Calculating Delta V for Orbit Change

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To calculate the Delta V required for changing a satellite's orbit from an inclined 66° to a polar orbit at 260.0 km altitude, it's essential to consider the velocities at both orbits. The discussion emphasizes that there isn't a single velocity for an orbit since it varies continuously. A deliberate velocity change is necessary to transition from the initial orbit to the target orbit. The process involves determining the specific velocities at the points of transfer for both orbits. Understanding these dynamics is crucial for accurately calculating the Delta V needed for the orbit change.
starchaser2020
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A satellite changes its orbit inclined 66° at 260.0 km altitude to a polar orbit at the same altitude. What Delta V was required?

... I am stuck.

do I figure it out using:

DeltaV1 = |V_transfer at orbit 1 - V_orbit 1|
and
DeltaV2 = |V_transfer at orbit 2 - V_orbit 2|

or is there another way?

Thank you in advance!
 
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starchaser2020 said:
|V_transfer at orbit 1 - V_orbit 1|
I'm not sure what two velocities those variables represent. One that thing that may be confusing is that while in an orbit there is no single velocity that goes with it - the velocity keeps changing.
Think of it this way: in order to switch from one orbit to the other, you have to get to a point on the target orbit. How is that going to happen? Will it require a deliberate velocity change? When that has happened, what velocity change is needed to complete the process?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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