**1. Evaluate the following expression: **

** **

**2. Evaluate the following expression: **

** **

**3. Let us play with the scale of the universe. Imagine that the solar
system has been shrunk to the size of a dinner plate, i.e. the diameter
of Pluto's orbit is now 20cm.
a. Look up the orbit of Pluto using the appendices of the textbook.
By what factor has the orbit been reduced to become only 20cm across? i.e.,
give the number you calculate when you divide the diameter of Pluto's orbit
by 20cm. **

**b. At that scale how big is:
i) a human?
ii) the radius of the Earth?
iii) the distance from the Earth to the Sun?
iv) the distance to the nearest star?
v) the distance to the center of the Milky Way?
vi) the distance to the nearest galaxy (M31)?
vii) the radius of the Universe? **

**Hint: Use information from the first two lectures and from the text
to get rough figures for the distances required. **

**4. We all watched in awe recently as NASA sent images back of the dwarf planet Pluto. For the spacecraft
to have reached its destination in seven years after launch, how fast must it have been travelling? **