How Fast Are Rockets Moving at Moon's Orbit?

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Homework Help Overview

The discussion revolves around the speeds of two rockets launched from Earth's surface as they cross the moon's orbit, with initial speeds given as 17 km/s and 22 km/s. Participants are exploring the application of energy conservation principles in the context of gravitational potential energy and kinetic energy.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of energy conservation equations but express confusion regarding the application of radius values in the equations. There is an attempt to clarify the definitions and roles of the radii involved in the calculations.

Discussion Status

The discussion is ongoing, with some participants providing insights into the setup of the problem and questioning the assumptions made about the radius values. One participant has indicated they resolved their confusion, but there remains a lack of consensus on the correct interpretation of the radius in the equations.

Contextual Notes

There is a mention of the need to consider the mass of the moon and the distance to the moon in the calculations, which may not have been initially included in the problem setup. Participants are navigating the implications of these factors on the solution.

darklich21
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Homework Statement


Two rockets are launched from Earth's surface, one at 17 km/s and the other at 22 km/s. How fast is each moving when it crosses the moon's orbit?


Homework Equations


Kf + Uf= K0 + U0
0.5mvf^2 -GMm/R = 0.5mv0^2 - GMm/R


The Attempt at a Solution


So I attempted to use the equation above, using the Earth's mass and the Earth's radius, It didn't work, my speeds came out to be exactly 17 and 22 just like from the start. I'm going to say that the radius of the moon and the mass of the moon comes into play here. Can someone help, with perhaps a better equation?
 
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Radius in this case the distance from M, and is different on each side of the equation. So it's R_1 and R_2. You could use the center of the Earth or the surface of the Earth as the origin, as long as you are consistent. the surface is probably easier. So the radius at the start is 0. And the radius at the moon is the distance from the Earth to the moon. Ignore the actual moon. it's not important here.

You should be able to handle it from here.
 
how can the radius be 0, the radius in my equation is in the denominator. it would make 1 part of the expression undefined
 
nvm i figured it out, but I am going to correct your response. The radius is NOT 0, but instead the raidus of the earth, while on the other side of the equation, it's the radius of the Earth + the distance to the moon.
 

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