How Can I Calculate the Mass of Io?

[aloshi]

http://www.pluggakuten.se/wiki/images/7/7b/Grav%2C.JPG

orbital time is 22 h and 50 min.
how can I rcalculate mssan for Io? The mass fore Jupiter is $$318\cdot 5,98\cdot 10^24$$
totally mean distance from Jupiter to Io is:
$$\frac{T^2}{r^3}=\frac{4\pi ^2}{GM}\rightarrow r^3=\frac{T^2GM}{4\pi ^2}\\= r= \sqrt[3]{\frac{T^2GM}{4\pi ^2}}$$

now I can calculate the radius of jupiter. but i don't now how i can calculate the mass fore Io

 

[Gokul43201]

1. Please state the complete question, exactly as it was given to you.

2a. How do you find the orbital period? Double check your numbers.
2b. What can you determine from the figure, other than the orbital period?

 

[aloshi]

1. Please state the complete question, exactly as it was given to you.

2a. How do you find the orbital period? Double check your numbers.
2b. What can you determine from the figure, other than the orbital period?

If you look at the planet Jupiter, the planet appears as a bright disc. Already at a
magnification of 10x, you can even discern the four "Galilean moons (Io,
Ganymede, Callisto, Europa). Below is a picture of it you can see if you are sending a
telescopes to Jupiter.
http://www.pluggakuten.se/wiki/images/6/6a/Namnl%C3%B6s.JPG
How Jupiter and moons looks naturally vary as moons rotate. Sometimes
you can not see all four moons display (Figure 2). The moons may, for example. positioned
behind or in front of Jupiter. They are then impossible to see.
By studying the moons positions at different times could make Galileo Galilei
many groundbreaking discoveries. Not only on Jupiter, but also the entire solar system.
Galilei constructed himself a pair of binoculars through which he discovered the moons. Later
we discovered many new moons orbiting Jupiter. Galileo Galilei lived 1564 --
1642nd
http://www.pluggakuten.se/wiki/images/7/7b/Grav%2C.JPG
The figures shown Ios extremes. The image is drawn at a scale of 1:1,0 ⋅ 1010th
Determine from the figures above as much factual information as possible about Jupiter and Io.

 

[Stonebridge]

From this data you can find the mass of Jupiter but not the mass of Io.
You can also find, from the scale measurements on the page, the size of Jupiter and Io's orbital radius.
The time you have measured is only half of Io's orbital period.

 

[aloshi]

From this data you can find the mass of Jupiter but not the mass of Io.
You can also find, from the scale measurements on the page, the size of Jupiter and Io's orbital radius.
The time you have measured is only half of Io's orbital period.

what is missing for the info to the determination / calculation of the mass of Io

 

[Stonebridge]

The question does not ask for the mass of Io. It asks for "as much ... as possible" about Jupiter and Io. The mass of Io is something you can't calculate.
When you have only this data for the orbit of a moon, it is not possible to calculate the mass of the moon. The mass disappears in the equation. The period of motion of Io around Jupiter depends on the mass of Jupiter only. (Plus it's distance from the planet.)
In order to calculate the mass of Io you would need some more data from Io. For example, data from an object falling on its surface, or something that was in orbit around Io itself.
The answers you can give are
mass of Jupiter
diameter of Jupiter
average density of Jupiter (from mass and volume)
radius of Io's orbit
period of Io's orbit
speed of Io in it's orbit

 

[aloshi]

The question does not ask for the mass of Io. It asks for "as much ... as possible" about Jupiter and Io. The mass of Io is something you can't calculate.
When you have only this data for the orbit of a moon, it is not possible to calculate the mass of the moon. The mass disappears in the equation. The period of motion of Io around Jupiter depends on the mass of Jupiter only. (Plus it's distance from the planet.)
In order to calculate the mass of Io you would need some more data from Io. For example, data from an object falling on its surface, or something that was in orbit around Io itself.
The answers you can give are
mass of Jupiter
diameter of Jupiter
average density of Jupiter (from mass and volume)
radius of Io's orbit
period of Io's orbit
speed of Io in it's orbit

how can I calculate the radius of Io's orbit?

 

[Stonebridge]

Measure it on the question paper.
You are given that the scale of the picture is 1: 1x10^10 (I think - it's not clear)
so 1cm on the page is 10^10cm for example.
This will work if you have the original paper question. If you only have this as a computer file, you need to be very careful about the size of the image on the screen, or the size of the printout. Make sure that you have no "zoom" that makes the size greater or smaller.