Starting with:
https://en.wikipedia.org/wiki/Chicxulub_impactor said:
the Chicxulub asteroid, was an asteroid or other celestial body some
10 to 15 kilometres (6 to 9 mi) in diameter
That doesn't have enough detail. Further basic results are also lacking in deail.
Finally:
Assessments of the energy, mass and size of the Chicxulub Impactor
Hector Javier Durand-Manterola and Guadalupe Cordero-Tercero
Departamento de Ciencias Espaciales, Instituto de Geofísica, Universidad Nacional
Autonoma de México
Arxiv March 19, 2014
https://arxiv.org/ftp/arxiv/papers/1403/1403.6391.pdf said:
... the aim of this study is to estimate the most relevant features of
this one such as the size, mass and kinetic energy. We found that the
kinetic energy of the impactor is in the range from 1.3x10^24 J to
5.8x10^25 J. The mass is in the range of 1.0x10^15 kg to 4.6x10^17
kg. Finally, the diameter of the object is in the range of 10.6 km to
80.9 km.
Since our hero was having difficulty with a much smaller rock having a
diameter of 1km, the following uses the lowest values from the ranges
of the estimate:
Diameter
1.06 10^4 m
Mass:
1.0 10^15 kg
Kinetic Energy (KE):
1.3 10^24 J
Then:
Volume:
6.2 10^11 m^3
Density:
1.6 10^3 kg/m^3
Speed:
5.1 10^4 m/s (51 km/s)
In support of these values,
Assessments writes:
In the second model, to calculate the kinetic energy of the impactor,
we needed crater diameter, density of the projectile, density of the
target, earth's gravity and impactor velocity. We considered the
density of the projectile as 1650 kg/m^3 for comets (Greenberg, 1998),
3400 kg/m^3 for stony asteroids (Wilkison and Robinson, 2000), and
8000 kg/m^3 iron asteroids (Hills and Goda, 1993). We took the target
density as 2460 kg/m^3, which is the modal density of the limestone of
Yucatan (Alonzo et al., 2003), and Earth's gravity as 9.80 m/s^2
(Tholen et al., 2000). Steel (1998) obtain ed an estimation of the
range of velocities for bodies that cross Earth's orbit. For asteroids
the interval is between 12.6 km/s and 40.7 km/s. This result is based
on measurements of the velocities of the asteroids that cross Earth's
orbit.
The range for comets is between 16 km/s and 73 km/s. This result is
obtained from a theoretical calculation of the expected velocity
distribution of bodies that come from the Öpik-Oort cloud.
Motion of 51 km/s is 1.84x10^5 km/hr, or 4.4x10^6 km/day.
(In comparison, Earths average orbital speed is about 30 km/s.)
Working from the equations of motion under constant acceleration,
and that relate force, mass, and acceleration:
Under constant acceleration:
D = 1/2 A T^2
Or:
A = 2 D / T^2
Definition of force:
F = M A
Then:
A = F / M
From which:
F / M = 2 D / T^2
Or:
F = 2 D M / T^2
Putting in:
The radius of the Earth:
D = 6.4x10^6 m
The mass of the asteroid:
M = 1.0 10^15 kg
The available time (one hour):
T = 3.6 10^3
Results in:
F = 1.0 10^15 kg m / s^2
Total
impulse is:
I = F T
I = 3.6 10^18 kg m / s
From:
http://www.b14643.de/Spacerockets_2/United_States_1/Saturn-5/Design/SaturnV.htm
The total impulse of the Saturn V for Apollo 17 (launched 12-Jul-1972) was:
I(SV) = 8.7x10^9 kg m / s
That is, pushing the asteroid out of the way would require the total
impulse of 2.4x10^8 (240,000,000, or 240 million) Saturn V's.
Notes:
The impulse requirements do not vary with the speed of the asteroid!
What matters is how long one has to push the asteroid out of the way.
That this should be the case can be seen by adopting an asteroid-centric
frame of reference, in which case the asteroid is still and
the earth which is in motion. When looked at from this frame of
reference, all that matters is how long until the Earth and the
asteroid collide, not how fast the earth is moving.
From the force and total impulse equations:
F = 2 D M / T^2
I = F T = 2 D M / T
The force requirement increases linearly with the distance and mass,
and decreases in portion to the square of the available time. But,
the total impulse requirement decreases linearly with the available
time. (That is, as the available time increases, while the necessary
force is reduced, the duration of application of that force increases,
moderating a square factor to a linear one.)
Requirements for an asteroid having a similar composition but having a
different radius vary according to the change of radius of the
asteroid. Changing from 10km to 1km reduces the force requirement by
a factor of 1000 (10^3). Note that a "small" 1 km asteroid, still
needs the total impulse of 240,000 Saturn V's.
Thx!
TomB