1. Force of gravity

(a) Almost every beginning physics course will teach you that the force on an object due to gravity is F = mg, where g is just the acceleration due to gravity at the surface of the Earth. In other words, this equation is just a specific example of Newton’s second law. The mass of the Earth is M⊕ and the radius of the Earth is R⊕. Write down an expression for g in terms of M⊕ and R⊕.

(b) Now, imagine that you discover two planets, which you cleverly name Planet A and Planet B. Each of the planets have exactly the same mass. The radius of Planet A is RA = 6482 km. The radius of Planet B is RB = 3241 km. Which of the planets has a larger acceleration of gravity at its surface? How many times larger is it (your answer should be something like “5 times larger”). Show all of your work.

2. Escape speed

(a) Write the formula of the escape speed starting from the total energy (kinetic energy + gravitational potential energy) and explain how you derived it.

(b) The escape speed from the “surface” of the Sun is 620 km/s, and the radius of the Sun is 7.0 × 105 km. Imagine that the Sun kept exactly the same mass, but was compressed to a much smaller radius. Compute the escape speed from the surface of the compressed Sun if the Sun is compressed to roughly the size of the Earth, with a radius of 7000 km. Give your answer in km/s.

(c) Compute the escape speed from the surface of the compressed Sun if the Sun is compressed to a radius of 70 km. Give your answer in km/s.

Hint: starting from the formula you obtain on point (a), write the ratio between escape velocity for the sun and the compressed sun.

3. Hotter Sun

Suppose that the surface temperature of the Sun were 3,000 K instead of 6000 K.

(a) Would the Sun appear redder or bluer to your eyes than it does now? Explain your answer.

(b) What would happen to the wavelength of the peak emission? Explain your answer.

(c) What would the ratio of surface brightnesses be if the temperature were 3,000 K instead of 6000 K? In other words, call the two surface brightnesses SBnow and SBhot, corresponding to the surface temperatures of 6000 K and 3,000 K, respectively. Then you want to find the ratio SBhot/SBnow. Show your work. Remember that the equation for surface brightness (power per square meter) is given by SB= σT4, where σ is a constant and T is the surface temperature of the object. This problem is much easier if you realize that if you have a fraction like x4/y4 it is the same as (x/y)4.

4. Atomic Terminology

Answer and explain with a sentence or two:

(a) What are the atomic number and the atomic mass number of a fluorine atom with 9 proton and 10 neutrons? If we could add a proton to this fluorine nucleus, would the result still be fluorine? What if we add a neutron to the fluorine nucleus?

(b) The most common isotope of gold has atomic number 79 and atomic mass number of 197. How many protons and neutrons does the gold nucleus contain? If the isotope is electrically neutral, how many electrons does it have? If it is triply ionized, how many electrons does it have?

(c) Uranium has atomic number 92, Its most common isotope is 238U, but the form used in nuclear bombs and nuclear power plants is 235U. How many neutrons are in each of these of uranium?

5. Electromagnetic spectrum

(a) Radio Station: What is the wavelength of a radio station photon from an AM radio station that broadcast at 1000 kilo-hertz? Remember that λ = c/f, where λ is the wavelength, f is the frequency and c is the speed of light (c = 300000 km/s)

(b) What is its energy? Remember that E = h f , where f is the frequency, E is the energy and h is a constant (h = 6.6 x 10−34 Joule sec).