Question

Question: A NEO distance from the Sun is 1.17 AU. What is the speed of the NEO (round your answer to 2 decimal places)

Answer 1

v = 2.75 10⁴ m / s

Step-by-step explanation:

For this exercise we must use Kepler's third law which is an application of Newton's second law to the solar system

F = ma

where force is the force of gravity

F =
`G (m M)/(r^2)`

acceleration is centripetal

a =
`(v^2)/(r)`

we substitute

G m M / r² = m v² / r

`(GM)/(r)` = v²

v =
`√(GM/r)`

indicate that the radius of the orbit is r = 1.17 AU, let's reduce to the SI system

r = 1.17 AU (1.496 10¹¹ m / 1 AI) = 1.76 10¹¹ m

let's calculate

v =
`\sqrt{(6.67 \ 10^(-11) 1.991 \ 10^(30) )/( 1.76 \ 10^(11)) }`Ra (6.67 10-11 1.991 10 30 / 1.76 10 11

v =
`√(7.5454 \ 10^8 )`ra 7.5454 10 8

v = 2.75 10⁴ m / s