Recent content by christianwos

This is a very complicated, perhaps impossible question to answer. All I am saying in my response is that, as far as numbers, even an open interval such as (0,1) (that is, all the real numbers between 0 and 1), is uncountably infinite. look up Cantor's work. But I attempt to make no...

Got it. Thank you for your infinite patience.

No problem mate. :)

Of course. I meant reals, assuming the person who posted meant the same thing.

No. 23, for example, is prime. But it is true that any number that is not prime is a product of primes.

If by the space between two numbers you mean the open interval (a, b), then yes. It is an infinite uncountable set.

Now I get v=(2MG/R)1/2.

To be honest, now that I started reading Ballentine, I have to admit that it is an excellent textbook. If you have a strong mathematical background I would strongly suggest you take a look at it. Gottfried and Yan is very good, too, in my opinion.

So the energy is E=-mMG/2R and the escape velocity should be twice the orbital?

The orbital velocity should be v=(MG/r)^1/2 which I get from mv^2/r=mMG/r^2, right?

The orbital velocity is jusr rdø/dt, while the escape velocity, for a stationary object shot vertically in a gravitational field, would be v=(MG/r)^1/2, where M is the mass of the planet or whatever the object is stationary on.

I am just setting the energy equation up. I generally find it easier to work with energy than with forces. Regarding the angular momentum, I meant that L is conserved until the impulse is delivered.

Here is the problem. A rocket of mass m is in a circular orbit around the Earth at a distance R from the center. (a) What tangential impulse, mΔv, must be given to the body so that it just escapes to infinity? My attempt: I set the problem in terms of energy...

Thank you for the suggestion. You were right, Ballentine is an excellent textbook, as far as I can tell.

Thank you. What about Sakurai?