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Total Mechanical Energy in a Circular Orbit

`E_"mech" = -1/2(G* m _E* m )/ r `
`(m)"Mass"`
`(r)"Radius"`
Tags
Physics

This equation computes the total mechanical energy, `E_"mech" = K + U`, where

`U = "gravitational potential energy" = (-G*m_E*m)/r`

`K = "gravitational kinetic energy" = 1/2 m*v^2 = 1/2 (m* G*m_E)/r`

So, `E = K +U = (1/2 (m* G*m_E)/r) - (G*m_E*m)/r = (G*m_E*m)/(2*r)`

Reference

  • Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 391, eq 12.9
  • Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 394, eq 12.10
  • Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 395, eq 12.12
  • Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 395, eq 12.13