Physics emergency?

Question

Find the centripetal accelerations at each of the following points due to the rotation of Earth about its axis.
(a) a point on the Equator of Earth
The average distance separating Earth and the Moon (center to center) is 384 000 km. Use the data in Table 7.3 to find the net gravitational force exerted by Earth and the Moon on a 3.00 104 kg spaceship located halfway between them.
N
Objects with masses of 210 kg and a 510 kg are separated by 0.320 m.
(a) Find the net gravitational force exerted by these objects on a 31.0 kg object placed midway between them.

Your answer differs from the correct answer by 10% to 100%. N
(b) At what position (other than infinitely remote ones) can the 31.0 kg object be placed so as to experience a net force of zero?

Your answer differs from the correct answer by orders of magnitude. m from the 510 kg mass

Also tell mne how to freaking set these up. THANKS

Answer 1

Centripetal acceleration is r*w^2, where w = angular velocity and r = radius. You have mainly a units problem here converting to consistent units from w = 2*π/24hrs and r = 4000mi. Convert hrs to sec, mi to meters to get m/sec^2.

Gravitational force is G*m1*m2/r^2, where G = newton's gravitational constant, r = distance between mass m1 (earth) and m2 (moon). You can look up values for G, m1 and m2.

The same formula is again for the three-object problem.

Finally, find the point where the gravitational attraction to the 210kg and 510kg objects are equal and opposite. Any mass there will have zero force.