Gravitational fields

• Newton's law:

  $F=$$GMm/r^2$

  In orbit:

  Fgrav = Fcen

  $GMm/r^2 =$$mv^2/r$

  Gravitational potential:

  $Ø =$$-GM/r$

  • At r= infinity ; Ø=0(max)
  • -ve sign indicates attractive forces

  G.P.E:

  = Ø x m

  $=$$-GMm/r$

  • Object approaching:

  gpeA - gpeB = keB - keA

  • Object receding:

  keA - keB = gpeB - gpeA

  Escape velocity:

  Change ke = Change gpe

  KE.surf - KE.infi = GPE.infi - GPE.surf

  $V=$$√(_GMm/r)$