Physics Help Forum What if mass is not constant?

 Special and General Relativity Special and General Relativity Physics Help Forum

 Jul 18th 2017, 01:04 AM #1 Senior Member     Join Date: Feb 2017 Posts: 205 What if mass is not constant? When we use the formula L= mxvxr. We usually hold mass to be constant. For example when the Earth orbits the Sun the r which is the separation distance gets smaller so to compensate and for conservation of angular momentum to be true the velocity should increase but mass is supposed to be constant. Now we come to relativity. Suppose the earth orbits the sun at the speed of light. Then its mass should increase. Now when we keep r constant that means the distance between the sun and earth is the same when Earth orbits the Sun. Now mass has increased due to higher speed. But r is constant so since mass has increased the velocity is decreased. So is this another way of proving Relativity?
 Jul 18th 2017, 04:35 AM #2 Senior Member     Join Date: Jun 2016 Location: England Posts: 963 I think I can pick out the gist of your argument, moving away from the impossible (earth at the speed of light) consider a smaller object, say a lead ion, being accelerated around a synchrotron ring. As the speed increases into relativistic realms, the increased relativistic mass should be noticeable in the increased magnetic energy required to steer the ion around the ring. The energy needed to hold the radius constant will not match the Newtonian equations. __________________ ~\o/~
Jul 18th 2017, 05:30 AM   #3
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 Originally Posted by avito009 Now we come to relativity. Suppose the earth orbits the sun at the speed of light.
Which is impossible. What you write below indicates that you're merely thinking of the Earth moving at speeds which are merely close to the speed of light. Let's go with that.

 Originally Posted by avito009 Then its mass should increase. Now when we keep r constant that means the distance between the sun and earth is the same when Earth orbits the Sun. Now mass has increased due to higher speed. But r is constant so since mass has increased the velocity is decreased. So is this another way of proving Relativity?
First off you're being unclear. First you wrote "Then its mass should increase" which, if speaking about the Earth's relativistic mass, is correct. An increase in speed results in an increase in mass. Then you go on to conclude so since mass has increased the velocity is decreased" which is contradicting what the assumption that you started with. The problem with your assumption is the expression L= mxvxr. This is only an approximation and as such it will only hold when the speed of the object is much less than the speed of light.

The correct expression is L = r x p

where p = mv. In this expression m is a function of v.

Regarding So is this another way of proving Relativity? - No. Relativity cannot be proved. No scientific theory can be proved.

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