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

1.36 times

Step-by-step explanation:

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

gSV= G ×
`(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 ×
`(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)

Answer 2

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

Step-by-step explanation:

G = Gravitational constant

M = Mass of sun

`r_e` = Distance between Sun and Earth =
`1.5* 10^(11)\ m`

`r_v` = Distance between Sun and Venus =
`1.1* 10^(11)\ m`

Gravitational field is given by

`g_e=G(M)/(r_e^2)`

`g_v=G(M)/(r_v^2)`

Dividing the two equations

`(g_e)/(g_v)=(G(M)/(r_e^2))/(G(M)/(r_v^2))\\\Rightarrow (g_e)/(g_v)=\left((r_v)/(r_e)\right)^2\\\Rightarrow (g_e)/(g_v)=\left((1.1* 10^(11))/(1.5* 10^(11))\right)^2\\\Rightarrow (g_e)/(g_v)=0.538`

`\\\Rightarrow g_v=(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