Challenge Questions

This week's Challenge Question:

John and Tom are Captain and Engineer on a spacecraft in 2120. The craft is made entirely from a transparent material and can shield the crew from extreme heat, radiation, etc. perfectly. John is currently practicing a dangerous slingshot maneuver around the Sun. In order for it to work Tom calculates that John has to fly directly at the center of the Sun until the Sun fills 80% of John's visual field as he stands facing straight ahead on the bridge. At that moment John will change direction in order to successfully slingshot the Sun. How close to the Sun will the spacecraft need to get for the Sun to fill 80% of John's visual field?

And the answer is....

John will have to get within about 25,000 km of the Sun for the Sun to fill 80% of his visual field. A human has a visual field of 60° downward, 75° upward, 100° to the left, and 100° to the right. If you approximate the visual field of a human as two half ellipses, adding the area of these two half ellipses and multiplying by .8 will give the area needed to cover 80% of that visual field. If you treat the Sun as a sphere, at ~25,000 km it will be big enough to fill 80 percent of a human's visual field, at which point John can initiate his tactical "slingshot" maneuver.