General Astronomy, 29:61
Fall, 2005
Ninth Homework Set...November 6, 2005.
Due November 11, 2005

Show calculations and give reasons for your answers.

(1) A charged particle has a velocity

$$\vec{v} = 3.0 \times 10^3 \hat{e}_x + 1.0 \times 10^3 \hat{e}_y \mbox{ m/sec }$$ (1)

and it moves in a magnetic field given by

$$\vec{B} = 1.0 \times 10^{-4} \hat{e}_x + 4.0 \times 10^{-4} \hat{e}_y \mbox{ Tesla }$$ (2)

and the charge of the particle is $q = 1.6 \times 10^{-19}$ Coulombs. What is the force acting on the particle? Be sure to remember that force is a vector.

(2) A electron is moving with velocity

$$\vec{v} = 0\hat{e}_x + V \hat{e}_y + 0 \hat{e}_z$$ (3)

in a magnetic field given by

$$\vec{B} = 0\hat{e}_x + 0\hat{e}_y + B_0\hat{e}_z$$ (4)

Does it move to the right (towards positive $x$) or to the left (towards negative $x$)? Explain your answer. The electric charge of an electron is $-1.6 \times 10^{-19}$ Coulombs.

(3) Is there any place in the atmosphere of Venus where you would feel comfortable (assuming you have an oxygen mask)? That is, is there any place where the pressure and temperature are approximately that of the room in which you are sitting? Give the basis of your answer.

(4) The surface temperature of Jupiter's moon Europa (we'll learn more about it later in the semester) is $\simeq 130$ K. Would you expect Europa to be able to retain an atmosphere of carbon dioxide? Give quantitative arguments for your answer.

(5) The acceleration due to gravity on a planet is

$$g= \frac{GM}{R^2}$$ (5)

where $G$ is the gravitational constant, $M$ is the mass of the planet, and $R$ is its radius. Consider the atmosphere of Saturn's moon Titan, which is the subject of intense current scientific interest. The main atmospheric constituent of Titan's atmosphere is $N_2$. What is the expected atmospheric scale height for the atmosphere of Titan? Hint # 1: You need to review some material from the first couple of lectures this semester. Hint # 2: You will have to root around in Chapter 11 for some crucial information to do the problem.