# If a body is heated its gravity will increase

#### wolram

Gold Member
it is my understanding that if a body is heated its
gravity will increase,
also if a body is given mommentum its gravity will
increase.
as both heat and mommentum are energy,there must
be a formula to convert energy into strength of gravity,
if correct, how would the orbital hight of a earth
satalite vary from day to night, and how much extra
energy would you have to give the satalite to
compensate? "keep it at constant hight".

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#### sridhar_n

What do u mean?

What do u intend to convey? Are u saying that the Heat and Momentum make the body more massive or more attracted by gravity. What do u mean by increase in gravity?

#### wolram

Gold Member
mass and energy are interchangable E=MC2
so if energy is added to a body it can be said
to be more massive,
so if a satalite is orbiting the earth "low orbit"
traveling dark "cold" region to light "hot" region
does it experiance more pull "gravity" when in
the light "hot" region than in the dark "cold" region?

#### LURCH

Originally posted by wolram
mass and energy are interchangable E=MC2
so if energy is added to a body it can be said
to be more massive,
so if a satalite is orbiting the earth "low orbit"
traveling dark "cold" region to light "hot" region
does it experiance more pull "gravity" when in
the light "hot" region than in the dark "cold" region?
I think not, since the satellite orbits the center of gravity of the earth. For temperature to make any difference in the satellite's orbit, the average temperature of the entire planet would have to change.

#### sridhar_n

Wolram,

The gravitational attraction between the Earth and the satellite is an effect of the interaction between the Centre of Mass of the Earth and the Satellite. So for the Satellite to gain more energy for it travel faster any point of time then either the net mass of the earth should increase or the net gravitational energy must increase. Earth gets heated so that there is always an equilibrium in the temperature of the Earth. So it is the Earth as a whole that influences the satellite and not specific regions of the Earth. So "the satellite does not accelerate or decelerate at any point of time due to changes in temperature".

Hope u can visualise this...

Sridhar

#### wolram

Gold Member
thankyou, lurch, sridhar-n.

yes something i will have to remeber, always use "center",
of mass.

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#### Aravind

What Crap!

Sorry to say that! But as far as I understood Mr.Wolram's question is - wud the extra mass gained by a sattelite due to raise in its temprature(or heat energy) affect its orbital path around the earth, because it has gained mass(m=heat energy gained/c^2).

Firstly, let me make it clear any sattelite revolves around the center of gravity of earth and not its center of mass.

Next, lets consider the mass gained by the sattelite:
mass gained=energy gained(during exposure to sun)/(c^2)

And heat enegy gained = MCT.Where T=temp. rise and M the actual mass and C the specific heat of sattelite material.

This means, net mass gained will be very very small.Inorder of 10^-16 kgs and this wudn't result in a increased garavitational force from earth in any significant way.

That is the sattelite suffers no wobble in its path as it revolves.

Hope this solves the problem!

Regards,
Aravind

#### sridhar_n

Aravind

Are u trying to say that the Heat from the Earth increases its mass??? It doesn't. For ur information, the satellite is constantly heated by the Sun and can undergo an expansion and gain energy....So why doesn't it speed up???

And again, the Earth's center of mass and center of gravity are the same and for rotational systems the centre of mass frame is considered. So I don't think there was any flaw in the answer. To answer your question, the previous answer that I gave meant that the Average Temperature of the Earth is going to affect the satellite and not the region over which the satellite is present. The Average Temperature of the Earth is pretty much a constant....So ur explanation is wrong!!!

#### NEOclassic

E=mc^2 reversibility questioned?

Originally posted by wolram
mass and energy are interchangable E=MC2
so if energy is added to a body it can be said
to be more massive,
Hi Wolfram and the string,

Pair production shows that a 1.02 MeV photon converts to an e+ and an e-.
Annihilation of an e+ and an e- converts to 2 or 3 photons (none greater than 0.511 MeV and totalling 1.02 MeV photons).

When the electron's rest mass is accelerated to, say, Beta = 11 equivalent electron masses and it is impacted on a target/s, the only mass that is available for conversion to photo energy (0.511 MeV) is the rest mass of the accelerated electron. The other ten masses can be converted uniquely to kinetic etc energy that amounts to 5.11 MeV.

In actuallity,in the case of several impacts the kinetic energy is carried by the electron which shares its energy with the targets that it impacts and that electron is never converted to photonic energy unless it finds a positron somewhere. Cheers, Jim

Staff Emeritus
Gold Member
Dearly Missed
When the electron's rest mass is accelerated to, say, Beta = 11 equivalent electron masses and it is impacted on a target/s, the only mass that is available for conversion to photo energy (0.511 MeV) is the rest mass of the accelerated electron. The other ten masses can be converted uniquely to kinetic etc energy that amounts to 5.11 MeV.
This is why so many physicists prefer to define the mass ("rest mass") as invariant and apply the beta to energy instead. Then the arithmetic works out without special codicils.

#### marcus

Gold Member
Dearly Missed
I should admit some responsibility here since I am one of those who has remarked on occasion that when something warms up it gets more massive

its true, amazingly enough, but the effect is very very slight

with an ordinary (macroscopic, human-size) object like a satellite and a change in temperature of only a few kelvin surely no known instrument and no conceivable experiment could ever detect the change in mass

and in the case of an artificial satellite even if you could suddenly DOUBLE the mass it would not make a detectable change in the orbit

(this is the Galileo dropping stuff from the Leaning Tower of Pisa business---a heavier weight does not fall detectably faster than a lighter one because the heavy one's inertia, the need for force to get it to accelerate, is greater in the same proportion as the pull of the earth on it)

a things orbit is really just a kind of falling (combined with sideways motion) so if you double or triple the mass of a satellite
as long as were talking manmade satellites and not something really massive like the moon it will not affect the orbit in any perceptible way

so there are two kinds of negligibleness here----first, heating something affects its mass only very very very slightly----second, for small objects like satellites changing the mass even by a hefty factor has only a very slight effect on the orbit, almost no effect.

that said, I have to admit that (although the effect is so tiny that you probably couldnt notice it in a billion years) the heating and cooling of a satellite does cause its mass to fluctuate and that logically must affect its orbit

this is a logical question wolram has asked, even tho the effects are too tiny to ever be noticed.

Lets try to answer it and see what happens.

Assume the satellite is 300 kg and that its heat capacity is 1/3 that of water and that it rises 10 degrees kelvin. By how much is the mass changed? Well it has taken on one million calories or 4 million joules of heat (thats how much is needed to raise 100 thousand grams of water by 10 kelvin)

to find the mass change, divide 4E6 joules by the square of the speed of light which is 9E16 in metric units and get (4/9)E-10 kilo.
This is around 44 nanograms. AIIEEE! that is very much too small to consider! The effect on the orbit would be unthinkably little, I cant make myself contemplate such a small change, much less calculate the change in the orbit----it is like comparing a nanogram to the mass of the earth. I have to give up and say the change in the orbit is zero.

but this (ordinarily miniscule) change in mass when something gets warmer or colder is the sort of thing Einstein was talking about in his original 1905 ee equal emceesquare paper so it wont do to forget about it altogether.

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#### wolram

Gold Member
thankyou all for responces,as usual MARCUS has given a full

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