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Energy of Elliptical Orbits
Energy of Elliptical Orbits
8. Centripetal Forces & Gravitation / Energy of Elliptical Orbits / Problem 2

A weather monitoring satellite with a mass of around 2000 kg needs to move from an initial circular orbit which is approximately located at a distance of about 500 km above Earth's surface to another circular orbit which is approximately located at a distance of about 37,000 km above Earth's surface. Determine what would be its speed on the first orbit and also find out its speed when it reaches the lowest point in an ellipse connecting both orbits.

Hint: Use the vis-viva equation v = GM(2r1a)\sqrt{GM\left(\frac{2}{r}-\frac{1}{a}\right)} where, a is the semimajor axis of the ellipse = r1+r22\frac{r_1+r_2}{2}.

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