ASTR 321 First Homework Assignmen

1. Before the era of radar, the distance between the earth and the sun - known as the Astronomical Unit - had been determined by other means. Research and describe the technique(s) used (as far back as the 17th century) to determine this distance.

2. Using the acceleration on a body in circular orbit in combination with the orbital velocity of the earth about the sun (which you need to compute), determine the mass of the sun in units of grams.

3. The solar constant, the amount of energy that is received by the earth at the top of our atmosphere is 1.4 x 10⁶ ergs cm^-2 sec^-1, Calculate the total luminosity of the sun in units of ergs per second.

4. Calculate the energy lifetime (amount of fuel / rate of burning) in years of the Sun under the following three scenarios:

Chemical Energy

45 x 10⁶ Joules per kg.

How many kg of gasoline would the sun have to burn each second to produce its current luminosity?

If the entire sun were made of gasoline, how long could it be fueled by this source of energy?

Gravitational Contraction - Determine the free fall time of the sun if its initial radius is 10 times its final radius. Then apply the virial theorem (as done in class) to estimate the total luminosity of the sun over this time scale. Is it consistent with what you determine in question 3 above.

Nuclear Reactions Assume that only 10% of the sun's mass is participating in nuclear fusion (e.g. E = mc²) and that the efficiency per reaction is 0.007 (we will prove this later in class).