Earth MAss if Helium and Hydrogen in suns propotions were added,

In summary, the conversation discusses the estimation of the mass of silicon in the Earth and the ratios of the masses of hydrogen and helium to silicon in the sun. The task is to calculate the mass of a body that would have been produced if hydrogen and helium had been added to the Earth in the same proportions as in the sun, and compare it to the mass of Saturn. The solution involves multiplying the mass of silicon by the ratios and adding it to the mass of the Earth, resulting in a value slightly larger than the mass of Saturn.
  • #1
TFM
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0

Homework Statement



The mass of silicon in the Earth is estimated to be 7x10^23 kg. The ratios of the masses of Hyrdogen and Helium to silicon in the sun are: H/Si = 850, He/Si = 250. Calculate the mass of the the body thatwould have been produced if H and He had been added to the Earth (present day mass M_E = 6x10^24 kg) in the smae proportions to Si as they are in the sun, esxpressing your answer as a multiple of M_E. How does this result compare with the mass of Saturn (= 100M_E)

Homework Equations





The Attempt at a Solution



does this question need me to convert the masses into number of molecules, or do I simply times the mass of Silicon by 250 and 850, and adde it to the mass of the the Earth?

Any help would be most appreciated,

TFM
 
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  • #2
If I just do it by mass an not atoms, I get a value of 5.95*10^26 for Hydrogen and 1.75*10^26 for Helium. Add this on to the mass of the Earth and I get 7.76*10^26, which is just over the mass of Saturn, does this look like the right thing to do?

TFM
 
  • #3


I would approach this problem by first converting the mass of silicon in the Earth to the number of moles using its molar mass. Then, using the given ratios, I would calculate the number of moles of hydrogen and helium that would be present in the hypothetical body if they were added in the same proportions as in the sun. From there, I would convert the number of moles back to mass and add it to the mass of the Earth to get the total mass of the hypothetical body.

To answer the question of how this mass compares to that of Saturn, I would calculate the mass of Saturn using its given mass in terms of Earth's mass. Then, I would compare the two masses to see their relative sizes.

Overall, this hypothetical calculation would give us an idea of how much the Earth's mass would change if it had the same proportions of hydrogen and helium as the sun. However, it is important to note that this is a simplified calculation and does not take into account other factors such as the Earth's composition and the effects of gravity. Therefore, the result should be interpreted with caution.
 

1. How would adding helium and hydrogen in suns proportions affect the mass of Earth?

Adding helium and hydrogen in suns proportions would greatly increase the mass of Earth. Helium and hydrogen are much more massive than the elements that make up Earth's composition, so the overall mass of the planet would significantly increase.

2. Would this change in mass impact Earth's orbit around the sun?

Yes, the increased mass of Earth would affect its orbit around the sun. This is due to the fact that the gravitational force between two objects is directly proportional to their masses. Therefore, the increased mass of Earth would result in a stronger gravitational pull towards the sun, altering its orbit.

3. How would the increased mass affect Earth's rotation?

The increase in mass would also affect Earth's rotation. The Earth's rotation is influenced by its mass and distribution of that mass. With the addition of helium and hydrogen, the Earth's mass would increase, causing a slower rotation rate due to conservation of angular momentum.

4. How would the added elements affect Earth's atmosphere and climate?

The added elements would have a significant impact on Earth's atmosphere and climate. Helium and hydrogen are both gases, and their addition would likely change the composition of Earth's atmosphere, leading to changes in temperature and weather patterns.

5. Is it possible for helium and hydrogen to be added to Earth in these proportions?

No, it is not possible for helium and hydrogen to be added to Earth in these proportions. The sun's proportions of these elements are much larger than the mass of Earth, and it would require an incredibly powerful force to add these elements to Earth in such quantities.

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