Calculating orbital velocity (1 Viewer)

[Sp3ctre]

In question 26c of the 2015 HSC, the answers expected you to calculate orbital velocity by using Centripetal Force = Gravitational Force and then manipulating the equation in terms of velocity. Can you not just use the formula Orbital V = sqrt(GM/r) that's taught in the course immediately instead of deriving this equation from Fc and Fg?

https://gyazo.com/fe725781429d1fc417b88457b4844ad6

 

[jazz519]

Nope any formulas not on the sheet they provide, must be derived or you will lose marks

 

[sgtgummybear]

The formula for orbital velocity isn't provided in the formula sheet though, so you're supposed to derive the equation to show the markers where the formula came from. That's what I've always been taught to do, anyway. Not sure if you'll get marks deducted for not doing it or not though.

 

[sgtgummybear]

Oh, guess you do lose marks then.

 

[Sp3ctre]

Thanks for the replies

 

[clementc]

Yeah, you need to derive it from scratch. This applies for escape velocity as well. It should be pretty straightforward anyway; takes literally 3 lines.

For orbital velocity (you must have the first line as well):
Fc = Fg
mv²/r = GmM/r²
v = sqrt (GM/r)

For escape velocity (include first line):
KE ≥ GPE
½mv² ≥ GmM/r (comparing just the magnitudes)
v ≥ sqrt (2GM/r)

 

[pikachu975]

Yeah, you need to derive it from scratch. This applies for escape velocity as well. It should be pretty straightforward anyway; takes literally 3 lines.

For orbital velocity (you must have the first line as well):
Fc = Fg
mv²/r = GmM/r²
v = sqrt (GM/r)

For escape velocity (include first line):
KE ≥ GPE
½mv² ≥ GmM/r (comparing just the magnitudes)
v ≥ sqrt (2GM/r)

Just a note for escape velocity, the first line would be Epi + Eki = Epf + Ekf
and both Epf and Ekf are 0 therefore Eki = -Epi
GMm/r = 1/2 mv^2
v = sqrt(2GM/r)

 

[Fizzy_Cyst]

Just a note for escape velocity, the first line would be Epi + Eki = Epf + Ekf
and both Epf and Ekf are 0 therefore Eki = -Epi
GMm/r = 1/2 mv^2
v = sqrt(2GM/r)

Damn, you’ve been taught well!