First Last - Homework #4



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import numpy as np

from astropy.table import QTable
from astropy import units as u
from astropy import constants as const

The dataset `PHA.cvs` contains data for 10 objects classified as potentially hazardous asteroids

Read in dataset PHA.csv
The columns for the dataset 'Objects.csv' are: Name, a, ecc, H, A



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Determine the speed of each of the PHAs at r = 1 AU.

Make sure you use units.
Express your answer SI units with 2 digits after the decimal.
Your output should be 10 lines that look like:
- The speed of [Name] at 1 AU would be [SPEED] [unit]



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Determine the kinetic energy each PHA whould have if they impacted the surface of the Earth

Express your answer in million of tons of TNT with 1 digit after the decimal
1 ton TNT $= 4.18 \times 10^9$ J.
Your output should be 10 lines that look like:
- The asteroid [Name] would hit the Earth with the energy of [X] million tons of TNT



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Determine how many 1 ton nuclear weapons will be needed to destroy each of the PHAs.

Assume $\rho$ = 3,000 kg/m$^3$
Express your answer in the number of 1 ton weapons with 1 digit after the decimal
Your output should be 10 lines that look like:
- It would take [X] 1 ton yield nuclear weapons to destory the asteroid [Name]



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Due Tue Oct 25 - 5pm

Make sure to change the filename to your name!
Make sure to change the Title to your name!
File -> Download as -> HTML (.html)
upload your .html and .ipynb file to the class Canvas page

Some Orbital Mechanics

Kepler's first law says: The orbit of every planet is an ellipse with the sun at one focus. The Semimajor axis a and the eccentricity ecc parametrize the size and shape of the ellipse. The units of a in our dataset are Astronomical Units (AU), the average distance between the Sun and the Earth.

For a closed elliptical orbit (orbits gravitationally bound to the Sun), $ecc = \sqrt{1 - {b^2}/{a^2}}$, where a and b are the semimajor and semiminor axes. As you can see from the equation, when a = b, ecc = 0 (a circle), and when a $>>$ b, ecc approaches 1. When ecc = 1, the orbit is a parabolic orbit (just bound). When ecc $>$ 1 the orbit is a hyperbolic orbit (unbound).

The speed of an object on an elliptical orbit around the Sun at a distance r from the Sun is:

$$ \large v\ =\ \sqrt{GM_{\odot}\ \left(\frac{2}{r} - \frac{1}{a}\right)} $$

Encountering the Earth

The encounter speed of an asteroid meeting the Earth at 1 AU is (assuimg aligned prograde orbits):

$$ \large V_{\textrm{encounter}}\ =\ V_{\textrm{asteroid at 1AU}}\ -\ V_{\textrm{Earth}} $$

Where $V_{\textrm{Earth}}\ =\ 30\ \textrm{km/s}$

Hitting the Earth

The impact speed of an asteroid hitting the Earth is:

$$ \large V_{\textrm{impact}}\ =\ \sqrt{V_{\textrm{encounter}}^2 + V_{\textrm{escape}}^2} $$

Where $V_{\textrm{escape}}\ = 11.2\ km/s$

Blowing up an asteroid

The self gravitational potential energy of a uniform sphere of mass (m) and diameter (d) is:

$$ \large PE \ = \ \frac{6}{5} \cdot \frac{Gm^2}{d} $$

This is the amount of energy you need to give the sphere to move all of its components pieces infinitely far away (i.e. to destroy it!).

Remember that the mass and diameter of the asteroid is derived from its absolute magnitude H and albedo A.