Respuesta :
Answer:
149.34 Giga meter is the distance d from the center of the sun at which a particle experiences equal attractions from the earth and the sun.
Explanation:
Mass of earth = m = [tex]5.976\times 10^{24} kg[/tex]
Mass of Sun = M = 333,000 m
Distance between Earth and Sun = r = 149.6 gm = 1.496\times 10^{11} m[/tex]
1 giga meter = [tex]10^{9} meter[/tex]
Let the mass of the particle be m' which x distance from Sun.
Distance of the particle from Earth = (r-x)
Force between Sun and particle:
[tex]F=G\frac{M\times m'}{x^2}=G\frac{333,000 m\times m'}{x^2}[/tex]
Force between Sun and particle:
[tex]F'=G\frac{mm'}{(r-x)^2}[/tex]
Force on particle is equal:
F = F'
[tex]G\frac{333,000 m\times m'}{x^2}=G\frac{mm'}{(r-x)^2}[/tex]
[tex]\frac{x}{r-x}=\sqrt{333,000}[/tex] = ±577.06
Case 1:
[tex]\frac{x}{r-x}=577.06[/tex]
x = [tex]1.49\times 10^{11} m=149.34 Gm[/tex]
Acceptable as the particle will lie in between the straight line joining Earth and Sun.
Case 2:
[tex]\frac{x}{r-x}=-577.06[/tex]
x = [tex]1.49\times 10^{11} m=149.86 Gm[/tex]
Not acceptable as the particle will lie beyond on line extending straight from the Earth and Sun.
