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An asteroid on the earth's orbit experiences a free-fall acceleration which is 8.0 times smaller than it would be on the earth. what is the distance between the asteroid and the earth's surface measured in the earth's radii? neglect the gravity of the moon.

Respuesta :

The the distance between the asteroid and the earth's surface measured in the earth's radius is 1.82 R

What are the Asteroids:

  • Asteroids are small, rocky objects that orbit the Sun. They are much smaller than planets.
  • They are found between the orbits of Mars and Jupiter, though some have more eccentric orbits.

here,

An asteroid experiences acceleration on earth's orbit which is 8.0 times smaller than it on the earth surface.

Free fall acceleration of Asteroid:

  • on earth's surface = g
  • on earth's orbit = g' = g / 8

so,

g' = GM /(R + x)^2 ------1

g = GM / R^2

g' = 1/8 ( GM / R^2 ) -------1

where G is gravitational constant

M is mass of earth

R is earth's radius

comparing both equations 1 and 2

GM /(R + x)^2 =  1/8 ( GM / R^2 )

8 R^2 = (R + x)^2

2√2 * R = R + x

x = R (2√2 - 1)

x = 1.82*R

hence, The the distance between the asteroid and the earth's surface measured in the earth's radius is 1.82*R

Learn more about earth's radius here:

https://brainly.com/question/4865936

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