
Net gravitational force
Hey:
I am trying to solve this problem, but getting nowhere, any help would be greatly appreciated!
What is the net gravitational force exerted on a 3.00 X 10^4 kg spaceship halfway between the Earth and the Moon. The average distance between the Earth and the Moon is 384,000 km. The Earth's mass is 5.98 X 10^24 kg, and the Moon's mass is 7.36 X 10^22 kg.
I am confused.
Thanks!

The Force of Gravity between two objects is given by
$\displaystyle F_g=G\frac{m_1m_2}{r^2}$
So the force of the earth on the ship is
$\displaystyle F_g=G\frac{m_sm_e}{d^2}$
and the force of the moon on the ship is
$\displaystyle F_g=G\frac{m_sm_m}{d^2}$
where $\displaystyle m_s$ is the mass of the ship
and where $\displaystyle m_e$ is the mass of the earth
and where $\displaystyle m_m$ is the mass of the moon
and where $\displaystyle d $ is the distance half way inbetween
and $\displaystyle G $ is gravitational constant
so $\displaystyle F_{net}=G\frac{m_sm_e}{d^2}G\frac{m_sm_m}{d^2}=G\frac{m_s}{d^2}(m_em_m)$
Just plug in the numbers to finish...