A spacecraft follows a highly elliptical orbit around the Earth. At its nearest point, the spacecraft was 6410 km above the Earth's surface, moving at a speed of 7.8 km/s. What was the spacecraft’s speed at its farthest point, 36,000 km above the Earth's surface?[The mass of the Earth = 5.972 × 10²⁴  kg.]

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 its speed would be 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 = $\sqrt{GM\left(\frac{2}{r}-\frac{1}{a}\right)}$ where a is the semimajor axis of the ellipse = $\frac{r_1+r_2}{2}$.