2:28 PM people.ucsc.edu iPad e 100%- 1. Here we\'re going to investigate the eff

Question

2:28 PM people.ucsc.edu iPad e 100%- 1. Here we're going to investigate the effect of a thick atmosphere on impactors. a) Venus has an atmospheric pressure of 9 MPa and a surface gravity of 9 ms. What is the column density of the atmosphere, that is, the total mass of the atmosphere per unit area, in kg m? [1] b) If a spherical impactor of radius R and traveling vertically downwards enters an atmosphere of column density , write down an expression for the total mass of atmosphere the projectile encounters assuming that it reaches the surface [1] c) Theoretical calculations show that an impactor will break up if the mass of atmosphere it encounters equals the mass of the impactor itself. Assuming an impactor density p, write down an expression for the radius R at which an impactor will break up for a given column density [3] d) For the case of Venus, what is the impactor radius at which break-up occurs if the impactor density is 2500 kg m3? [1] e) Using the expression from your notes, calculate the smallest size of impact crater you would expect to see on the surface of Venus. Assume an impact velocity of 15 km/s. How does your answer compare to the actual observations? [4] f) If the impactor came it at an oblique angle, rather than vertically, what would happen to the break-up radius and why? [1] g) If the impactor was made of ice rather than rock, would the minimum crater size be bigger or smaller? [2] [13 total]

Explanation / Answer

a) in this case it is given that pressure is 9 mpa ( 1 mpa = 106pa, hence 9mpa= 9 x 106 pa, we need si unit of pressure hence we have converted mpa to pa).

Pressure = force / area.................. (Equation 1)

Since force =mass x acceleration , equation 1 becomes

Pressure = (mass x acceleration) /area............... (equation 2)

Now

Mass /area = pressure/acceleration....................)(from equation 2)

= (9 x 106)/9

=106 kg/m2

= column density

b) we know the column density = mass/ area

But area of sphere is 4 pi r2

Hence above equation becomes

Column density = mass / 4 pi r2

So mass = current density x 4 pi r2

c) density of impactor =mass/volume

From (b) solution we know that mass = column density x 4 pi r2 and Volume (V) =4/3 pi r3

Put it in above equation

density of impactor = (column density x 4 pi R2)/(4/3 pi R3)

We get density = (3 x column density) /R

R=( 3 X column density) /density of impactor

4) from above equation

R=( 3 x 106)/2500

= 1200 m

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