Eccentricity Definition and 57 Threads

This one question has me totally beaten. And I thought I was pretty good in co-ordinate geometry. Here it is: If the equation ax^2 + 2hxy + by^2 =1 represents an ellipse, find the square of the eccentricity of the ellipse. I know that the ratio of the distance from the directrix to the...

Sir, The eccentricity of Earth's orbit is 0.0167. What is the ratio of its maximum speed to its minimum speed in its orbit? I solved it in the following way: Let its maximum and minimum speed be v1 and v2 respectively. Let a and b be the semi length of the major and minor axis...

For a planet moving in an elliptical orbit, fraction of maximum and minumum angular is given to be n \frac{\dot{\theta}_{max}}{\dot{\theta}_{min}} = n Show that \varepsilon = \frac{\sqrt{n}-1}{\sqrt{n}+1}. I keep finding \varepsilon = -\frac{n^2-1}{n^2+1} Can someone show a path to correct...

You make a 100 m diameter tunnel that goes from the north pole to the south one. You put into orbit a tennisball by dropping it in the tunnel from the north hemisphere Supposing it makes an ellipse 99 m the minor axe and the Earth radius the bigger axe wouldn't the ball get into an orbit...

Given the mass of the sun, the gravitational constant, the period of Earth's orbit, and the semi-major axis of Earth's orbit, is it possible to find the eccentricity of the orbit? If yes, how?

How would I find the eccentricity of the ellipse: x^2/49 + y^2/64 = 1 :confused:

How is eccentricity of an orbit affected by the angular momentum of the orbiting body (mathematically, that is)? How does torque affect angular momentum? How is a torque exerted? What is a torque?