Chapter 4



4.6  Brightness/luminosity

Luminosity is what a source produces, brightness is what we see.  For example, a 100 watt light bulb is brighter the closer we are to it, but its luminosity remains the same - 100 watts.

4.9  If a spaceship appraoching us a 0.9 times the speed of light shines a laser beam at Earth, how fast will the photons in the beam be moving when they arrive at earth?

The speed of light - c = 3 x 108 m/s.

4.11  In our sky, the angular diameter of the Sun is about 30 minutes of arc.  Now imagine that you have been transported to Neptune, 30 AU from the Sun.
a.  What would be the angular diameter of the Sun as seen in Neptune's sky?
b.  Would the Sun appear as a small disk or as a point of light?
c.  How bright would the Sun appear compared to its brightness as seen from Earth?

a.  It would appear 30 times smaller, or 1 arc minute in angular diameter.

b.  It would look like an extremely bright star (we can't resolve 1 arc minute with our eyes).

c.  The brightness would be 302 = 900 times dimmer than from Earth.

4.12  c = wavelength x frequency = 3 x 108 m/s.

If f = 7.9 x 105 Hz, the wavelength is:  c/7.9 x 105 Hz = 380 m.

If f = 98.3 x 107 Hz, the wavelength is:  c/98.3 x 107 Hz = 3.05 m.


4.16  The average temperature of Earth's surface is about 290 K.  If the Sun were to become 5% more luminous, how much would Earth's temperature increase?

The relationship between energy and temperature is that E is proportional to T4.  If E increased by 5% (1.05), the temperature would increase as the fourth root of 1.05 = 1.0123.  290K x 1.0123 = 293.6K.  The average temperature would go up by 3.6K - doesn't sound like much, but most of the Earth's ice caps would melt!