Finding Jupiters Mass with one of its Moons

In summary, the conversation discusses using a given equation and values to calculate the mass of Jupiter and one of its moons. The gravitational constant, γ, is also provided. The solution is calculated, but the result is incorrect. It is suggested to check for consistent and correct units and to double check the arithmetic.
  • #1
wiegetz
20
0

Homework Statement


One of Jupiters Moons runs on a circle with the radius r1= 420000km in T1=1,77d. How big is Jupiters Mass? Can you calculate the Mass of the Moon with this as well?
γ = 6,672*10-11m3*kg-1*s-2 (gravitational constant)

Homework Equations


I used following equation: T2=4*Π2*r3/γ*M

The Attempt at a Solution


I solved the equation above to [/B]

M = 4*Π2*r3/T2*γ

Inserted the data and I get 1,399281324x1028 as a Result, which is wrong. What have I done wrong?I needed to translate the question to english, so if anything is bad explained I will try to explain it so good as I can.
 
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  • #2
wiegetz said:

Homework Statement


One of Jupiters Moons runs on a circle with the radius r1= 420000km in T1=1,77d. How big is Jupiters Mass? Can you calculate the Mass of the Moon with this as well?
γ = 6,672*10-11m3*kg-1*s-2 (gravitational constant)

Homework Equations


I used following equation: T2=4*Π2*r3/γ*M

The Attempt at a Solution


I solved the equation above to [/B]

M = 4*Π2*r3/T2*γ

Inserted the data and I get 1,399281324x1028 as a Result, which is wrong. What have I done wrong?I needed to translate the question to english, so if anything is bad explained I will try to explain it so good as I can.
Did you use consistent (and correct) units? Remember, G (γ) uses seconds, meters, and kilograms.

Did you check your arithmetic? Sometimes, numbers don't get squared or cubed like they should.
 

1. How can we find Jupiter's mass using one of its moons?

To find Jupiter's mass using one of its moons, we can use Kepler's Third Law of Planetary Motion. This law states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. By measuring the orbital period and semi-major axis of one of Jupiter's moons, we can calculate Jupiter's mass.

2. Why is using a moon to find Jupiter's mass more accurate than other methods?

Using a moon to find Jupiter's mass is more accurate because it relies on a physical measurement rather than mathematical calculations. This method also takes into account the gravitational influence of other objects in the solar system, making it more precise.

3. Which moon of Jupiter is typically used to find its mass?

The most commonly used moon to find Jupiter's mass is Io, the innermost of the four Galilean moons. It has a strong gravitational interaction with Jupiter and has a well-known orbital period and semi-major axis.

4. How does the mass of Jupiter affect the orbit of its moons?

Jupiter's mass has a significant impact on the orbit of its moons. The stronger the gravitational pull of Jupiter, the faster the moons will orbit around it. This means that the orbital period and semi-major axis of the moons can be used to calculate Jupiter's mass.

5. Are there any limitations to using this method to find Jupiter's mass?

While using one of Jupiter's moons to find its mass is a reliable and accurate method, there are some limitations. This method assumes that the moons are in circular orbits and that there are no other significant gravitational forces at play. Any irregularities in the moon's orbit or the presence of other massive objects can affect the accuracy of the calculation.

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