What is the Direction of the Net Force on Earth?

[laxanimal]

Hi all,

I've been working on this problem for a long while and just can't get the answer.

When the Earth, Moon, and Sun form a right triangle with the Earth located at the right angle, the Moon is approaching its third quarter. (The Earth is viewed here from above its north pole.) Find the magnitude and direction of the net force exerted on the Earth.

I found the magnitude to be 3.52e22 N but can't figure out what the direction is (been using tan**-1(force exerted by moon/force exerted by sun). Thanks in advance.

 

[mezarashi]

Independently find the gravitational forces acting on the Earth due to the Sun and Moon. Then add the vectors together, which is in effect a pythagoreas in magnitude because of the right triangle geometry.

 

[laxanimal]

Thanks, I found the magnitude, but can't find the direction (the angle clockwise from the ray from Earth to sun) any suggestions?

 

[mrjeffy321]

This is a gravity question I assume, where the forces acting on the Earth are due to the forces of gravitational attraction between the Earth and the Sun/moon.

To find the resultant force acting on the Earth, you found the force caused by the moon, then force caused by the sun. These two forces are perpendicular to each other along the sides of right triangle, so you are able to calculate the resultant using the pythagorean theorem.
But there is another nifty thing you can employ since it is a right triangle, you know that the tangent of the angle is equal to the opposite "leg" of force / the adjacent "leg" of force.
Tan(angle) = opp / adj
or that,
Sin (angle) = opp / resultant, or
Cos(angle) = adj / resultant
Solving for the angle using anyone of these will work.


EDIT:
If you have been using,
tan^-1(force exerted by moon/force exerted by sun)
then your calling the force from the moon the opposite "leg" force, and the force from the sun, the adjacent "leg". The angle you will get would be the angle above the adjacent leg.

 

[laxanimal]

Thanks, I guess I don't know what angle I'm looking for. I found all of the angles in the triangle (90, 89.7, 0.328) and none of them work. Any help? Thanks.

 

[Astronuc]

One can determine the angle between the resultant force and either the line between the sun and earth, or the line between the moon and earth, the latter line being the tangent to the Earth's orbit based on the problem statement.

I have not evaluated the magnitudes of the forces, but the angles are probably about right. Draw a right triangle, and the resultant vector should be inside the triangle with it's base at the right angle vertex, and the point tilted slightly toward the sun.

 

[yogesh the hy]

what is force acting at right angle should be