A satellite will travel indefinitely in a [nearly] circular orbit around a planet if the normal component of the acceleration of the satellite is equal to g(R/r)2, where g is the acceleration of gravity at the surface of the planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. 92 Knowing that the diameter of the Sun is 1.39 Gm and that the acceleration of gravity at its surface is 274 m/s² (NOTE: 28 times Earth g), determine the radius of the orbit of the Earth around the Sun assuming that the orbit is circular. Consider for Earth: (v mean) orbit = 107 Mm/h. an v² an = g R² r2

A satellite will travel indefinitely in a [nearly] circular orbit around a planet if the normal component of the acceleration of the satellite is equal to g(R/r)2, where g is the acceleration of gravity at the surface of the planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. 92 Knowing that the diameter of the Sun is 1.39 Gm and that the acceleration of gravity at its surface is 274 m/s² (NOTE: 28 times Earth g), determine the radius of the orbit of the Earth around the Sun assuming that the orbit is circular. Consider for Earth: (v mean) orbit = 107 Mm/h. an v² an = g R² r2

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 11PQ

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Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

Please help me find out the values used to get the answer below. I dont know which units should be placed where and what units I should convert. Please show which values to put to get the answer below.

PROBLEM 11.153
A satellite will travel indefinitely in a [nearly]
circular orbit around a planet if the normal
component of the acceleration of the satellite is
equal to g(R/r)2, where g is the acceleration of
gravity at the surface of the planet, R is the radius
of the planet, and r is the distance from the center
of the planet to the satellite.
92
Knowing that the diameter of the Sun is 1.39 Gm
and that the acceleration of gravity at its surface is
274 m/s² (NOTE: 28 times Earth g), determine the
radius of the orbit of the Earth around the Sun
assuming that the orbit is circular.
Consider for Earth: (v mean) orbit = 107 Mm/h.
an
22
r
R²
an = 92
r
22
== g
r
R²
R²
:9 √²
r = 149.8 Gm
93

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