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Space debris left from old satellites and their launchers is becoming a hazard to other satellites. (a) Calculate the speed of a satellite in an orbit 900 km above Earth’s surface. (b) Suppose a loose rivet is in an orbit of the same radius that intersects the satellite’s orbit at an angle of 90º relative to Earth. What is the velocity of the rivet relative to the satellite just before striking it?

Respuesta :

Answer:

Part a)

[tex]v = 7407.1 m/s[/tex]

Part b)

[tex]v_{rel} = 1.05 \times 10^4 m/s[/tex]

Explanation:

Part a)

As we know that orbital velocity at certain height from the surface of Earth is given as

[tex]v = \sqrt{\frac{GM}{R+h}}[/tex]

here we know that

[tex]M = 5.98 \times 10^{24} kg[/tex]

[tex]R = 6.37 \times 10^6 m[/tex]

[tex]h = 900 km = 9.0 \times 10^5 m[/tex]

now we have

[tex]v = \sqrt{\frac{(6.67 \times 10^{-11})(5.98 \times 10^{24})}{6.37 \times 10^6 + 9.0 \times 10^5}}[/tex]

[tex]v = 7407.1 m/s[/tex]

Part b)

When a loose rivet is moving in same orbit but at 90 degree with the previous orbit path then in that case the relative speed of the rivet with respect to the satellite is given as

[tex]v_{rel} = \sqrt{2} v[/tex]

[tex]v_{rel} = 1.05 \times 10^4 m/s[/tex]

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