Keplers second law

Hi

Can someone please help me with these questions?

Question 1: in June 2018, the spacecraft Hayabusa2 arrived at an asteroid called Ryugu. The asteroid orbits the sun in an elliptical orbit as shown.

The diagram is not drawn to scale. Indicate with a letter X on the orbit where the asteroid would be moving at maximum speed.

I’ve attached a picture of where I think it is..

I’m not sure if this is right. Can someone let me know ? And if it’s wrong explain why and where it is ?

Question 2: use Keplers second law to explain your answer to ai)

For this question I put

Kepler’s second law states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. As planets move on their elliptical orbit around the sun, their speed is not constant. When a planet is closer to the sun it moves faster. Keplers second law states that if the time interval from X to Y is the same as for P to Q (eg 1 month) the areas A and B must be the same.

Idk if I need to add anything or take anything away or if I’m completely wrong so pls help someone ?

(edited 3 years ago)

Reply 1

Sonnysingh22

There’s also a follow up question involving a graph

I thought as G = 6.67 x 10^-11

But the question doesn’t give the mass of the asteroid so I’m a bit confused but I then thought it’d be something to do with this:

The gradient of the graph = change in Vg / change in r

Vg = - GM/r
So g = - (GM/r)/r
So g = -GM

Like that ?

The second question then says use the gradient of the graph to show that the mass M of the asteroid is about 4.6 x 10^11kg

So I found the gradient as -30.43478261

Then did g = -GM —> M = g/-G = -30.43../ (6.67 x 10^-11) = 4.56 x 10^11

Like this?

Reply 2

Sonnysingh22

There’s also a follow up question involving a graph

Reply 3

Joinedup

Yeah argument based on kepler 2 is fine... If you're a bit confused about what's going on you can think about it as energy being converted back and forth between gpe and KE as it goes around its elliptical orbit. at apoapsis the GPE is minimimum and the KE is maximum.

Reply 4

Sonnysingh22

Original post by Joinedup

Thank you !

Reply 5

Sonnysingh22

Can someone help me with the last question (part C) plsss or guide me through it

Reply 6

小柠檬

@Sonnysingh22, I'm not sure, I actually just had this question come up in an exam today and was wondering about the answer, but enough background, the question.

In the exam, I used v = sqrt(2gh), calculating the magnitude of g using GM/r, with r = h = 600m. As far as I can tell, this is a massively flawed argument.

What I believe would have been better, would've been if I'd used the same concept (∆Ug = ∆Eₖ), but had instead worked out the individual values for Ug at the height and then at the surface (this isn't 0), then equating the difference in those two energies to the Eₖ gained (as initial Eₖ = 0), rearranging this for v should yield the correct answer.

I will now go off and figure how many orders of magnitude off the actual value I was. Though, I will leave the calculation as an exercise to you, as you were only looking for a guide and it's always better to work through things yourself. I hope I was able to be of help (: