A satellite moves around the Earth in a circular orbit of radius r . (Use G for

Question

A satellite moves around the Earth in a circular orbit of radiusr. (Use G for the universal gravitation constant,M for the mass of the Earth, and r, asappropriate, when answering parts (a), (b), and (c) below.) (a) What is the speed v0 ofthe satellite? (Use G, M, and r, as necessary.)


(b) Suddenly, an explosion breaks the satellite into two pieces,with masses m and 4m. Immediately after theexplosion the smaller piece of mass m is stationary withrespect to the Earth and falls directly toward the Earth. What isthe speed vi of the larger piece immediatelyafter the explosion? (Use G, M, and r, as necessary.)


(c) Because of the increase in its speed, this larger piece of mass4m now moves in a new elliptical orbit. Find its distanceaway from the center of the Earth when it reaches the other end ofthe ellipse. (Use G, M, and r, as necessary.)

(a) What is the speed v0 ofthe satellite? (Use G, M, and r, as necessary.)


(b) Suddenly, an explosion breaks the satellite into two pieces,with masses m and 4m. Immediately after theexplosion the smaller piece of mass m is stationary withrespect to the Earth and falls directly toward the Earth. What isthe speed vi of the larger piece immediatelyafter the explosion? (Use G, M, and r, as necessary.)


(c) Because of the increase in its speed, this larger piece of mass4m now moves in a new elliptical orbit. Find its distanceaway from the center of the Earth when it reaches the other end ofthe ellipse. (Use G, M, and r, as necessary.)

Explanation / Answer

a. the formula is v = GM/r b. mv prior = mv after prior: The satellite prior to the explsion has amass 5m travelling at GM/r After the explosion, mv of the smaller piece is 0 since v is0 So, 5mv1=4mv2 Rewrite to solve for v2 v2=5mv1/(4m) v2=(5v1/4), and v1 wasGM/r, so v2=(5/4)GM/r c. see equation 4.18 on this page: http://www.braeunig.us/space/ Ra is the distance from the center of the Earth at the otherend of the ellipse. Rp is the original distance before theexplosion, and Vp is the new velocity after the explosion. Ra is the distance from the center of the Earth at the otherend of the ellipse. Rp is the original distance before theexplosion, and Vp is the new velocity after the explosion.

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