Help with circular velocity question (unit conversions?)

AI Thread Summary
To find the orbital velocity of a satellite in low Mars orbit, the radius must be calculated by adding Mars' radius (3396 km) to the altitude (300 km), resulting in 3696 km. The formula for circular velocity is Vc² = GM/R, where G is the gravitational constant and M is Mars' mass. The calculations require converting kilometers to meters, leading to R = 3,696,000 meters. The correct computation involves multiplying Mars' mass by the gravitational constant, dividing by the radius, and then taking the square root to find the velocity in meters per second. Attention to unit conversion is crucial for accurate results, and the final velocity should be interpreted in the correct units.
BilboBombadillo
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Homework Statement


Consider a satellite in circular low Mars orbit 300km above the planetary surface.
R = 3396km
M = 6.419 x 1023kg
G = 6.674 x 10-11m3/kg/s2
Find the orbital velocity of the satellite (using the given values, I assume, as there is some inaccuracy in the real-life mass value. Consider it irrelevant).

Homework Equations


Vc2 = GM/R

The Attempt at a Solution



I understand the radius of this equation to refer to M2's (satellite) distance from the center of M1 (Mars), and so simply added the Mars radius and given orbital distance from the surface together.
To get R = 3696km
As it is given, I know the mass of Mars to be 6.419e+23 (or 6.419 x 1023) (is this how notation works?)Given my limited math ability, I'm having trouble interpreting (in the mental sense) the numerous measures at the end of the "gravitational constant". Those being: m3, kg, and s2

How do i go about plugging all this into a calculator? Do I ignore the units of measurement and treat everything as their values alone?

Multiplying the mass of Mars by the gravitational constant gave me:
4.2840406e+13, which i then divided by the radius of 3696
This gave me
11591018939.4
I then took the square root of this (on account of the given equation), which equaled:
107661.594542
This seems a bad number, considering known orbital velocities (I also don't understand this number. Would that read as 107661 km? or 10.7661 km? Even still this velocity would eject the satellite, no?)

I suspect I am faulting in the units of measurement and the misinterpretation of the scientific notation.

Somebody please help me, or otherwise professionally solve the equation with the given values, and then deconstruct your process for me.
 
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You must pay attention to the units of the numbers and make sure that they cancel out to give the units of the desired answer. Notice that km = 1000m. Put that factor of 1000 in your calculations and your answer should be right. Also notice how all the units in numerators and denominators cancel out to leave the units m2/s2. Those are the proper units for V2
 
Thankyou. That is what I suspected.
I think I need further explanation, however. You may underestimate my inproficiency at math. How precisely do go about doing as you've suggested? Where do I change the values?
 

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