Calculating orbital velocity (1 Viewer)

Sp3ctre

Active Member
Joined
Nov 29, 2016
Messages
178
Location
NSW
Gender
Male
HSC
2017
Uni Grad
2022
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
 
Last edited:

jazz519

Well-Known Member
Joined
Feb 25, 2015
Messages
1,027
Location
Sydney
Gender
Male
HSC
2016
Uni Grad
2021
Nope any formulas not on the sheet they provide, must be derived or you will lose marks
 

sgtgummybear

Member
Joined
May 17, 2016
Messages
68
Gender
Female
HSC
2017
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.
 

clementc

Awesome Member
Joined
Jan 31, 2011
Messages
149
Location
My couch
Gender
Male
HSC
2011
Uni Grad
2016
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

I love trials
Moderator
Joined
May 31, 2015
Messages
2,400
Location
NSW
Gender
Male
HSC
2017
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)
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top