# Dr Harry’s Questions

### Who is Dr Harry?

Dr Harry Desmond is a physicist – or, theoretical cosmologist, to be precise! – who works as a researcher at St John’s and the Department of Physics at the University of Oxford. Before entering the world of research, Harry completed his first degree at Oxford (MPhys in Physics) before going to the United States to complete his PhD at Stanford University in California.

### What kind of research does Dr Harry do?

Dr Harry looks at how galaxies move and change to learn about the pieces that make up the universe, and how it is evolving. He is particularly interested in using measurements of galaxies to tackle two key questions in the field of cosmology:

1. What is “dark matter”? How can we define the identity and phenomenology of “dark matter”, which exists throughout the universe yet doesn’t emit light and hence can’t be seen directly.
2. What is the nature of gravity? Despite extensive testing in the Solar System and on Earth, the reigning theory of gravity — Einstein’s General Relativity — has not been directly proven on larger scales.

### What are Dr Harry’s Questions?

Dr Harry’s Questions are a mixture of Physics-oriented questions, puzzles and brainteasers designed to challenge anyone and everyone interested in studying Physics. Some of them are the kinds of questions you might find in a university Physics course, some are just for fun. If you love Physics and want to see some questions you might never have seen before, then this is place for you!

1. Hubble’s Law states that for every 3.3 million light-years of distance from the Milky Way, a galaxy recedes from us at an additional 70 km/s. Estimate the age of the universe. (The speed of light is 300,000 km/s.)
2. 2.2e-18 Joules are required to separate the proton and electron that constitute hydrogen. How big are atoms? (The charge of an electron is 1.6e-19 C.)
3. Our Solar System is at a distance 2.5e17 km from the centre of our galaxy, the Milky Way, and orbits it at a speed of 220 km/s. Estimate the total mass enclosed within the orbit of the Sun. Around fifty billion stars are located in this region — is stellar matter all there is? (The mass of the Sun is 2e30 kg.)
4. To grow vegetables in England, it’s useful to know that the average solar irradiance during the day is 130 W/m^2. This is around 10% of what one could expect without clouds. Given that the mass of a Hydrogen nucleus, Helium nucleus and the Sun are 1.67e-27 kg, 6.64e-27 kg and 2e30 kg respectively, calculate the rate at which Hydrogen atoms are fusing into Helium in our star.
5. The nearest star to the Sun, Proxima Centauri, appears to move through an angle of 0.00043 degrees (relative to the distance stars) between June and December. How far away is it? (The distance to the Sun is 150 million km.)
6. The Arctic is mainly ice on water, and the Antarctic mainly ice on land. Which contributes more to sea level rise given global warming?
7. During a Solar eclipse the moon almost precisely blocks out the light from the Sun. The distance to the moon is 384,400 km and to the Sun is 150 million km, and the radius of the moon is 1,740 km. How big is the Sun?
8. The “HI” line of atomic hydrogen has a frequency of 1420 MHz in the lab, but from a particular galaxy is observed to have a wavelength of 23cm. What is the velocity of that galaxy relative to us? Recalling Hubble’s law (for every 3.3 million light-years of distance from the Milky Way, a galaxy recedes from us at an additional 70 km/s), estimate its distance. (The speed of light is 3e8 m/s.)
9. In theory there’s a thin layer in the atmosphere where all the helium balloons that kids accidentally release go. Estimate the location of this given that the scale height of the atmosphere — the height over which atmospheric pressure falls by a factor of e — is about 8 km. (The density of helium is 0.18 kg/m^3 while that of air is 1.2 kg/m^3 at sea level; assume temperature does not vary significantly over several scale heights.) Is there any chance of being able to see the balloons up there? The angular resolution of the human eye is about 1/60 degrees.
10. The surface gravity of the moon is 1.6 m/s^2. How high could you jump?
11. The first light (the “Cosmic Microwave Background”) was emitted when the volume of the universe was a billion times less than it is today. We observe these photons with a temperature of 2.7 K. What was the temperature of the universe when they were emitted?
12. The surface of a black hole (the “event horizon”) is the radius at which not even light is fast enough to escape. Calculate the size the Earth would have if it collapsed into a black hole. (The mass of the Earth is 6.0e24 kg.)
13. According to quantum mechanics, all bodies exhibit wave-like behaviour. The scale over which this behaviour is manifest is known as the body’s “Compton wavelength”, which for a non-relativistic speed v is given by h/mv, where m is the body’s mass and h is Planck’s constant, 6.6e-34 m^2kg/s. Calculate this for the electron in hydrogen orbiting the nucleus, and for you when you’re walking. Why don’t we experience quantum phenomena in everyday life? (The mass of an electron is 9.1e-31 kg, the charge of an electron is 1.6e-19 C and the size of a hydrogen atom is 1e-10 m.)
14. You are in a lift accelerating downwards at 9 m/s^2. You drop a ball. What happens to it? The lift then begins accelerating faster, first at 9.8 m/s^2 and then at 11 m/s^2. What does the ball do in each case? Describe your own sensations during this period.
15. You are in a windowless ship travelling smoothly across the water. Describe how you could determine your velocity.
16. Galaxies are thought to be surrounded by huge spheres of dark matter called halos. Assuming the density of the dark matter is proportional to r^-n, where r is the distance from the halo centre, calculate the value of n required for the rotation velocity of a star to be independent of its distance from the centre of the halo and hence generate the “flat rotation curve” that observations suggest.
17. Instead of postulating the existence of dark matter to explain galaxy dynamics, some theories seek instead to modify the laws of gravity or inertia. One of them (“Modified Newtonian Dynamics”, or MOND) proposes that Newton’s second law is only approximately valid at relatively high accelerations, and at low acceleration takes instead the form F = m(a/a0)^n where a0 is a fundamental constant. For a roughly spherically-symmetric galaxy of mass M, what value of n is required for a flat rotation curve?
18. You drill a hole through the centre of the Earth to other side and drop a ball down. What does it do?
19. What velocity must an ambulance have for its the frequency of its siren to halve as it passes you?
20. Special Relativity predicts that moving clocks run slow. How can you travel into Earth’s future?
21. General Relativity predicts that massive objects deflect light towards them in just the same way as they deflect particles. This is known as “gravitational lensing”. Suppose there is a light source behind a black hole in the distant universe — how will the light from that source appear to us?