# Net gravitational force

• Feb 23rd 2008, 05:38 AM
Yonkersnerd
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!
• Feb 23rd 2008, 07:08 AM
TheEmptySet
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 $\displaystyle F_{net}=G\frac{m_sm_e}{d^2}-G\frac{m_sm_m}{d^2}=G\frac{m_s}{d^2}(m_e-m_m)$

Just plug in the numbers to finish...