<P> ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 + ∂ 2 f ∂ z 2 = 1 r 2 ∂ ∂ r (r 2 ∂ f ∂ r) + 1 r 2 cos ⁡ θ ∂ ∂ θ (cos ⁡ θ ∂ f ∂ θ) + 1 r 2 cos 2 ⁡ θ ∂ 2 f ∂ φ 2 (\ displaystyle (\ frac (\ partial ^ (2) f) (\ partial x ^ (2))) \ + \ (\ frac (\ partial ^ (2) f) (\ partial y ^ (2))) \ + \ (\ frac (\ partial ^ (2) f) (\ partial z ^ (2))) \ =\ (1 \ over r ^ (2)) (\ partial \ over \ partial r) \ left (r ^ (2) (\ partial f \ over \ partial r) \ right) + (1 \ over r ^ (2) \ cos \ theta) (\ partial \ over \ partial \ theta) \ left (\ cos \ theta (\ partial f \ over \ partial \ theta) \ right) + (1 \ over r ^ (2) \ cos ^ (2) \ theta) (\ partial ^ (2) f \ over \ partial \ varphi ^ (2))) </P> <Table> <Tr> <Td> <P> </P> </Td> <Td> <P> </P> </Td> <Td> <P> </P> </Td> </Tr> <Tr> <Td> <P> </P> </Td> </Tr> </Table> <Tr> <Td> <P> </P> </Td> <Td> <P> </P> </Td> <Td> <P> </P> </Td> </Tr> <Tr> <Td> <P> </P> </Td> </Tr>

J2 term of the gravitational field of the earth