Total Energy Problem

1. Apr 6, 2005

apchemstudent

The answer to the problem is a), the orbital speed will decrease but the total energy will become larger. How is this? It's kinetic energy has decreased and the gravitational potential energy should also have decreased from this equation

GM(earth)m(object)/r where r has been increased, thus smaller Gravitational potential energy. Can some one explain this? Thanks

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2. Apr 6, 2005

Davorak

Gravitational Potential energy is negative, so when r gets bigger you potential energy gets less negative, or bigger.

3. Apr 6, 2005

Andrew Mason

The change in potential is positive.

$$U(r) = \int_{R{_0}}^\infty \frac{GMm}{r^2}\hat r \cdot d\vec{s} = \int_{R{_0}}^\infty \frac{GMm}{r^2}dr \hat r$$

$$U(r) = 0 -\frac{GMm}{R_0}$$

So as r increases, U(r) becomes less negative.

AM