When is G 6.67 x 10^-11 and when is it 9.81?

The generic force from gravity equation is F_g = \frac{G m_1 m_2}{r^2}. This G is the 6.67\times 10^{-11} \frac{m^3}{k\cdot s^2}

If we use this equation specifically at the surface of the earth, with the mass of the earth, the \frac{G m_2}{r^2} simplifies to 9.81 \frac{m}{s^2}, letting you write F_g=m_1g.

So, if youâ€™re calculating the force from gravity close to the surface of the earth, like we do for most of our problems not involving satellites or planets, you can use the shortcut 9.81. Alas, you could still use the long version, but it would be way more work than you need to do.

ok thank you so much!