mod5 - satellites (2 Viewers)

[Idontevenknow1234]

when we say that a satellite has a negative value for its total energy, then it is gravitationally bound meaning that it can't escape the gravitational field/ can't escape whatever its orbitting. at an infinite distance away from this object its orbitting we also say that total energy = 0. I understand that this is a case of it being "relative". But this total energy negative cannot be because we are inputting kinetic energy to get away from earth since kinetic energy decreases as r approaches infinity. So other than it being 'relative' is there another explanation for this?

 

[Idontevenknow1234]

Another q i had was that for a satellite orbiting earth as it enters an orbit of a smaller radius (moves closer towards earth) the velocity technically decreases right? But i find this weird because as you get closer to earth doesnt KE increase and since KE is proportional to velocity squared, if KE increases shouldnt velocity also increase?

 

[C2H6O]

Is this total energy negative because we are inputting kinetic energy to get away from earth?

Yes, as to get further away we would need to increase the total energy by inputting kinetic energy into gravitational potential. But as we know when the object is at infinity it has escaped the gravitational field, and thus now has 0 GPE. Because energy must increase towards 0, we make it negative. Here is the proof, given that GPE is negative, to find total energy

 

[C2H6O]

Another q i had was that for a satellite orbiting earth as it enters an orbit of a smaller radius (moves closer towards earth) the velocity technically decreases right? But i find this weird because as you get closer to earth doesnt KE increase and since KE is proportional to velocity squared, if KE increases shouldnt velocity also increase?

Velocity would increase the closer it gets to the earth (refer to velocity formula in previous message). I think of it as how mercury which orbits close to the sun has a year of 88 days or something and something like Uranus has a crazy long year (like decades)

 

[Idontevenknow1234]

Yes, as to get further away we would need to increase the total energy by inputting kinetic energy into gravitational potential. But as we know when the object is at infinity it has escaped the gravitational field, and thus now has 0 GPE. Because energy must increase towards 0, we make it negative. Here is the proof, given that GPE is negative, to find total energyView attachment 46430

When we say input kinetic energy we mean like quite literally mechanically somehow add more kinetic energy cos for a satellite, kinetic energy naturally decreases as we approach infinity right

 

[C2H6O]

Velocity would increase the closer it gets to the earth (refer to velocity formula in previous message). I think of it as how mercury which orbits close to the sun has a year of 88 days or something and something like Uranus has a crazy long year (like decades)

Unless you account for the fact that the closer you get the more air resistance there is, which may influence velocity

 

[Idontevenknow1234]

Unless you account for the fact that the closer you get the more air resistance there is, which may influence velocity

disregarding drag since doesn't hsc physics neglect it

 

[C2H6O]

When we say input kinetic energy we mean like quite literally mechanically somehow add more kinetic energy cos for a satellite, kinetic energy naturally decreases as we approach infinity right

Yeah, by burning fuel or something to increase orbital velocity. As orbital velocity increases, the satellite will go further from the planet with an outward spiral trajectory

 

[C2H6O]

disregarding drag since doesn't hsc physics neglect it

Maybe I’m misremembering but I might’ve seen a question that took air resistance of low earth orbit into account, but it wasn’t a calculation based question it was just talking about like discussing fuel efficiency or smth. But yeah normally we don’t care about air resistance definitely never in calculations

 

[Idontevenknow1234]

Maybe I’m misremembering but I might’ve seen a question that took air resistance of low earth orbit into account, but it wasn’t a calculation based question it was just talking about like discussing fuel efficiency or smth

ohh lol cos I haven't seen any calc qs which say drag isn't negligible cos that's js too complicated for hsc lvl I think

 

[Idontevenknow1234]

Velocity would increase the closer it gets to the earth (refer to velocity formula in previous message). I think of it as how mercury which orbits close to the sun has a year of 88 days or something and something like Uranus has a crazy long year (like decades)

but then what abt orbital decay where ke decreases although it gets closer to earths surface

 

[C2H6O]

but then what abt orbital decay where ke decreases although it gets closer to earths surface

In orbital decay you’re loosing altitude, so losing GPE. This energy is “lost” to kinetic as the object speeds up due to closer orbit, or to friction from air resistance (maybe ask your teacher whether they’d like you to account for air drag in ‘discuss’ orbital decay questions). This can be seen in the formula for kinetic energy, and you can always link back to conservation of energy, where if GPE is decreasing ke must increase

 

[Idontevenknow1234]

In orbital decay you’re loosing altitude, so losing GPE. This energy is “lost” to kinetic as the object speeds up due to closer orbit, or to friction from air resistance (maybe ask your teacher whether they’d like you to account for air drag in ‘discuss’ orbital decay questions). This can be seen in the formula for kinetic energy, and you can always link back to conservation of energy, where if GPE is decreasing ke must increase

Huh but when a satellite enters orbital decay ke decreases not increases

 

[C2H6O]

Huh but when a satellite enters orbital decay ke decreases not increases

I could swear it increases cause it makes sense using mathematical models. GPE decreases but not ke, to observe conservation of energy. The only case where both would decrease is if the satellite is falling (loss of gpe), and the satellite is slowing down and losing ke to friction and air drag (loss of ke). Im 99% but sorry if im wrong

 

[:():]

I could swear it increases cause it makes sense using mathematical models. GPE decreases but not ke, to observe conservation of energy. The only case where both would decrease is if the satellite is falling (loss of gpe), and the satellite is slowing down and losing ke to friction and air drag (loss of ke). Im 99% but sorry if im wrong

but during orbital decay, v decreases so wouldnt ke decease too? cos ke=1/2(mvsquared)

 

[C2H6O]

but during orbital decay, v decreases so wouldnt ke decease too? cos ke=1/2(mvsquared)

V increases in orbital decay bc r is reducing (v^2=GM/r)