They probably expect you to assume that the magnitude varies sinusoidally with time, although that is NOT true for delta Cephei. Its brightess reaches maximum in about half the time it takes to return to minimum. Also, they (or you) got the amplitde of the variation wrong. It is +/- 0.35 magnitude, not 3.5. They did get the period right, it is 5.4 days.
I will leave you to figure out whether to use the false data they gave you or the true data.
Magnitude = 3.95 + A sin (2 pi t/5.4) would approximately model a sinusoidal variation with period 5.4 days, if t is in days. "A" would be the true variation amplitude (which should be 0.35). I have made use of the fact that the mean magnitude is 3.5 for that star, although they did not mention that.
A variable star is one whose brightness alternately increases and decreases.
For the variable star Delta Cephei, the time between periods of maximum brightness varies by +/- 3.5 magnitude.
(a)Find a function that models the brightness of Delta Cephei as a function of time.
How do I do this?
I see I have the period to be 5.4 so
T = (2pi)/w
I solved for omega got 2.7/pi
I do not know were to go form here is +/- 3.5 the phase shift???
is the average brightness (or magntiude) of the star 4.0 the amplitude???
THANKS!
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My next to last sentence should have read .."the mean magnitude is 3.95 for that star, although they did not mention that."
1 answer