Graph of velocity against radius?

[pconstantino]

Hello, we been set a physics assignment where we are given a table of data, a spaceship approaches a planet, and the velocity and radius are given at certain points, we have to graph velocity against 1/r and hence find the mass of the planet.

I really don't get this question, i tried slope and area under graph but can't reach a conclusion.

Any help please?

 

[JaredJames]

There are two ways to go about this, the first is to use the graph (green - the one I think you need) the second is without (red). The final section (blue) is completed regardless of which initial method (green or red) you choose:Because the graph is 1/r, working out the gradient between two radius points will give you the time it took to travel between them. (Units on the graph will be m/s and 1/m so they solve to leave s.)

Once you have this, using the equations of motion you can work out acceleration = a = (V_A-V_B)/t.

This acceleration (assuming the rocket engines are off) is gravity between the two points.If you know the velocity at point A (V_A) radius A (r_A) and the velocity at Point B (V_A) radius B (r_B) you can work out the acceleration between those two points.

Using the equations of motion you know: initial velocity = V_A, final velocity = V_B and distance = r_A-r_B.

Plug in those values and you'll get the acceleration between the two points.

That acceleration (assuming the rocket engines are off) will be the gravity value between those two points.You repeat this between each set of coordinates to gain various g values.

Now, g = Gm/r².

Where G is the gravitational constant and you know your r values along with g from above. Leaving you to rearrange and solve for m which is the mass of the planet.

Hopefully, they should all be within an acceptable range of each other to give you an approximate mass.

 

[pconstantino]

wow, amazing, this helps a lot, thank you so much my friend.