The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 5.0 earth years. What are the asteroid's orbital radius and speed?

Respuesta :

Asteroid's orbital and speed will be calculated as V1:

Asteroids are stony bodies in space that can range in size from a few hundred feet to several hundred miles. They are thought to be leftover solar system formation detritus.

T1 = 5years = 5 ·365·24·3600s = 1.5768· 10^8, G= 6.67·10^-11 Nkg^2/kg^2,  Msun = 1.99·10^30 kg, The gravitational force between the sun and the orbiting asteroid is: F= G msunma/r1^2, The asteroid is affected by centripetal acceleration because it moves in a circular orbit F = mac ac = v^2/r, According to the Newton's law, we have: F= mac Gmsunma/r1^2 = ma·v1^2/r1 Gmsun/r1 = v1^2, The speed of the asteroid is: v=Θ/T, Θ= 2πr1, v1 = 2πr1/T1

Asteroid's orbital speed is By substituting the period in equation 2 we find the speed: V1= 2πr1/T1 V1 = 2·3.14·4.39·10^11m/1.5768·10^8s V1 = 1.7·10^4 m/s

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