How to find Density/ Radius of planetesimals

In summary, the ice rich planetesimals that formed the cores of the Jovian planets had a density of 2g cm-3 and were about 10 times more massive than Earth. To find the radius of such an ice ball, the formula for volume of a sphere was used, which resulted in isolating the radius and taking the cubed root of the final answer. This radius can then be compared to Earth's radius.
  • #1
Cherrio
4
0
The ice rich planetesimals that formed the cores of the Jovian planets were about 10 times more massive than Earth. Assuming such an ice ball has a density of 2g cm g-3, what would its radius be? How does this compare to Earth's radius.


I need Help =\
 
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  • #2
What have you tried?
 
  • #3
I was thinking of multiplying the Earths mass by 10 then using the fomula m=dv

and use the formula for volume of a sphere to get r? IDK
 
  • #4
Sounds like a good plan.
 
  • #5
okay so that would be m=dv


10 x 5.97 x 1024 Kg which is 5.97x 1025Kg

then convert from Kg to g 1kg= 1000g

5.97x 1025Kg x 1000 g= 5.97x 1028g
volume of a sphere= (4/3) pi r3

5.97x 1028g= (2g cm-3)((4/3)pir3)

im not to sure how to isolate R
 
  • #6
You just need a bit of algebraic manipulation. It might help if you use the letters instead of numbers right until the end.
 
  • #7
ok so it would be


m=d 4/3 pi r3

then m/ d(4/3)pi =r3 ?

then r = cubed root of that anwser?
 
  • #8
Yes, that looks good.
 

1. How do you calculate the density of a planetesimal?

The density of a planetesimal can be calculated by dividing its mass by its volume. The mass can be determined by measuring the gravitational force it exerts on another object, while the volume can be estimated by measuring its size and assuming a spherical shape.

2. What factors affect the density of a planetesimal?

The density of a planetesimal can be affected by various factors, such as composition, temperature, and pressure. For example, a planetesimal made mostly of heavy metals will have a higher density than one made mostly of ice.

3. What methods are used to measure the radius of a planetesimal?

There are several methods that can be used to measure the radius of a planetesimal. One common method is to measure the time it takes for the planetesimal to pass in front of a star, which can give an estimate of its size. Another method is to use radar or other imaging techniques to directly measure the size of the planetesimal.

4. How do you determine the volume of a planetesimal?

The volume of a planetesimal can be calculated using the formula for the volume of a sphere: V = (4/3)πr³, where r is the radius of the planetesimal. As mentioned before, the radius can be estimated using various methods, such as transit observations or radar imaging.

5. Can the density and radius of a planetesimal change over time?

Yes, the density and radius of a planetesimal can change over time due to various processes such as collisions or heating from nearby stars. These changes can affect the overall structure and composition of the planetesimal, making it important for scientists to continuously study and monitor these objects.

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