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1. ### Relative speed of orbiting rockets in Schwarzschild metric

I know the norm of any 4-vector is Lorentz invariant, but the only expression which comes to mind that contains the gamma factor would be the energy. E=-\vec{p}\cdot\vec{e_t}=m\gamma I guess the mass from the momentum ##\vec{p}## and from the right hand side would cancel.
2. ### Relative speed of orbiting rockets in Schwarzschild metric

Using the mass-energy equivalence principle? E^2-\vec{p}\cdot\vec{p}=m^2
3. ### Relative speed of orbiting rockets in Schwarzschild metric

Proper time of B in A's frame ? Isn't the notion of proper time tied to one reference frame ? i.e. there is just one proper time of B: that measured by B. Or do you mean "how would A compute the proper time of B?" In which case I would guess by creating two new 4 velocity vectors, one in which A...
4. ### Relative speed of orbiting rockets in Schwarzschild metric

I would think it is the ratio between the two as I previously posted. That would measure how the proper time of A ellapses relative to the proper time of B.
5. ### Relative speed of orbiting rockets in Schwarzschild metric

I already did that, see my first post in the attempt at a solution part.
6. ### Relative speed of orbiting rockets in Schwarzschild metric

The γ factor is dt/dτ, which is the time-component of the 4-velocity. I have already expressed it above in the derived equations.
7. ### Relative speed of orbiting rockets in Schwarzschild metric

Actually I am not sure what that means ... Is it just: \frac{\gamma_B}{\gamma_A}=\frac{(\mathrm{d}t/\mathrm{d}\tau)_B}{(\mathrm{d}t/\mathrm{d}\tau)_A}
8. ### Relative speed of orbiting rockets in Schwarzschild metric

Homework Statement Two rockets are orbiting a Schwarzschild black hole of mass M, in a circular path at some location R in the equatorial plane θ=π/2. The first (rocket A) is orbiting with an angular velocity Ω=dΦ/dt and the second (rocket B) with -Ω (they orbit in opposite directions). Find...
9. ### Deriving equation of potential energy of H2

Homework Statement Derive the equation for the potential energy of a system of 2 hydrogen atoms as a function of internuclear distance. Homework Equations For electron/electron and nucleus/nucleus repulsion: V_E=\frac{e^2}{4\pi\epsilon_0 R} For electron/nucleus attraction...