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In 2000, NASA placed a satellite in orbit around an
Chapter 13, Problem 47P(choose chapter or problem)
Problem 47P
In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1.0 × 1016 kg and a radius of 8.8 km.
a. What is the speed of a satellite orbiting 5.0 km above the surface?
b. What is the escape speed from the asteroid?
Questions & Answers
QUESTION:
Problem 47P
In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1.0 × 1016 kg and a radius of 8.8 km.
a. What is the speed of a satellite orbiting 5.0 km above the surface?
b. What is the escape speed from the asteroid?
ANSWER:
Step 1 of 4
a.)
We have to find the speed of a satellite orbiting \(5.0 \mathrm{~km}\) above the surface of an asteroid.
The speed of the satellite in a circular orbit around the asteroid can be found using the equation.
\(v=\sqrt{\frac{G M}{r}}\)
Where,
\(G =6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\)
\(M =\text { Mass of asteroid }\)
\(=1.0 \times 10^{16} \mathrm{~kg}\)
\(r=\) distance between the centre of the asteroid and the satellite in \(\mathrm{m}\)