1. Volume is a measure of how much space an object occupies. If you divide the volume of one object into the volume of a second, you'll determine how many of the first objects will fit into the second. Dividing one volume by another volume is called the relative volume.
2. The volume of a sphere is given by the equation V= (4/3) n R3 where R is the sphere's radius. Recall that the radius is just half the diameter. Since we want to compare the Sun to other objects, let us simplify the standard equation for volume and write it as
V = K (Diameter)3 whereK= pi/6=O.5236
3. Record the following information from your textbook:
DiameterE~h _______________________km
Diameter5~~ _______________________km
Di ameterJUPhffi~__________________km
4. Calculate the relative volume of the Earth to the Sun:
Relative Volume = (DiameterSUdDiameterE~)3
Relative Volume =
5. Calculate the relative volume of Jupiter to the Sun:
Relative Volume = (Diameter~~dDi ameterjupfter)3
Relative Volume =
6. How many Earth's will fit into the Sun? How many Jupiter's? From this determine how many Earth's will fit into Jupiter.
7. It has been determined that the super red giant star Antares has a diameter of 5.1 A.U. Recall that an A.U. (astronomical unit) is the average distance between the Earth and the Sun. 1 A.U. = 1.5x 108 km (150,000,000 kin).
DiameterM~~ =________________________km
8. Calculate the relative volume of the Sun to Antares:
Relative Vol u me = (Di ameterM~~~IDi ameter~~~)3
Relative Volume =
9. What does your calculation in # 8 tell you? How does the Sun compare to other stars?
10. Next, let us compare the density of the sun to other stars. Density is a number that tells you how tightly matter is packed in an object. It is usually denoted by the Greek letter "rho" (p). The average density of an object is found using the following formula:
p = Mass/Volume
11. To calculate the average density (p) of the Sun, we must first find its volume. Recall that Volume = K (Diameter)3 where K = n/6 = 0.5236
Volume~~~ = K (Diametersurj3 Volume~~~ =
Volume~~~ =
Facts:
km3
cm3
1 km3 = 1015 cm3
1 cm3 is about the volume of a sugar cube
Convert the Sun's mass in kilograms into grams by multiplying by i03.
(Mass)~~~ = _________________kg
(Mass)9~~ = __________________gram
psun = _______________________gm/cm3
12. Record the following data from your textbook.
PEWIh = _______________________gm/cm3
P~upiter =__________________________________________gm/cm3
** To give you a feeling for density, the liquid water in a drinking glass has a density of 1 gm/cm3. **
13. In one paragraph compare the average densities of the Sun, Earth, and Jupiter. Discuss what you think might account for the differences or similarities.
14. Sirius in the constellation Canis Major ("Big Dog") is the brightest star in the night sky
and has a companion star called Sirius B. Sirius B has a mass 1.1 times that of the Sun and a
diameter 0.008 times that of the Sun.
a. Calculate the following information for Sirius B:
Diameter~1~~95 = _____________________________________km
Mass~1~.5____________________gm
b. Calculate the average density of Sirius B. K= ri/6=0.5236
Volume = K (Diameter~1~~)3
Volume91~~~ B =________________________km3
Volume~1~~8 B = ___________________cm3
PSInus B _________________________gmVcm3
15. In one paragraph discuss the differences in the average density of the Sun and Sirius B.
1. Datasheet #1 lists measurements made by satellites in orbit above the Earth's atmosphere. In one paragraph discuss the effects on Planck's curve for the Sun if the measurement instrument had been used at the Earth's surface instead of in an orbiting satellite.
2. Use datasheet # 1 to draw a graph between wavelength and flux. The resulting graph is known as "Planck's curve" and it can be used to find the temperature of the object (in this case the Sun) by using Wiens Law.
3. Wein's Law states that the maximum wavelength on Planck's curve is given by the following formula:
AMax = 2.898 X 1O7fT~*~iein
AMaX is measured in Angstrom (A)
~is measured in Kelvin (K)
Wein's Law states that the maximum wavelength (i.e. color) of the photon emitted by an object is inversely related to the temperature of that object. In other words, as the temperature goes up, the wavelength gets shorter; and as the temperature goes down, the wavelength gets longer. In one paragraph, and using the example of a fireplace poker changing colors as it gets hotter in a fire, explain why this inverse relationship is true.
4. Using the graph drawn in step B2, determine the maximum wavelength for Planck's curve for the Sun. Record this information in the following and use Wein's Law to calculate the temperature of the Sun's photosphere (i.e. Wein's temperature):
AM3X A
Twein = K
= C
= F
Facts: 0F = 1.8 00 + 320
0C = 0.556 (0F - 320)
K = 0C+2730
0C = K - 2730
5. The solar constant is the amount of energy from solar photons that we receive here at the Earth per unit area per time. To determine the solar constant, complete Worksheet #1. Sum the last column of numbers to determine the value of the solar constant. Summing the last column estimates the area underneath Planck's Curve using the trapezoidal rule of integral calculus.
Solar Constant = ergs/cm2/sec
6. From the solar constant you can determine the solar luminosity which is the total energy per time emitted at the Sun's surface each second. To do this, you need to use the following formula:
EnergyT~ = Solar Luminosity =B (Dlstanceb~32 (Solar Constant)
where B = 4ri = 12.566
and DistanceE~h = 1.5 x 1013 cm.
Solar Luminosity ergs/sec
7. Professional astronomers have measured the solar luminosity and found the actual value to be 3.90 x 10~ ergs/sec. Compare your estimated value with the actual value. Calculate the relative error using the following formula: Relative Error = 100 (Actual - Estimated)/Actual
Relative Error =