Gravitational fields

• Newton's law

  $F=$$GMm/r^2$
• In orbit:

  Fgravivational = Fcentripetal

  $GMm/r^2 =$$mv^2/r$
• Gravitational potential (Φ):

  $Φ =$$-GM/r$

  At r= infinity, Φ= 0(max potential)

  -ve sign indicates an attractive force
• Gravitational potential energy :

  Gpe = Φ x m

  $Gpe =$$-GMm/r$

  • When objects approaches; GPEa - GPEb = KEb - KEa
  • When objects recedes ; KEa - KEb = GPEb - GPEa
• Escape velocity:

  KE surface - KE infinity = GPE infinity - GPE surface

  $V =$$√(2GM/r)$