One of the brightest stars in the sky is Vega, which is about twice as massive a

Question

One of the brightest stars in the sky is Vega, which is about twice as massive as the Sun. The distance to Vega is 25.3 light years.

a) If you were to take a trip to Vega, at what distance from the Sun would the two gravitational forces that you experience (i.e. from the Sun and from Vega – ignoring all the other stars) balance? Give your answer in light years.
Tip: for this problem, you don’t need to look up the gravitational constant, the mass of the Sun, or even the conversion of light years to meters, or km.

b) Does the location of this `balance point’ depend on the mass of the object that is going on the trip, and if so, how? That is, does it matter if it is you, your cat, or an elephant? Justify your answer.

Explanation / Answer

We need to balance the force on any object (mass m) at a particular location x from our sun ( mass M) and that from vega ( mass 2M). The gravitational force on the object much balance and net force on the body is zero, therefore we get an equation G M m/(x^2) = G 2M m/(25.3 - x)^2 Solving the equation we have 2x^2 = (25.3 - x)^2 taking positive root sqrt(2)x = 25.3 - x x = 25.3/(sqrt(2) +1) x = 10.479 light years B) since it is seen that the location of the point is independent of the mass of the object concerned so it doesnt matter if the object is an elephant or cat or anything. Hope it solves your problem. If you have any other query then do let me know!

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