# Help with an Energy Question please

1. Feb 6, 2006

### sopi

Hello. I'm stuck on this question. Any help would be appreciated:

The orbit of the Earth about the Sun is almost circular. The closest and farthest distances are 1.47x10^8 km and 1.52x10^8 km, respectively. Determine the maximum variations in a) potential energy, b) kinetic energy, c) total energy, and d) orbital speed that result from the changing Earth-Sun distance in the course of 1 year.

I got part a) no problem. However, I'm not sure about b), c) or d).

Thanks,
Mike

2. Feb 6, 2006

### Triss

You can easily calulate the velocity of the Earth at any arbitrary point on the ellipse:
$$v = \left[ GM_sM_e\left(\frac{2}{r}-\frac{1}{a}\right)\right]^{1/2}$$
and the total energy as
$$E = -\frac{GM_sM_e}{2a}$$
The semi major axis a for the Earth orbit is $a = 149.6\cdot 10^6km$

Last edited: Feb 6, 2006