Question

below you will find the data for five ffictional asteroids/comets. using your model on the previous page, complete the table. you will need to cross reference with your solar system objects data table, and might need to covert au into kilometers and vice versa (though your model may allow you to avoid this step)!!
which of the above objects is at risk of colliding with earth. support your claim with numeric evidence.

Explanation:

Step1: Convert AU to kilometers

We know that \(1\ AU = 149.6\) million kilometers.
For Piranesi:

• Perihelion distance \(d_{p}=0.92\times149.6 = 137.632\) million kilometers
• Aphelion distance \(d_{a}=3.0\times149.6=448.8\) million kilometers

For Hav:

• Perihelion distance \(d_{p}=0.40\times149.6 = 59.84\) million kilometers
• Aphelion distance \(d_{a}=0.67\times149.6 = 100.232\) million kilometers

For Princeps:

• Perihelion distance \(d_{p}=0.57\times149.6=85.272\) million kilometers

Earth's distance from the Sun is approximately \(149.6\) million kilometers.

Step2: Check for overlap in orbital distances

Piranesi's orbital range (\(137.632 - 448.8\) million kilometers) includes Earth's orbital distance (\(149.6\) million kilometers).
Hav's orbital range (\(59.84 - 100.232\) million kilometers) does not include Earth's orbital distance.
Gethen:

• Convert distances:
• \(1701.7\) million kilometers \(= 1701.7\div149.6\approx11.37\ AU\)
• \(5086.4\) million kilometers \(=5086.4\div149.6\approx34\ AU\) (Kuiper - belt region, far from Earth)

Minotaur 2000:

• \(414.7\div149.6\approx2.77\ AU\) (Jupiter - Trojan region, far from Earth)

Princeps:

• Aphelion is in the Oort - cloud (\(2347\ AU\)), but perihelion (\(85.272\) million kilometers) is less than Earth's \(149.6\) million kilometers, but the large aphelion makes it a long - period comet, but the key is the perihelion - aphelion range for collision risk.

Answer:

Piranesi is at risk of colliding with Earth. Its perihelion distance is \(0.92\ AU\approx137.632\) million kilometers and aphelion distance is \(3.0\ AU\approx448.8\) million kilometers. Since Earth's distance from the Sun is \(1\ AU = 149.6\) million kilometers, and \(137.632\lt149.6\lt448.8\), Piranesi's orbital path can intersect with Earth's orbital path.