An astronaut 60kg stands on a tiny moon of mass 1.0x10^18kg and radius 1.0x10^4m. How fast ...run to orbit?

Question

An astronaut 60kg stands on a tiny moon of mass 1.0x10^18kg and radius 1.0x10^4m. How fast would he or she need to run to put himself into orbit? could this be done?

What does it mean to put yourself into orbit? is it something like moon around earth? Please explain and provide examples.

wow i got an answer of about 8.2m/s which is very far from your answer

What does it mean to put yourself into orbit? is it like when the cerntripetal force is greater than the gravitational force of attaraction?

Answer 1

As said above:
The centripetal force has to equal the gravitational force.
so,
m * v² / r = G * M * m / r²
or, dividing by r:
m * v² = G * M * m / r
or, moving m the other side:
v² = G * M * m / m * r = G * M / r
or
v = sqr (G * M / r)
v = sqr (6.6742E-11 * 1E18 / 1E4)
v = sqr (6.6742E-11 * 1E14)
v = sqr (6.6742E3)
v = 81.695 m/s (and not 8000...)

Answer 2

From the given data g= G M / R^2
where G = universal gravitational conastant =6.6X10^-11
M=mass of moon
m=mass of man
R radius of moon

therfore g = 0.66 m/s sq obviously which is very less and a man needs to move on the moon so that he has to balance his mass otherwise he /she go ino the space , the g force is balanced by centripital force and mv^2 / R = G Mm/R^2 or v = sq root ( GM/R)
and finally after substitution we get v = 8000 m/s ( approx )

Answer 3

newtons theroy working only on earth, if you realy want to know about your question then you must have to do practicle in same position