ASTR 1100 Introduction to Astronomy Lab: Planetary Properties Introduction: This lab exercise explores the fundamental properties of density, gravity, and solar radiation and temperature for objects in the solar system. The goal is to begin to understand the similarities and differences in solar system objects and some of the causes of these properties. Density: Density is a property of an object that is useful in understanding the state and types of material the make up an object. The density of planets helps us in knowing their properties and understanding their origin and development. Density is defined as the mass of an object divide by its volume (i.e. mass per unit volume) and has units of g/cm3 or kg/m3. The density of liquid water is 1 g/cm3; since we can relate the density of objects to that of water we will use units of g/cm3 in this lab exercise. Volume is the three dimensional space occupied by an object. For spherical objects such as a planet the volume is V = 4/3 R3 = 4.188 R3 1. What is the volume of the earth with its radius of 6.372 x 108 cm? 2. The mass of the earth is 5.98 x 1027 g. What is the density of the earth? 3. 4. The table below gives the mass and volume of selected planets, calculate the density of each and enter it into the table. Planet Radius (cm) Volume (cm3) Mass (g) Density (g/cm3) Venus 6.05 x 108 9.29 x 1026 4.87 x 1027 Jupiter 7.15 x 109 1.53 x 1030 1.97 x 1030 Uranus 2.54 x 109 6.86 x 1028 8.76 x 1028 5. In the table below enter the density values you calculated for the earth, Venus, Jupiter, and Uranus. Using the densities of the other planets from Table 8-1 page 158 in your textbook enter these values in the table. Earth Jupiter Mars Mercury Neptune Saturn Uranus Venus 5. How do the densities of the planets compare to the density of water? 6. Put the planets in the table in order from the lowest to highest density? 7. Divide the planets into two groups, one with density greater than 2.5 g/cm3, and the other with density less that 2.5 g/cm3. 8. What explanation can you give to for this grouping of the planets based on density? 9. What are the densities of the Moon, Pluto, and the Sun? How do these objects compare to the planets? With which group does each object fit with the best? Gravity: The surface gravity of a planet depends on both its mass and its size. We can calculate the value of the gravitational acceleration, gp, for the planet from Newton’s Law of Universal Gravitation as: gp = G Mp/ R2 Where Mp is the mass of the planet, and R its radius. Hence, the gravitational acceleration of the earth is: gp = G Mp/ R2 gp = (6.67 x 10-8 dyne cm2/g2)(5.98 x 1027 g)/(6.372 x 108 cm)2 = 980 cm/s2 We would like to get an idea of the gravitational acceleration (gravity) of other planets. To simplify our calculations let us express the gravity of the other planets in terms of the gravity of the earth, hence the gravity of the earth will be 1. Therefore, if the gravity we calculate for another planet is 3.5, that means the planet has a gravitational acceleration is 3.5 times that of the earth (i.e. if you weigh 100 pounds on the earth you will weigh 350 pounds on this planet). We can simplify the calculation of gravity on other planets if we express the mass of the planet in earth masses, and the radius of the planet in earth radii. For example, what is the gravity on the moon in earth gravity units? The mass of the moon is 7.35 x 1025 g, and the radius of the moon is 1.74 x 108 cm. The mass of the moon in earth masses is: Mm = 7.35 x 1025/5.98 x 1027 = 0.012 and the radius of the moon in earth radii is Rm = 1.74 x 108/6.372 x 108 = 0.27. Hence the gravitational acceleration of the moon in earth gravity units is gm = 1 (0.012)/ (0.27)2 = 0.165 Our calculation shows that the acceleration of gravity on the Moon is 0.165 or 16.5 % of that on earth. If you weight 100 pounds on the earth then you would only weigh 16.5 pounds on the Moon. The table below has the mass and radius of selected planet and the Sun expressed in terms of the earth. Calculate the gravity on the surface of these objects in earth gravity units. Object Mass (Me) Radius (Re) Gravity (ge) Venus 0.81 0.95 Mars 0.11 0.53 Jupiter 329.0 11.2 Neptune 17.2 3.8 Sun 332775 109.0 10. For which of the above objects would it be the easiest to launch satellites into orbit? 11. If you weight 120 pounds on the earth and you land on Neptune what will be you weight? Did your mass change? 12. For the objects in the table which one is most likely to have a thin or non-existent atmosphere? Why? Solar Energy: The energy that planets and other objects in our solar system receive comes from the sun. The planets intercept sunlight at their orbit and this is the principal source of energy to heat the planets. The flux of sunlight is the amount of energy received on a given area in a certain amount of time; we will use units of Watts/m2. The energy from the sun travels out uniformly in all directions, as a result its flux decreases as you get farther away from the sun. At the earth’s orbit the flux of solar radiation is 1366 Watts/m2. The relationship between the flux of solar radiation and distance from the sun is an inverse square law (similar to the gravitational for between two masses). Hence, we can express the flux of solar radiation for a planet in terms of that for the earth if we know the distance from the sun to the planet in terms of the earth-sun distance (i.e. A.U.). As an example suppose we wish to know the flux of solar radiation at Neptune. The average distance of Neptune from the Sun is 30 AU. The flux of solar radiation is then: INeptune = Iearth / (30)2 = 1366/900 = 1.51 Watts/m2 The table below gives the average distance from the sun to selected objects in the solar system. Calculate the flux of radiation at each object in Watts/m2 and enter the value in the table. Object Distance from Sun Flux of Solar Average Surface (AU) Radiation Temperature of (Watts/m2) Object (K) Mercury 0.38 Venus 0.72 Mars 1.52 Jupiter 5.20 Uranus 19.2 Pluto 39.5 13. Based on you table what do you predict regarding the temperature of these planets, keeping in mind that their principal source of energy is the sun? 14. Look up the surface temperature of these planets and enter the value (in degree Kelvin) in the table. 15. Do these temperatures agree with your conclusion above? 16. What factors could modify and influence the temperature of these planets?