Download PHYS 1470 3.0 W16/17 Highlights of Astronomy Assignment #2

PHYS 1470 3.0 W16/17
Highlights of Astronomy
Assignment #2
Deadline: March 2, 2017.
The solutions including the equations must be typed or a penalty will be
incurred
1. Compare the atmospheres of Venus, Earth and Mars. Write a ~1-page essay with
single-line spacing and font size 12.
2. Can a celestial body hold an atmosphere? The average molecular kinetic energy of a
gas at temperature, T, is given as
. This energy is equal to the kinetic
energy of the molecules moving at an average speed, v. For a gas to escape
permanently from the surface of a celestial body, the average speed of the
molecules needs to be greater than 1/6 the escape velocity, vesc, for that body.
a. Compute the average speed of O2 molecules for the average surface
temperature of the moon when the surface is exposed to the sun.
b. Compute the escape velocity for the moon.
c. Would the O2 gas eventually escape from the surface of the moon?
d. Repeat the computations from a. to b. for Earth.
e. Will O2 gas eventually escape from the surface of Earth?
f. Repeat the computations from a. to b. for H2 molecules at the “surface” (cloud
top) of Jupiter.
g. Will the hydrogen gas eventually escape from Jupiter?
Consult the book for astronomical parameter values and the web for the masses of
the molecules and list the values and the masses when you use them for your
computations.
3. Calculate the blackbody temperatures (K) from the peak wavelengths given in a)
through b), and the peak wavelength (m) from the temperatures given in c) through
d):
a. 180 nm (surface of hot star)
b. 2.4 microns (surface of cold star)
c. 60 K (interstellar cloud)
d. 3 K cosmic microwave background radiation left over from the Big Bang.
4. Given a value for Venus’ radius of 6050 km, an albedo of Venus of 0.59, and Venus’
distance from the Sun of 0.72 AU, then:
a. determine the power, Psq.m, of the radiation from the Sun flowing through and
area of 1 m2 facing the Sun with the area located at a distance of Venus from
the Sun of 0.72 AU.
b. What power, Pabs, is absorbed by Venus?
c. What would Venus’ surface temperature, T, be, assuming that Venus
radiated into space an amount, Pem , that is equal to the power it absorbed?
d. What is the mean temperature on Venus, how much is it different from the
temperature you computed in c) and what is the reason for the difference (if
the difference is large)?
5. Repeat the computations in 4a to 4d, but now for Mars with a radius of 3400 km, an
albedo of 0.15 and a distance from the Sun of 1.52 AU.
6. A spherical asteroid has an average temperature of 200K, an albedo of 0.2 and a
circular orbit around the Sun. Based on your considerations under 4) and 5), what is
the asteroid’s orbital period, P?
7. A hypothetical spherical asteroid with a diameter of 2 km composed of rock with an
average density of 2500 kg m-3 strikes Earth with a speed of 12 km s-1.
a) What is the kinetic energy of the asteroid at the moment of impact?
b) How does that energy compare with the energy of 8.4•1013J released by a
20-kiloton nuclear bomb?