Please help me figure out what this graph is called

[Tommy1995]

Please help me figure out what this graph is called!

My teacher made us copy down this graph which represents both the kinetic energy and gravitational potential energy of an mass due to its its distance away from the centre of the earth. The graph takes the form of a gravitational potential energy graph with the reference point at infinity.

He never told us what the graph was called and now I'm finding difficulty understanding how it works, could someone please tell me what the graph is called so i could research about it... If you could also explain it that would be awesome haha.

 

[grzz]

Where is the graph?

 

[Mandelbroth]

My teacher made us copy down this graph which represents both the kinetic energy and gravitational potential energy of an mass due to its its distance away from the centre of the earth. The graph takes the form of a gravitational potential energy graph with the reference point at infinity.

He never told us what the graph was called and now I'm finding difficulty understanding how it works, could someone please tell me what the graph is called so i could research about it... If you could also explain it that would be awesome haha.

Based on the rather minimal amount of information, I think you are trying to describe the graph of $U_g = \displaystyle \int_{r}^{\infty} F_g \ dr = \int_{r}^{\infty} G\frac{m_1 m_2}{r^2} \ dr = -G\frac{m_1m_2}{r}$. This is a hyperbola reflected over the r axis. If you want the equation for the kinetic energy, just multiply the equation for gravitational potential energy by -1.

 

[Tommy1995]

SOrry about the lack of information, i finally got it photoscanned, check out the attachment, the graph is down at the bottom of the page.. The horizontal dotted lines are meant to represent the kinetic energy i think and the position of the value on the function represents the potential energy.

please help!

 

[Mandelbroth]

SOrry about the lack of information, i finally got it photoscanned, check out the attachment, the graph is down at the bottom of the page.. The horizontal dotted lines are meant to represent the kinetic energy i think and the position of the value on the function represents the potential energy.

please help!

As I predicted, the graph you have shown is a hyperbola describing the relation between distance and gravitational potential energy. If you want the value of the kinetic energy for part of that graph, just flip the graph over the r axis (horizontal axis).

 

[Tommy1995]

! LOL, by the R axis do you mean the x axis?

But yea i flipped it over the x-axis and i by finding the value of a point along the horizontal axis i got a nice representation of the kinetic energy as the distance away from the central mass is increased or decreased so thanks for clearing that up!

Btw, would you have any clue what the name of this kind of graph is called? not the function but the name haha :P

 

[HallsofIvy]

I have no idea what you mean by the "name of this kind of graph". You have already been told that is is a hyperbola (strictly speaking it is one branch of a hyperbola). You could also call it a "graph of gravitational potential energy against distance".