Question

Earth is 1.5 ✕ 1011 m from the Sun. Venus is 1.1 ✕ 1011 m from the Sun. How does the gravitational field of the Sun on Venus (gSV) compare to the gravitational field of the Sun on Earth (gSE)?

Answer 1

Answer:

The gravitational field of Sun on Venus is 1.1 times the gravitational field of Sun on Earth

Explanation:

G = Gravitational constant

M = Mass of sun

$r_e$ = Distance between Sun and Earth = $1.5\times 10^{11}\ m$

$r_v$ = Distance between Sun and Venus = $1.1\times 10^{11}\ m$

Gravitational field is given by

$g_e=G\frac{M}{r_e^2}$

$g_v=G\frac{M}{r_v^2}$

Dividing the two equations

$\frac{g_e}{g_v}=\frac{G\frac{M}{r_e^2}}{G\frac{M}{r_v^2}}\\\Rightarrow \frac{g_e}{g_v}=\left(\frac{r_v}{r_e}\right)^2\\\Rightarrow \frac{g_e}{g_v}=\left(\frac{1.1\times 10^{11}}{1.5\times 10^{11}}\right)^2\\\Rightarrow \frac{g_e}{g_v}=0.538$

$\\\Rightarrow g_v=\frac{1}{0.538}g_e\\\Rightarrow g_v=1.1g_e$

The gravitational field of Sun on Venus is 1.1 times the gravitational field of Sun on Earth

Answer 2

Answer:

1.36 times

Explanation:

gSE=G × $\frac{M}{r_e{2} } }$.........................................(1)

gSV= G × $\frac{M}{r_v^{2} } }$.........................................(2)

where

gSE= gravitational field of the sun on the earth

gSV= gravitational field of the sun on venus

M= mass of the sun

$r_{e}$= distance of the earth from the sun

$r_{v}$= distance of venus from the sun

form equation 1,

GM = gSE ×  $r_{e}$².....................................(3)

from equation 2,

GM = gSV × $r_{v}$²......................................(4)

equating equation 3 and 4

gSE ×  $r_{e}$² = gSV × $r_{v}$²

gSV = gSE × ( $r_{e}$² ÷ $r_{v}$²)

= gSE ×  $\frac{1.5* 10^{11} }{1.1 * 10^{11} }$

gSv= gSE × 1.36

∴ the gravitional field of the sun on venus (gSV) is 1.36 times the gravitational field on the earth (gSE)