Physics Help Forum Motion in a central force

 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

 Apr 1st 2009, 05:32 PM #1 Junior Member   Join Date: Feb 2009 Posts: 3 Motion in a central force Hello, I have a problem with 2 questions of an exercie about an circular motion in a central force, which can help me are welcome; We 're interested in an artificial satellite, mass $\displaystyle m$, in circular orbit of radius $\displaystyle R$ around the Earth mass $\displaystyle M_E$ and radius $\displaystyle R_E$. I have already shown that the motion of the satellite was uniform by the Newton's laws of motion. Now I'd like some help to answer the following question : Show that the mechanical energy "E" of the satellite is related to its kinetic energy $\displaystyle E_k$ by E =- $\displaystyle E_k$.
 Apr 1st 2009, 07:56 PM #2 Physics Team   Join Date: Feb 2009 Location: India Posts: 365 You know that the orbital velocity of a satellite is given by - V = sqrt(GM/r), where M is the mass of the earth and r is the distance of the satellite from the centre of the earth. If mass of the satellite be m then its kinetic energy K = (1/2)mV^2 = (1/2)GMm/r ..........(1) Next, its potential energy is given by U = - GMm/r ..............................(2) Mechanical energy (E) is the sum of the two- E = K + U = - (1/2)GMm/r ..............(3) From eq (1) and (3) it is clear that E= -K

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