W1.3 Asteroid
You have taken a job working as part of a team of people searching for asteroids that may collide with the Earth. It is an important job, as current theories suggest that the dinosaurs and other organisms became extinct when the Earth was struck by a large asteroid around 65 million years ago. Were such a collision to happen again, it could be very Bad News indeed for us.
Your job is to scan space for asteroids over a certain size that might be on a collision course with Earth. Clearly, a dangerous size of asteroid is around the same size as the one that is thought to have wiped out the dinosaurs. But how big was that?
It is known that following the asteroid impact 65 million years ago, dust from the impact was sent into the upper atmosphere all around the globe, where it stayed for several years, blocking out sunlight from reaching Earth. One fifth of the asteroid’s mass ended up settling out as dust on the Earth’s surface, spread uniformly over the surface. Geological exploration shows a layer 0.040 grams which is chemically different from the Earth’s rock covered each square centimeter of the Earth’s surtface on average. The typical density of an asteroid is approximately 2.0 g/cm3.
What size of asteroid should we be worried about?
Hint
Reveal

Hint
You’ll need to know that the radius of the Earth is about 6380 km.
Watch out for units here, and don’t put numbers in until you have to...
Solution
Reveal

Solution
I’ll start the solution from the strategy part of our FDPEE model
The strategy we need to adopt is as follows:
- We need to assume both the earth and asteroid are spherical
- Find mass of the dust layer (from coverage given, cast, and surface area of the earth, AE, which comes from given radius of the earth rE)
- Find the mass of the asteroid (from the mass fraction given f)
- Find the size of the asteroid (from the formula for volume and the given density, ρast)
1. Mass of dust layer, Mdust
To convert coverage given (cast, in gcm-2) to kgm-2 multiply data given by
2. Mass of asteroid is given by
3. Volume of asteroid is given by . Need to convert ρ given into kgm-3 (
)

Putting numbers in here, we get Vast=2.0×1010m3, which equates to an asteroid radius of approximately 2 km (using V=4/3πr3).
That’s not a bad estimate, as this story shows