More astrophysics questions!

[kingwinner]

1) If the earth shrinks into a black hole, what will be the radius of the earth?

Solution:
Since the minimum escape speed is v(esp)=c=3x10^8m/s
v(esp)=square root of (2GM/r)
3x10^8=square root of [2(6.67x10^-11)(5.98x10^24)/r)]
r can be found.

As we know, light CAN'T escape from a black hole. But, if we substitute the escape speed as the speed of light, that means speed can escape the black hole's gravitational field. Why can't we substitute c as the escape speed, as the solution does?

2) What is the total amount of energy needed to place a 2000kg satellite in circualr Earth orbit, at an altutide of 500km.
[Is the answer simply Et=1/2 Eg=-5.80x10^10 J or is it the change in total energy or something? I don't get what the question is asking for.]

3) The mass of the Moon is 6.7x10^22 kg, and its radius is 1.6x10^6 m. If a woman can raise her centre of gravity 2.0m vertically in a high jump at earth's sruface. How high can she jump with the same muscular effort on the Moon's surface?
[My question is, will the initial velocity of the woman be the same on the earth and on the moon? What I am thinking is that the earth and the moon have different values of Fg, so if she applies the same muscular strength (or same applied force), wouldn't the initial speed as she leaves the ground be different?]

Thanks everyone for explaining!

[Jay-qu]

hey kingwinner

not to sure what you want to know about the first question.. but number 2 wants to know the change in gravitational potential energy, that will equal the total energy needed to move it to that altitude.
The trick in this one is that at 500km above the surface the gravity due to the earth has dropped to about 8.5, so you cant do a straight E=mgh calculation.
What you really have to do is to intergrate an mg graph against altitude between the two points (earth surface and then earth surface +500km)

3) this is an energy problem, velocity will be different, try calculating how much energy she would need to raise herself 2m of earth and then see how high that will get her on the moon

[sebbysteiny]

Hi Kingwinner,

1) I've never heard such a stupid question. Einstein would be turning in his grave. A black hole made out of Earth???? We might as well say, if we were all wierd space creatures from another universe, would we still like chocolate?

However, if you can't find the money to buy a gun to shoot who ever wrote that, they you should consider this. The fastest possible speed anything can go (including light) is C (although anything with mass will never quite reach that speed. This is relativity and it requires at least a first year undergraduate knowledge of physics. Technically, black holes are all about general relativity, but thankfully, not much is asked on that one.

If you really want to know why light will move away from the BH at c, it's because light ALWAYS moves at C. If it misses the black hole, even by a couple of tenths of a milimeter, it will still move at c relative to it. It's all or nothing.

2) Do you remember when I said that a reference point other than at infinity was scientifically meaningless but a good question could nevertheless ask you for the potential energy difference between two points? Well the reason for asking about the DIFFERENCE is that the energy difference is the energy required to get the object from one place to the other.

Jay_qu has given you one correct method to do the calculation, but there is an easier way. 1) work out the GPE of the satalite at the Earth's surface (bog standard question identical to B4). 2) Work out the GPE of the satalite in orbit (same bog standard question). Subtract 2 from 1 (bog standard maths). You should get a +ve answer which means work needs to be done on the satalite.

3) Jay_qu is right. Nothing more to add except that I think the INITIAL velocity will be almost the same. However, it will be slightly more on the moon because the legs will need to overcome less gravity allowing more force on the jump. But this is too much detail for this question. Nevertheless the legs can put in more energy into a jump on the moon than on the Earth, but only slightly. This is because two legs can apply a force of about, say, 7 times your body weight. Gravity reduces your body weight by about a half, say. Therefore, on the moon, the jumping force is about 7.5 times your body weight. In other words, less energy is used in actual the jump on the moon than on the Earth. If you like getting questions wrong by over complicating them, they you should seriously consider these issues.

[infamous]

Originally Posted by sebbysteiny

Hi Kingwinner,

1) I've never heard such a stupid question. Einstein would be turning in his grave.

To coin a phrase; "There are no such things as stupid questions, only stupid answers". Actually sebbysteiny, given enough pressure a mass the size of the earth could be converted into a black hole. The formula; radius of a black hole = 2G*Mass/c^2 is correct. Remember the theory that suggests there may be mini black holes lurking around that were created shortly after the big bang? Not really a stupid question at all my friend. Questions that cause one to think new and unusual thoughts are anything but stupid, they are the source of most inspired scientific research....................Infy

[C1ay]

1. http://scienceworld.wolfram.com/phys...ildRadius.html

[Erasmus00]

Originally Posted by kingwinner

1) If the earth shrinks into a black hole, what will be the radius of the earth?

Solution:
Since the minimum escape speed is v(esp)=c=3x10^8m/s
v(esp)=square root of (2GM/r)
3x10^8=square root of [2(6.67x10^-11)(5.98x10^24)/r)]
r can be found.

As we know, light CAN'T escape from a black hole. But, if we substitute the escape speed as the speed of light, that means speed can escape the black hole's gravitational field. Why can't we substitute c as the escape speed, as the solution does?

The solution is correct, but the question is awfully misleading. It is only through a remarkable coincidence of mathematics that the classical and GR escape velocities just happen to be the same. This means that plugging in c as the escape speed will work. Just keep in mind that, in general, physics beyond Newton's laws must apply to black holes.
-Will

[Jay-qu]

Originally Posted by sebbysteiny

Hi Kingwinner,

1) I've never heard such a stupid question. Einstein would be turning in his grave. A black hole made out of Earth???? We might as well say, if we were all wierd space creatures from another universe, would we still like chocolate?

However, if you can't find the money to buy a gun to shoot who ever wrote that, they you should consider this.

This kind of talk is not accepted here, it will only earn you red boxes as you can probably see. Kingwinner was just asking a question it is unfair for you to speak this way to him, especially when you yourself are incorrect.

Jay-qu

[kingwinner]

Hi everyone,

1) A black hole has the property that the escape speed is GREATER than the speed of light. (i.e. light can't escape a black hole)

The solution did it this way, by substituting c as escape speed:
3x10^8=square root of [2(6.67x10^-11)(5.98x10^24)/r)

This means that with a speed of 3x10^8m/s, light CAN escape a black hole, which is not true, right? So is the solution wrong?

2) I was told that Total energy = Eg + Ek, and I can find the total energy at the point where the satellite is in orbit (using the altitude and speed of the satellite). The questions asks for total energy, and I am not sure if this "Total energy" is the required answer...

3) Is it valid to say that the initial velocity will be the same on the earth and the moon and use the kinetic equations to solve this problem?

But the weight is different, the applied force is the same, the time interval of upward acceleration (i.e. to jump) is the same, so wouldn't that initial velocity as she leaves the ground be completely different?

[Jay-qu]

2. The question asks for the total energy to put it in orbit, and it will be equal to its gravitational plus the kinetic required to give it a circular orbit. Im not sure if you should assume that its initial velocity (due to earth spinning) is negligible..

3. Dont worry about initial velocities. If she could raise herself 2m then she had to put in energy equal to mgh, on the moon g is different, so you end up with:
:the mass cancels so


hence

where


and height jumped on moon

[sebbysteiny]

You make some good points about perfectly good theories of little black holes. I've always been a little skeptical of them, but if they do exist, I doubt they will make much difference to us as they are too small to have a large gravitational effect.

However, an object the size of the Earth can never become a black hole. Maybe an object the size of a proton, or an object the size of a huge star, but nowhere in between.

The Earth simply does not have the gravitational power to push protons and electrons (ie fermions) into high enough energy states for the Earth to collapse into a black hole.

If the there is such a thing as an Earth sized black hole, then you might as well throw all of statistical mechanics and much of quantum mechanics out of the window.