Bypass time of satelite arround Mars

[antoman]

Homework Statement

On high 150km above the surface of Mars, there is satelite That is ciculating arround Mars. What's his bypass time? Radius of Mars is 3400km.

Homework Equations

The Attempt at a Solution

I found equation like this :

t= (2*r(R+h)^(3/2))/(sqrt(g0*R^2))
R=r+h
r=3400km
h=150km

But when i try to calculate like this, i totally miss the actual time. I know bypass time(solution) is 110 minutes.

 

[SteamKing]

What value of g0 are you using? What units for r and R are required?

 

[tiny-tim]

welcome to pf!

hi antoman! welcome to pf!

On high 150km above the surface of Mars, there is satelite That is ciculating arround Mars. What's his bypass time? Radius of Mars is 3400km.

let's put that into english …

At a height of 150km above the surface of Mars, there is a satellite that is orbiting Mars. What's its period? The radius of Mars is 3400km.​

hmm … don't you need to know either the mass of Mars, or the gravitational acceleration (g) at the surface?

 

[antoman]

What value of g0 are you using? What units for r and R are required?

g0=9,81m/s^2

hmm … don't you need to know either the mass of Mars, or the gravitational acceleration (g) at the surface?

i could calculate g at surface using g=g0*R^(2)/(R+h)^2, but then again i have no idea what to use it for
.. nevermind g0 is different on Mars then on Earth so..

 

[antoman]

Ok i made some changes, so now

t= (2*r(R+h)^(3/2))/(sqrt(g0*R^2))
r=R+h
R=3400km
h=150km
g0=3,7 m/s^2... assuming i should of know g0 from mars.

I calculated and it came out t=7261412,315 km/s...

 

[SteamKing]

You've got R and h in km and g0 in m/s^2. Don't you think you have a problem with your units?

 

[antoman]

You've got R and h in km and g0 in m/s^2. Don't you think you have a problem with your units?

I used 3.6*10^-3 km/s^2 for g0 when i calculated, so its (km*km^(3/2))/sqrt(km*s^(-2)*km^2). Then km^(3/2)/km^(3/2)=1, so all it stays is km*s.
Repair me if I am wrong :)

 

[SteamKing]

I'm repairing you.
Do you have the right formula?
What if R and r have to be in meters instead of km?

 

[antoman]

I'm repairing you.
Do you have the right formula?
What if R and r have to be in meters instead of km?

No, i don't think the formula is right, that's why i asked for help.

 

[SteamKing]

Perhaps you are trying to use a formula like those from this article:

http://en.wikipedia.org/wiki/Orbital_period

Specifically, the period for a small body orbiting a central body.

 

[antoman]

Now i know what was the problem :D

Correct formula is:
t=(2∏*(...))/sqrt(...)
+ g0 to km/s^2, and it all works out perfect, iven makes more sense :)