To what precision, are we able to know the direction that gravitational force acts (for example the sun's) ? Possibly, it may exceed light speed ? Therefore it's untouched ?

About my question, allow me to expound a little..... Apparent position of the sun is fixed on the celestial sphere (it's a phenomenon, "Light-Time Correction"). So, apparent position is the position that the sun was 8 minutes odd before. Therefore if gravitational force comes at infinite speed, "emitted position" is different. The difference is a 2 degree odd angle (Maximum).

[P.S.] "Light-Time Correction" is a phenomenon based on the rest frame. So common explanation is complicated.
[P.S.] It's supposed that we can know the coming direction of gravitational force sufficiently. And it is not affected by the motion of the sun and the earth.

Very Sorry, i made a silly error (yesterday's post is wrong, i can't erase). Allow me to correct by the following.

There is a space ship. It is at a standstill in the aether. Therefore every aberration (including secular aberration) doesn't occur on the loaded telescope. The sun (distance from the space ship is 1.5 hundred million km) is passing at the speed of 400 km/sec. Because of "Light-Time Correction", apparent position of the sun is the position that the sun was 8 minutes odd before. Therefore if gravitational force comes at infinite speed, "emitted position" is different. But this difference is slight. Below a 0.1 degree angle (Maximum). Can we distinguish it ?

[P.S.] From the earth, the same measurement will be possible logically. Because the motion of the earth relative to the aether is measurable.

If distance to the sun is shorter, above difference will be detectable easily.

I’m sorry. Yesterday’s post is wrong.

To administrator ; Erase yesterday’s and this post, please.

Suppose that speed of propagation of gravity is the same to light speed and propagation follows aether frame (like light-time correction). If so, it’s conceivable that because of the motion of the solar system, direction of gravity (at the earth’s surface) deviates from the center of gravity of the earth (and direction of deviation changes because of rotation of the earth). If speed of the solar system is 400km/sec, deviation is nearly a 0.2degree angle (at maximum). It may be detectable.

In "Encyclopaedia Britannica" 1969, there is a passage as follows (in item "Gravitation" ; original text). "If the action of gravitation were not absolutely instantaneous"(omission)"All experiments and observations were, however, consistent with the law, from the short distances employed in laboratory experiments to the long ranges used in interplanetary calculations". It says, action is instantaneous. What !? What about that light cone ?

If the speed of gravity (gravitational force) is not infinite (the same as light speed), orbit of a planet seems to be affected characteristically by the sun's gravity. The sun is moving in an uniform linear motion. This line is supposed to cross the orbit (supposed to be true circle) at two point, A and B (like Greek letter φ phi). If the speed of gravity is independent of the motion of the sun (supposed to follow the frame of aether [as light]), strength of gravity at A and B will be different. Then, the orbit will warp.《P.S.》 Imagine a wave source and point A and B (distance from the source is the same) that are moving (on a straight line) on the surface of water. Power of waves that A and B receive is different.

If the light speed were slower and as a result, if apparent position of the sun (at the zenith) is the position that the sun was 6 hours before (in fact, it's the position that the sun was 8 minutes odd before), outline of the speed of gravity will be found. But a suitable heavenly body (to examine it ; under actual light speed ; including artificial body) may exist in our solar system.
[P.S.] Situation is also related to the rotational speed of the body and to the distance to the sun.
[P.S.] i must say sorry again. A post (date is 4 Jan 2011) seems to be valid partially.

Even on the ground, there will be apparatus that react to the gravity of the sun. When this apparatus turns (about 2000 seconds per one turn), the answer (to the speed of gravity) seems to be shown. Such a experiment will be one of laboratory experiments that "Encyclopaedia Britannica" mentions.

If there is certain minimum limit (like quantum) in gravitational force, Seeliger's paradox (version of Olbers's paradox on gravity) will not stand up.

Allow me to ask. Are there any error in the following passage ?

A body (gravitational mass ; M) is hung from the roof by a string. Because of gravity of the earth, the string is tightened in a constant strength Mg. Above all are turned to the left a 90 degree angle. So, the roof is on the left and the earth is situated on the right (the earth is far. gravity is 1/100g). Now the string is cut, the body begins to "fall" to the right. To continue drawing from the right by a string (drawing force is 1/100Mg ; the earth vanishes) will be the same situation (if gravity is 1/99g, force 1/99Mg will cause the same acceleration as fall). The same acceleration (will be) by the same force. Namely, gravitational mass and inertial mass (of this body and of every body) will be the same.

Allow me to raise a hypothesis.

Inertial force will occur by the motion (excludes uniform linear motion) of a body relative to the aether frame. If it's true, equivalence principle is wrong. And every difficulty will be dispelled.

《P.S.》 Gravity and inertial force act independently (Vector composition is possible in appearance). Both are reflection of different physical causes.《Differences》 -Gravity- Not affected by the motion of body. Force that occurs in gravitational fields only. It occurs in inertial frames and in non-inertial frames. Not isotropic. -Inertial force- Affected by the motion of body. Force that is caused by external forces (includes gravity and centripetal force). Occurs only in non-inertial frames. Isotropic.《P.S.》 In the air, a elevator is in free fall. Both forces are not the same.

On a level surface, when a body is being accelerated by force 1/100Mg, inertial force is -1/100Mg. On this point, in free fall, the role and effect of gravity is not special at all (one of external forces). But, both forces act on every atom directly. Therefore there is no-weight. Is equivalence principle invalid ?

If an elevator car (box) is high, strength of gravity at floor and roof is different. Equivalence principle will be wrong.

There is a space ship (regard inside as an elevator car). In this space ship, there is a man who is feeling 1g. Now he starts a jet engine in motion (jetted out downward ; power is weak). If 1g is caused by gravity, the space ship doesn't move (because power is weak ; at a stand still on the ground). But if 1g is caused by an accelerated motion, 1g will be increased somewhat. In short, equivalence principle seems to be wrong.

Equivalence principle seems to deny momentum and the law of causality (causal relationship). If so, matters that are brought will be invalid.

There is a small space ship (regard this as an elevator cabin) in free fall. A crew man doesn't feel gravity. But if this space ship is in a non-gravitational field and moves in an accelerated motion (by 1g ; by jet emission), he feels "gravity" 1g (because, external force = gravity acts on every atom directly. but external force = jet emission and its inertial force does not). In short, equivalence principle seems to be wrong.《P.S.》 On the ground, gravity acts to the floor. In an accelerated space ship, accelerated force acts from the floor.

By accelerated motion, no change of gravity will be caused. Change of inertial force only will be caused. If it's true, equivalence principle is wrong.

On a space station (on every atom), gravity and centrifugal force (an inertial force) is acting independently. Free fall is caused by gravity (not be offset by centrifugal force). In short, equivalence principle seems to be wrong.

Equivalence principle will be inconsistent with Newton's formula on universal gravitation.

On a slanting rail (at a 45 degree angle), an elevator cabin is in free fall (without friction). Effect of gravity is obvious. In vertical free fall, it will be the same.

Imagine gravity and centrifugal force that act on every point of a rotating blade of windmill (zero-weight point occurs instantaneously). Equivalence principle will be wrong.

A windmill (three blades) is rotating. Mass of the blades is the same, but shape is different. So, centrifugal force that acts on the fixed part of the blades is different. How does the equivalence principle explain ?

On guide rails of elevator, graduations are marked. Momentum (potential energy also) of an elevator cabin in free fall is changing

Besides, relativity of non-uniform accelerated motion seems to be unimaginable.

In a elevator cabin in free fall, g is increasing (in a deep hole [underground], decreasing). In non gravitational field, g is zero.

There is a space ship in an accelerated motion (to the above ; non-uniform accelerated motion). A body is hung with an elastic string from the ceiling. Motion of the body will not be the same as the motion caused by the change of gravity (if two bodies are hung with two strings [length is different], it will be more clear).

Newton's second law (F = Ma) will stand up on gravity also. And above formula will be meaningful not only on a falling body but also on a body on the ground (differently from a contact force). But in falling and on the ground, how about the value of F and a (g) ? Both will be the same. If so, M is the same. Therefore the sameness of gravitational mass and inertial mass will be natural.

There are two elevator cabins. Now one begins free fall. After a few seconds, the other begins free fall also. Motion of the both isn't a uniform motion. How does equivalence principle explain ?

《correction》 Above post (Jun 5th ; Two elevator cabins) was mistake. Both will continue a uniform motion (Relatively). Very sorry.

-To administrator- Please erase above and this posts if it's possible. i am thankful for this forum always.

In the air, an elevator cabin is in "free fall". Eventually, falling speed reaches the terminal speed (at the same time, inertial force fades). This "free fall" will be better (to ascertain the relation between gravity and inertial force) than Einstein's free fall (at least).

About the equivalence principle ; A little
《1》 Two small space ships are in free fall. But speed of one of them was decelerated (by jet emission ; downward), and then, was accelerated (by jet emission ; upward) for a while. During the deceleration and acceleration, a crewman (of the latter) would feel -a and a. Equivalence principle will be wrong.
《2》 Allow me to ask. Are there any error in the following passage (ignore rotary motion). There is a small body. It will be able to ascertain that no external force is acting (except for gravity) on it. So if there is some internal force, it's caused by gravity !! Equivalence principle will be wrong.

Are there any errors in the following passages (all occur in vacuum) ? There is a tall steel tower. Along this tower, an elevator cabin is in free fall. On this tower, light sources are set at intervals of ten meters. Lights are emitted from these and pass through horizontally a hole on the wall of this cabin (supposed to be the left wall ; timing is arranged). Light will reach somewhat upper point on the right wall. It will not be the same phenomenon occurs in non-gravitational field (even if steel tower is supposed to be accelerated upward).

An elevator cabin is at a standstill in non-gravitational field. On the side wall (supposed to be the left wall), there are ten holes (at regular intervals ; vertically). The sun light is coming from the just left and passing through the holes. Then, on the right wall, there are ten projections (spot-lights ; don't move). But, if this elevator cabin begins free fall (downward), projections will move upward.

On the ground, there are slanting rails (45 degrees). On this rails, an elevator cabin was accelerated upward at 1G and then at 2G. Can equivalence principle explain the change of resultant force (by inertial force and gravity) ?

In non-gravitational field, there is a space ship (mother ship). Now, two probes separate from the mother ship and begin an accelerated motion to opposite direction (at 2g and 1g. by gas jet). No gravitational field will occur on the mother ship.

A tall elevator cabin is in free fall. In this cabin, pressure of gaseous body is different (because value g is different). Equivalence principle will be wrong.

An elevator cabin is accelerating upward. With the roof, a small body collided (came vertically). And after 10 seconds, a second body (the same mass) collided (came vertically also). This situation will not be the same to an elevator in gravitational field (at a standstill).
- P.S.- Some books today say that accelerated motion is not relative.

"Accelerated motion is not relative". It’s a subheading of a book (in Japanese). Yes, time dilation in gravitational field is written to be real (one sided ; not relative). But in many books, it seems to be written that "accelerated motion is relative"

“Accelerated motion is not relative”, ”Equivalence of every frame including accelerated frame”

The two above seem to be inconsistent. These are subheading of books (in Japanese ; published in 1998 and 1999).

On a point mass, inertial force acts only in one direction always. Gravity isn’t so. Equivalence principle will be wrong.

Under every situation, the law of universal gravitation will act.