# Can gravity cause an expansion of a sphere?

by Jano L.
Tags: expansion, gravity, sphere
 P: 1,027 Hi everybody, some time ago our teacher has shown us the following example from the theory of elasticity: Calculate how the gravity of the sphere changes its size. The sphere is made of ideal linear material (in practice, perhaps some metal) with Young modulus $E$ and Poisson ration $\nu$. The amount of the material is such that if the gravity did not act, the radius of the sphere would be $R_0$. Now imagine the gravity is "turned on". Do you think the sphere will shrink or expand? Teacher said (and the same can be found in Landau Lifgarbagez, Theory of elasticity, p. 21) that the sphere as a whole will actually expand due to gravity. Do you think such a strange conclusion can be correct?
P: 3,543
 Quote by Jano L. Hi everybody, some time ago our teacher has shown us the following example from the theory of elasticity: Calculate how the gravity of the sphere changes its size. The sphere is made of ideal linear material (in practice, perhaps some metal) with Young modulus $E$ and Poisson ration $\nu$. The amount of the material is such that if the gravity did not act, the radius of the sphere would be $R_0$. Now imagine the gravity is "turned on". Do you think the sphere will shrink or expand? Teacher said (and the same can be found in Landau Lifgarbagez, Theory of elasticity, p. 21) that the sphere as a whole will actually expand due to gravity.
Here is that page:

Do you mean problem 12? It is about a spherical cavity in an infinite medium. What sphere do you have in mind? A solid uniform sphere or an empty shell?
 P: 1,027 It is the problem 3, p. 21. The problem 12 with the cavity is at the page 24.
P: 3,543

## Can gravity cause an expansion of a sphere?

 Quote by Jano L. It is the problem 3, p. 21
Okay, it is page 19 in the Google version: