Due on **Wednesday, June 14th** at the beginning of class (10:10 AM)

Show All Work and Explain your answers.

100 points total

### This Greenhouse isn't so good for the Plants

- Contrary to popular belief, some amount of greenhouse effect is useful; Earth would be a much colder planet without it. What, then, is the fear we have of dumping lots of carbon dioxide (CO
_{2}) and other "greenhouse gases" into Earth's atmosphere? - Suppose a planet had an atmosphere that was opaque at optical wavelengths but transparent in the infrared. Describe how the effect of this type of atmosphere on the planet's temperature differs from the greenhouse effect.

- Contrary to popular belief, some amount of greenhouse effect is useful; Earth would be a much colder planet without it. What, then, is the fear we have of dumping lots of carbon dioxide (CO
### Terrestrial vs. Jovian Planets

Compare and contrast five properties of the jovian planets with those of the terrestrial planets.### I know Io

What sort of activity has been seen on Jupiter's moon Io, and what is Io's heat source thought to be?### When Snowballs Attack

The kinetic energy of a moving body is given by KE = (1/2)mv^{2}, where m and v are the mass and speed of the body, respectively. If m is given in grams and v in cm/s, the units of energy turn out to be*ergs*. 1 megaton of TNT is equal to about 4 x 10^{22}ergs.- Suppose a comet is heading on a collision course with Earth. If the comet is a sphere of radius 1 km, with a density (mass per unit volume) of 1 g/cm
^{3}(like water ice), what is its mass? - If the comet's speed relative to Earth is 40 km/s, calculate its kinetic energy in ergs (be sure to keep track of your units).
- Convert your answer to megatons of TNT. This is the energy that will be deposited by the comet when it collides with Earth.
- For comparison, very powerful nuclear weapons typically release an energy of 50 megatons of TNT. By what factor is your answer in part (c) larger than this? Are you likely to have a good day when the comet hits?

- Suppose a comet is heading on a collision course with Earth. If the comet is a sphere of radius 1 km, with a density (mass per unit volume) of 1 g/cm
### Distant Worlds

Suppose Star Cabra is approaching you with a speed of 150 km/s.- Will absorption lines in the spectrum of Star Cabra be blueshifted, redshifted, or unshifted from their laboratory wavelengths?
- Calculate the expected wavelength of H
_{}line (the second hydrogen Balmer line, n = 2 to 4 transition), whose laboratory wavelength is_{0}= 4861.3 Å. (Recall that /_{0}= v/c and c = 3 x 10^{5}km/2.) - Now you would like to know if Cabra has any planets around it. What would you look for in the spectrum of Cabra?

- Will absorption lines in the spectrum of Star Cabra be blueshifted, redshifted, or unshifted from their laboratory wavelengths?
### How far, how bright?

Let's consider parallax and the distances of the stars.- What is the distance to a star whose parallax is 0.4 arc seconds?
- What is the parallax of a star whose distance is 25 parsecs?
- Star Buffy has a parallax of 0.3 arc seconds as measured from Earth. A mad scientist sends a probe into orbit around the Sun at a distance of 3 AU from the Sun. The probe measures the parallaxes of stars with the same general technique used on Earth. What is the corresponding parallax of Star Buffy measured by the probe?

Now let's consider star Angel who is at a distance of 20 parsecs

- if Angel is suddenly moved to a distance of 200 parsecs, what will his new apparent brightness be, relative to his old apparent brightness?
- How will his
*luminosity*be affected by the change in distance?

- What is the distance to a star whose parallax is 0.4 arc seconds?
### What's the Flux?

Flux is a name we give the for a quantity such as apparent brightness of an object, such as a star. b = L/(4d^{2}), where d is the distance to the object, L is the luminosity of the object. It is the amount of energy received (at a given distance) per unit area per unit time.- calculate the brightness of the Sun at the distance of Earth, in units of ergs * s
^{-1}* cm^{-2}, using a luminosity L = 3.83 x 10^{33}ergs/s and a distance

d = 1.5 x 10^{13}cm (which is 1 AU). - What is the brightness of a 100 Watt light bulb that is 10 cm away? (NOTE: 1 Watt = 10
^{7}ergs/s) - Compare your answers in parts (a) and (b). What can you conclude?

- calculate the brightness of the Sun at the distance of Earth, in units of ergs * s
### Center of Mass

Suppose Stars Fred and Wilma constitute a double-star system. Fred is 4 times as massive as Wilma. Calculate Fred's distance from the center of mass relative to Wilma's distance from the center of mass.

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