Question

A probe orbiting Venus exerts a gravitational force of 2.58 × 103 N on Venus. Venus has a mass of 4.87 × 1024 kg. The mass of the probe is 655 kilograms.

Answer 1

The radius of the probe from the center of Venus is
`9.08*10^(6)\ m`.

Step-by-step explanation:

Given that,

Gravitational force
`F_(g) =  2.58*10^(3)\ N`

Mass of Venus
`M= 4.87*10^(24)\ kg`

Mass of probe m= 655 kg

Suppose we find the radius of the probe from the center of Venus

We need to calculate the radius

Using gravitational force

`F_(g)=(GmM)/(r^2)`

Put the value into the formula

`2.58*10^(3)=(6.67*10^(-11)*655*4.87*10^(24))/(r^2)`

`r^2=(6.67*10^(-11)*655*4.87*10^(24))/(2.58*10^(3))`

`r=\sqrt{(6.67*10^(-11)*655*4.87*10^(24))/(2.58*10^(3))}`

`r=9.08*10^(6)\ m`

Hence, The radius of the probe from the center of Venus is
`9.08*10^(6)\ m`.

Answer 2

The correct answer is:

9.08 x 10⁶ meters.

Step-by-step explanation:

Fg = 2.58 x 10³ N

Mv = 4.87 x 10²⁴ Kg

Md = 655 Kg

So, Fg = G Mv Mp / r²

By putting in the values,

r² = 8.2466 x 10¹³

r = 9.08 x 10⁶ meters.