ALGEBRA

PROBLEM 2.

When a solar flare occurs on the Sun, it can send out a blast wave that travels through interplanetary space at a speed of 3 x 10^6 km/h.

a. How long would it take for such a solar flare blast wave to get to Earth where it could be detected by a satellite in orbit? (Recall from the preceding chapter that for a satellite close enough to Earth, we can use the Earth-Sun distance of 1.5 x 10^8 km for the satellite-Sun distance.)

Solution: Since distance = speed x time,

1.5 x 10^8 km = (3 x 10^6 km/h) (time).

Then time = [(1.5 x 10^8)/(3 x 10^6)]h = 0.5 x 10^2 h,

or 50 h (about two days).

b. When such a solar flare is detected, it is interesting to study the source. Since the Sun is rotating, we must determine how far the source has turned between the emission and the detection of a solar flare. Because the Sun is a dense gas rather than a solid body, it does not have a uniform rotation rate; on the average the Sun makes one complete revolution in 25.4 days. How many degrees would it rotate (on the average) during the time the blast wave traveled to the orbiting satellite?

Solution: Since the Sun rotates 360 degrees in 25.4 days, it rotates (360 degrees/25.4)/day, so

the solar rotation rate = 14.2 degree/day

= (14.2 degrees/day) x ( 1 day/24 hours)
= 0.59 degrees/h.

In 50 hours, the Sun rotates 50 h x 0.59 degrees/h = 29.5 degrees.

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