Solutions to Assignment #10
Astronomy 1 - Physics 1513
November 25, 1998

Chapter 11 (Jupiter) 
 Review Question #10 
 Problems #7 and #10 

Q#10
The Galilean Satellites are like a miniture solar system in the following ways:
(a) The inner satellites are rocky and higher density while the outer 
ones are more lower density and more deficient in rocky materials
(b) The orbits of the satellites are nearly circular and nearly lie in the 
equatorial plane of the central body.
(c) The inner satellites are the smaller (terrestial planets)
with the third out being the largest (Jupiter), and the
farthest out being the 2nd largest (Uranus-Neptune)
(d) The formation of the galilean satellites was probably along with Jupiter 
in the same sense as the planets and the Sun.

Prob#7
Calculate the size of Jupiter's Tidal force on Io relative to Io' own surface gravity.
The problem is to compare the diffence in the gravitational force of Jupiter
between the center and surface of Io 
AND 
the gravitational force of Io on its own surface

We will need the following data:
	MJ = Jupiter Mass			318 M(Earth) 	
	M(Earth) = 81 M(Moon)		25760 M(Earth)
	MI = Io Mass				1.22 M(Moon)
	d = Distance of Io from Jupiter		422,000 km
	R = Radius of Io			   1820 km

Differential Gravitational Tidal Force ~ MJ/d3
	FJ = F(Jup on Io) ~ MJRI/d3
	FI = F(Io at RI) ~ MI/RI2
The ratio of these two are:
	FJ/FI = [MJRI/d3]/[MI/RI2]
		= (MJ/MI)(RI/d)3
		= (25760/1.22)(1820/422,000)3 = 0.0017 = 1/590
So the pull of Io's own gravity is only 590 times that of Jupiter.


Prob#10
Compare the apparent sizes of the Galilean satellites as seen from Jupiter cloud tops 
with the angular diameter of the Sun as seen from Jupiter. State if there could be solar
eclipses.
	Angular size of Sun with be  (1 AU)/(5.2 AU) 31' arc = 6.0 ' arc
	Radius of Jupiter is needed = 71,500 km
	Relation for angular size in ' arc = (dia/dist)x57.3x60

 ALSO: Draw the Configuration of Jupiter's Satellites for 
November 25 at 6pm AST (Use  the Configuration diagram in the 
Observers's Handbook or available on the Nov 16  lecture notes) 

Convert to UT (diagram for UT)
6 pm AST + 4 hours = 10 pm UT = 22 hr UT 
Draw a horizontal line on the diagram 11/12 of the way from the 25 to 26 line.


Ganymede and Europa are difficult to separate but are on the left side and in front 
Io has just come from behind Jupiter
(sorry to give such a difficult configuration - L.Bogan)

 Chapter 12 (Saturn) 
 Review Questions #11, #15 
 Problem #7 
 Project #1 (you can use ECU) 

Q#11
Why does Titan  have a dense atmosphere when other large satellites do not?

Titan is in a colder part of the solar system where water ice could trap ammonia 
and method during formation. When the satellite was then heated internally by 
radioactivity, the atmosphere was released.


Q#15

Image being on the satellite Hyperion. Describe Sunrises and Sunsets. What would 
Saturn look like?

Hyperion has chaotic rotation and hence nothing is repeatable. Sunrise and sunset 
would be unreliable. Because the rotation is not locked to the revolution about 
Saturn, Saturn would wobble back and forth in the sky as the period varied.


Prob#7
Show that Titan's surface gravity is 1/7 that of Earth and determine its escape speed.
	g ~ M/R2		vesc = (2GM/R)1/2
So..
	gT/gE = (MT/ME)(RE/RT)2
		= (1.83 MM/81 MM)(6370km/2575km)2 = 0.138
		= 1/7.2
AND
	vesc= (2 x 6.67x10-11Nm2/kg2x1.35x1023kg/2.58x106m)1/2
		= 2640 m/s =2.64 km/s

Project 1
- How fast in degrees per year does Saturn move among the stars?
- What Constellation is Saturn in right now?
- Where will Saturn be next year at this time?

Saturn has a siderial period of 29.4 years 
and moves 360 deg/29.4 years = 12 degrees/year

At the present time Saturn is in Pisces (RA = 1h 50m)
(from ECU set for Nov 17, 1998)

Next year it will have moved 12 degrees farther east (increased RA)
and should be at 2h 38m (12 deg = 48 minutes of RA)
ECU gives RA = 2h 45m and it will be near the head of Cetis