Why Is GM Set to 900 in the Vis-Viva Equation for AU and KM/s?

[visviva]

When distances are measured in AU and speed in KM/s the variable in the vis-vva equation: GM=900 explain why this is so.

Vis-Viva equation: V^2 = GM( 2/r -1/a)i tried subbing in AU for R and A and and solving the equation to see if it equals out, i just don't know where to start.

 

[DrClaude]

I think you got confused by the homework template. You should leave the text included in the template, and simply add your own stuff in-between.

As for your question, start in SI units, and then modify the GM factor until it corresponds to the units specified for distances and speed.

 

[visviva]

I think you got confused by the homework template. You should leave the text included in the template, and simply add your own stuff in-between.

As for your question, start in SI units, and then modify the GM factor until it corresponds to the units specified for distances and speed.

by modify the GM factor what are you referring to, I haven't taken anything physics related in about 5 years so I am struggling here. My first instinct here was to use the SI unit version of GM ( M^3/S^2) and then find wht value that is equivalent to 900 in the other unit ( Km^3/S^2) but I am pretty sure that's not write as that would not show why when distance are in AU and speed in KM GM = 900.

 

[DrClaude]

by modify the GM factor what are you referring to, I haven't taken anything physics related in about 5 years so I am struggling here. My first instinct here was to use the SI unit version of GM ( M^3/S^2) and then find wht value that is equivalent to 900 in the other unit ( Km^3/S^2) but I am pretty sure that's not write as that would not show why when distance are in AU and speed in KM GM = 900.

Indeed, you should not assume that you know the value.

To give you an example of how to proceed, consider the equation for the force our to gravity near the surface of the Earth:

F = 9.8 m

Written like this, this equation is valid if m is in kg and returns F in Newtons. If you wanted to know how to change that so that m is in grams and F is dynes (CGS system), you would first find the conversion factor needed to go from kg to g, i.e. 1000, and then change the 9.8 accordingly, and so on until the result is in dynes.

 

[visviva]

I tried making an equation equivalent/ converted the original Vis-Viva equation in SI units: V^2 = GM(2/R-1/A) what i did was look at each value and convert it to the value required in the question to try and creat a new equation, 0.001V^2 =GM(2/1.496x10^8KM - 1/ 1.496x10^8 KM) am even doing anything near what is being suggested?