Can you ride a sungrazing comet around the Sun by staying on the dark side? Maybe not! When you get close enough sunlight reaches around the comet and lights up the dark side. How does that work?
This reminds me of bicycle chains and gears. How long does a chain have to be to reach around two gears? How many teeth fit into the chain as it wraps around?
Here is a picture with gears the same size and a chain wrapped around them. This is the same as gears being very far apart. The chain leaves both gears at the top and bottom of each gear. The same number of teeth are used on both gears. We can think of the Sun heating the comet in a similar way when the comet is far from the Sun. Sunlight warms only one hemisphere. But what happens if you get much closer to the Sun?
If the left gear is made much larger than the right gear we get this picture. Now the chain leaves the large gear at the arrow, far from the top and meets the small gear away from the top. More teeth are used on the large gear, but fewer on the small. This shows that light from the Sun reaches past the one hemisphere and lights up the dark side of the comet. As comet gets really close to the Sun even someone standing on the dark side will see the sunrise.
But that sunrise will not be a little Sun coming up in the East. It will look more like a total solar eclipse fading away. A bright ring will surround the edge of the comet and slowly fill your sky to the horizon as you get closer. You would be able to see the corona first, followed by the chromosphere, and finally the bright photosphere. This effect, also called the two-pulley problem, means that comets absorb sunlight over a larger area close to the Sun than they do far away. This helps them sublimate more rapidly.
Life on a sungrazing comet would sure be different!
Check out our 3-D rendering of the orbits of sungrazing Comets ISON and Lovejoy. It shows both orbits near perihelion. You can explore why different satellites see comets differently.
