Recent content by Jack3145

I am looking for how to solve the geodesic path, I. Something like this except taking into account initial conditions: I = \int[(1-2m/r)^{-1} + r^{2}(d\theta/dr)^{2} + r^{2}(sin\theta)^{2}(d\phi/dr)^{2} - (1-2m/r)(dt/dr)^{2}]^{1/2} dr

Homework Statement A point: [x_{0}, y_{0}, z_{0}, t_{0}] It's velocity: V_{a} = [v_{1}, v_{2}, v_{3}, v_{4}] What is wrong with this equation: x^{b} = [x_{0} + v_{1} * t, y_{0} + v_{2} * t, z_{0} + v_{3} * t, t_{0} + t]

Let’s say an asteroid is about to enter earth’s atmosphere(it will burn up of course). The initially sitting is at: point = [x_{0},y_{0},z_{0},t_{0}] = [r_{0},\\theta_{0},\\phi_{0},t_{0}] With a 4-velocity: V = [v_{1},v_{2},v_{3},v_{4}] The momentum at 0+ p_{0+} = mass*V =...

Sorry for the abomination. I know that Minkowski Space has no external gravitational forces acting on it.

Let's say there is a small object heading towards Earth (it will burn up). It is first observed at: x^{\\mu}=[x^{1},x^{2},x^{2},x^{4}]=[x_{0},y_{0},z_{0},t_{0}] with a velocity: V_{v}=[v_{1},v_{2},v_{3},v_{4}] The metric is: ds^{2} = dx^{2} + dy^{2} + dz^{2} -c^{2}*dt^{2} g_{\\mu\\v} =...

The Schwarzschild solution at ds^2 = 1/(1-2*m/R)*dR^2 + R^2*d\theta^2 + R^2*(sin(\theta))^2*d\phi - (1-2*m/R)*dt^2 What if R --> infinity then the object would be a fixed point in the sky never waivering so d\theta --> 0 d\phi --> 0 giving you the Minkowski Metric.

What tells the weight? g_{ab}=(1,0,0,0;0,r^{2},0,0;0,0,r^{2}*(sin(\theta))^{2},0;0,0,0,-c^{2}*t^{2}) (-det(g_{ab}))^{1/2} = r^{2}*sin(\theta)*c*t

Given a Riemann Curvature Tensor. How do you know the weight and rank of each: R^{i}_{jki} R^{i}_{jik} R^{i}_{ijk} Is the Ricci tensor always a zero tensor for diagonal metric tensors?

The path of a satellite reentering the atmosphere from a very high orbit has two components, one gravitational and the other from the atmosphere. Could there be a discussion of the two separate components using Newtonian gravity with gravity as: g = GM/r^2 that change with elevation as a...

The Ricci Tensor comes from the Riemann Curvature Tensor: R^{\beta}_{\nu\rho\sigma} = \Gamma^{\beta}_{\nu\sigma,\rho} - \Gamma^{\beta}_{\nu\rho,\sigma} + \Gamma^{\alpha}_{\nu\sigma}\Gamma^{\beta}_{\alpha\ rho} - \Gamma^{\alpha}_{\nu\rho}\Gamma^{\beta}_{\alpha\sigma} The Ricci Tensor just...

Is the Metric Tensor derived directly from Schwarzschild Metric or is it derived from the spherical metric of a sphere?

Will the Schwarzschild metric work for the atmosphere, the edge of the atmosphere? Are there any hints on formulating the Schwarzschild metric into the Metric Tensor.

I would like to know the Metric Tensor of the Earth in the form of g = [g11,g21,g31;g12,g22,g32;g13,g23,g33].