, we can calculate its orbital period as follows:

${�}^2=(2.751\text{AU}{)}^3$

${�}^2=20.027{\text{AU}}^3$

Now, take the square root of both sides to find $�$:

$�=\sqrt{20.027}\text{years}$

Calculating this, we get:

$�\approx 4.48\text{years}$

So, the orbital period of asteroid 128 Nemesis is approximately 4.48 years.

2. To find the distance of asteroid 372 Palma from the Sun in astronomical units (AU), you can use Kepler's third law as well. Given that the orbital period ($�$) of 372 Palma is 5.585 years, you can rearrange the formula to find $�$:

$�=\sqrt[3]{{�}^2}$

Substitute the given orbital period into the formula:

$�=\sqrt[3]{(5.585\text{years}{)}^2}$

$�=\sqrt[3]{31.132225{\text{years}}^2}$

Now, calculate the cubic root:

$�=3.61904\text{AU}$

So, the distance of asteroid 372 Palma from the Sun is approximately 3.62 astronomical units.