# What is the effect of motion on the gravitational field of a massive object?

• hover
In summary, the conversation discusses the amount of energy in a moving mass and how it can be calculated using the equation E=MC^2/sqrt(1-(V^2/C^2)). The correct answer for the energy of a 1kg object moving at .9c is 2.064741605e17 joules. The conversation also delves into the concept of gravitational field and how it is affected by the motion of an object. In general relativity, gravity is caused by energy and momentum, not just mass, and it is described as a curvature of space-time. The conversation also touches on the concept of tidal forces and how they are affected by the motion of an object. Overall, the conversation discusses the relationship between
hover
My first question
I want to know the amount of energy in a moving mass. Using the equation E=MC^2/sqrt(1-(V^2/C^2)) (Which is the full form of E=mc^2 i think) i should be able to find out the amount of energy there is of a mass plus its movement altogether. So say a person sees a 1kg object moving an .9c in a straight line in space. Now doing the calculation out -
1*C^2/sqrt(1-((.9*C)^2/C^2) which = 2.064741605e17 joules. Is this the correct answer??

Once this is answered i will ask my second question.

I'm always telling people this, but if your initial data only has one significant figure (a la "1kg"), it's misleading to pretend to express 10 significant figures in your result. But sure, the formula looks reasonable, what's the second question?

err... according to me the answer should be:9.37526713 * 10^16 Joules.
Also this magnitude is equivalent to the total energy of the body,ie if the body is converted to energy while it is moving,then the energy would be equivalent to the above figures.

in the above case the person will see the person's kinetic energy to be

:
(γ-1)m(o)c^2=K.E

I hope this helped

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oh sry calculation mistake in squaring 0.9c.Sry sry

Ok then. My second question-

From the person's reference frame watching the object moving at .9c, could he say that the mass moving at .9c has a greater gravitational field because it has more energy?? Does this make any sense?

hover said:
Ok then. My second question-

From the person's reference frame watching the object moving at .9c, could he say that the mass moving at .9c has a greater gravitational field because it has more energy?? Does this make any sense?

GR states that gravity is produced by energy and momentum, not just mass.

ranger said:
GR states that gravity is produced by energy and momentum, not just mass.

So it is safe to say that the person watching the object moving at .9c could say it has a greater gravitational field due to an increase of momentum... interesting. Say the mass moving at .9c is in deep dark space has no frame of reference it can depict from to get its true speed. To that mass it could be considered not moving at all. From the mass' reference frame could you say that it has the same gravitational as before when it wasn't moving? I hope this makes sense.

hover said:
So it is safe to say that the person watching the object moving at .9c could say it has a greater gravitational field due to an increase of momentum... interesting. Say the mass moving at .9c is in deep dark space has no frame of reference it can depict from to get its true speed.
Fundamental error here: there is no such thing as "true speed"! All speed is relative.
To that mass it could be considered not moving at all. From the mass' reference frame could you say that it has the same gravitational as before when it wasn't moving? I hope this makes sense.
That makes perfect sense because from the mass' reference frame is still isn't moving!

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A lot depends on what you mean by the term "gravitational field".

Your question has been discussed previously - see for instance

You might also want to check out, for background, the simpler question of what the electric field of a moving charge looks like.

See for instance http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_15.pdf

and if you want more detail on this related topic, try looking at different page "numbers" than 15.

The short answer for a moving charge is that the parallel component of the electric field is not affected by motion, while the transverse components are boosted. One also has additional terms which are known as the "magnetic field".

In Newtonian physics, the term "gravitational field" is usually implied to mean a force. Unfortunately, there is no way to directly measure this "force" unless one has a gravitationally neutral test particle as a reference. And there isn't any such thing as a gravitationally neutral reference.

Just as GR says that it is energy, not mass, which causes gravity, GR also says that gravity is not a force, but a curvature of space-time. GR also offers a recipe to convert this curvature back into forces for slowly moving objects. Unfortunately, this recipe fails for quickly moving objects - its only an approximation.

Under most circumstances, this curvature, mathematically described by the Riemann tensor, can by physically interpreted as a "tidal force". (This identification is actually still not quite perfect, but it's reasonably close. The identification works perfectly only when the observer measuring the tidal force is free-falling).

So, while there turns out not to be any unambiguous way to determine the "force" of gravity of a moving object (I have a rather long-running argument with another poster on this point, BTW), it is quite possible (and in the context of GR, even natural) to talk about the "gravitational field" in terms of the Riemann tensor, or in terms of tidal forces.

A tidal force is just the force/unit length caused by the change in gravity. For instance, if you stand in the Earth's gravity field, your head is further away from the center of the planet than your feet. This causes a slight, but measurable difference in an accelerometer mounted at your feet and and a different one mounted on your head. This difference, per unit length, is just a tidal stretching force. While it is very small in magnitude, it can be measured with a sensitive enough instrument (such as a Forward mass detector).

Now that we've discussed the background, we can talk about the actual result of the gravitational tidal force generated by a moving mass. The result is not intuitive - it says that if you directly approach or move away from a massive object, there is no effect on the tidal force(s) at all.

If you move tangentially to the object, the tidal force(s) increases.

Thus, for instance, an observer falling directly towards a black hole (following a geodesic) at nearly light-speed will not see any change in the tidal force from that black hole. (This is in the textbooks, MTW's "Gravitation" discusses this).

However, an observer moving in such a manner as to orbit a black hole at nearly light speed (still following a geodesic) will see an increased tidal force from the black hole. (This example is not in the textbooks, but can be worked out with enough knowledge and effort).

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## 1. What is the definition of "energy of a moving mass"?

The energy of a moving mass refers to the kinetic energy that an object possesses due to its motion. It is a type of energy that is directly proportional to the mass and velocity of an object.

## 2. How is the energy of a moving mass calculated?

The energy of a moving mass can be calculated using the equation E = 1/2 * m * v^2, where E is the energy in joules, m is the mass in kilograms, and v is the velocity in meters per second.

## 3. What are the units of measurement for the energy of a moving mass?

The units for energy are joules (J) in the International System of Units (SI). However, in some cases, the units of kilojoules (kJ) or electron volts (eV) may also be used to measure energy.

## 4. How does the energy of a moving mass affect its motion?

The energy of a moving mass is directly related to its motion. An increase in energy will result in an increase in the speed or velocity of an object, while a decrease in energy will result in a decrease in speed or velocity.

## 5. Can the energy of a moving mass be converted into other forms of energy?

Yes, according to the law of conservation of energy, the energy of a moving mass can be converted into different forms of energy, such as potential energy or thermal energy, depending on the situation.

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