Some astronomers have suggested that cooled white dwarf are made of diamond. Why might it be impractical to mine them?

Answer 1

The surface gravity of a white dwarf is very high, of the order of #200,000# times stronger than Earth's surface gravity, and its density in similar proportion.

A typical white dwarf with mass approximately #0.6# times our sun but the size of the Earth would have #200,000# times the mass of the Earth, but the surface at the same distance from the centre. Therefore the surface gravity would be #200,000# times greater than Earth's.

Even if you were able to gather some material from the white dwarf, the high surface gravity would make it extremely difficult to escape its gravitational pull - which brings me to my second point.

The material you are attempting to collect from the white dwarf is on average #200,000# times denser than similar material on Earth. So for a given volume of material, its mass would be #200,000# greater, but its weight in that gravity would be a staggering #200,000 xx 200,000 = 4 xx 10^10# times the weight of the corresponding volume of material on Earth.

I think making diamonds at home is easier.

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Answer 2

Olivia Aldridge

Due to the extreme conditions found on these celestial objects, such as high temperatures and strong gravitational forces, mining cooled white dwarfs for diamonds would be impracticable; additionally, the cost and technological difficulties involved in reaching and extracting materials from white dwarfs would probably outweigh any potential benefits.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.