# Tutor profile: Joseph M.

## Questions

### Subject: Physics (Electricity and Magnetism)

Calculate the electric field at the center of a 1 meter conductive cube held 2 meters directly above an infinite sheet of $$-1 \ C/{m^2}$$ charge, as measured from the center.

The field is zero. There's no electric field in the interior of a good conductor; any field would tend to move electrons around until they cancel out the would-be internal field. Charge will build up on the surface of the cube, in response to the field from the charged sheet.

### Subject: Calculus

Describe the difference between continuity and differentiability.

Continuity refers to the "connectedness" of a function. A very small change in input will result in a small change in output, without any sudden jumps or holes. A differentiable function must have a well-defined derivative across its domain. You can think of this as being able to draw an unambiguous, non-vertical tangent line on its graph at any point. All differentiable functions are continuous, but the reverse isn't true.

### Subject: Aerospace Engineering

Why are the maneuvers used to rendezvous in orbit typically counter-intuitive (initially slowing down to catch up to a target, etc)? Also, what is the minimum delta-V needed, assuming the two satellites start co-orbital but out of phase?

The maneuvers work by changing your orbit's period to catch up to the target. Slowing down/burning retrograde tightens your orbit around the planet, which reduces the period. This lets you catch up over time. For example, you might lower your orbit such that it takes you 5 hours to make 1 rotation, while it takes your target 6 hours to do the same thing. You would wait for the difference in periods to bring you to the target, then you would speed up to match velocities and periods. There isn't a clear minimum delta-V for this type of rephasing. The difference in periods, which is roughly proportional to the delta-V needed, can be as small as you want. The trade-off is that you will need to wait longer to catch the target using a small difference. It might only take 1 cm/s of delta-V to shift the period by 1 second, but you would spend years or decades waiting for that tiny difference to add up.

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