Momentum of a planet?

Question

^ D-->

| C A |

<--B v

so A arrow points down... B arrow points left.... C arrow points up... and D arrow points right...

A planet with a mass of 4e+23 kg travels around a star in a nearly circular orbit in the xy plane, as shown in the diagram. Its speed is nearly constant at 4.9e4 m/s.

What is the momentum of the planet when it is at location D?

What is the change in the momentum of the planet in going from location D to location A? (Remember that means final value minus initial value)

What arrow best indicates the direction of (Delta P)?

choice are basically N, NE, E, SE,S, SW, W, NW

The arrows in the diagram represent the momentum of the planet when it is at particular locations, labeled by letters.

Answer 1

That is a vector addition problem.

Momentum is Mass times velocity, or MV. So in your example the momentum at A is 4e23 * 4.9e4. = 1.96e28

The speed is always the same so the momentum is always the same absolute value. But the velocity has changed because direction of speed has changed by 90 degrees. Vector addition says draw the two velocities as two arrows with their tails touching. Then the velocity change is the vector from head of the first one to the head of the second one. In the case of two equal length vectors at right angles to each other, the answer is SQRT(2) times either one (hypotenuse of an equilateral right triangle), or SQRT(2) * 4.9e4 =  6.23e4. That is the velocity change. The momentum change is Mass times the velocity change, or 4e23 * 6.23e4 = 2.77e28. The direction of the change is the direction of that arrow, which would be to the upper right, which I would describe as NE.

Answer 2

good answer, CambelP - but one question - I am pretty sure that vector addition has you chain them head to tail, and not tails together.... granted it&#039;s been over a decade since I formally studied that.

If I&#039;m in a boat going across a river that flows 3 m/s southward, and the water velocity of the boat is 4 m/s east, how fast is my boat going over the riverbed? 5 m/s at compass heading 120 degrees. If I put the tails together, wouldn&#039;t I come up with 60 degrees in stead of 120? (heading NE in stead of SE?)