Question

How far from the earth must a body be along a line toward the sun so that the sun’s

Answer 1

Answer:

r = 1.63×10^5 mi

Explanation:

Let r = distance of object from earth

Rs = distance between earth and sun

Ms = mass of the sun

= 3.24×10^5 Me (Me = mass of earth)

At a distance R from earth, the force Fs exerted by the sun on the object is equal to the force Fe exerted by the earth on the object. Using Newton's universal law of gravitation,

Fs = Fe

GmMs/(Rs - r)^2 = GmMe/r^2

This simplifies to

Ms/(Rs - r)^2 = Me/r^2

(3.24×10^5 Me)/(Rs - r)^2 = Me/r^2

Taking the reciprocal and then its square root, this simplifies further to

Rs - r = (569.2)r ----> Rs = 570.2r

or

r = Rs/570.2 = (9.3×10^7 mi)/570.2

= 1.63×10^5 mi