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lecture23

# lecture23 - Lecture 23 Orbital Mechanics 1 Brief Review of...

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Lecture 23 Orbital Mechanics 1 Brief Review of Gravity Gravitational force In general ~ F = - GMm r 2 ˆ r where r = | ~ r 2 - ~ r 1 | is the distance between the centers of the two objects, and the minus sign indicates that the force is attractive. Near the surface of Earth, the gravitational force is approximately constant so we can write this as F = - m ( GM R 2 r = - mg ˆ r Note, we often write this as acting in the -y direction instead of using - ˆ r . The ˆ r here just means it points toward the center of Earth. If we are approximating Earth’s surface as Fat, we often use the coordinate y instead. Gravitational Potential Energy Since gravity is a conservative force, we can de±ne a potential energy between two objects U = - GMm r where we have de±ned reference such that U=0 at r equals in±nity. PUZZLERS 2 Orbital Mechanics 2.1 Special Case: Circular Orbit ²irst let’s consider a circular orbit from the energy stand-point

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lecture23 - Lecture 23 Orbital Mechanics 1 Brief Review of...

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