Question

The escape velocity of a bullet from the surface of planet Y is 1983.0 m/s. Calculate the escape velocity from the surface of the planet X if the mass of planet X is 1.31 times that of Y, and its radius is 0.903 times the radius of Y.

Answer 1

Escape velocity is given by:\[v _{e}=\sqrt{\frac{ 2GM }{ r }}\]where ve is the escape velocity; G is the gravitational constant; M is the mass of the planet; and r is the radius of the planet.

Answer 2

Do you see a way of using the formula to solve your problem?

Answer 3

yes, but the two planets kind of confuse me

Answer 4

Why do they confuse you?

Answer 5

Like how "X is 1.31 times that of Y, and its radius is 0.903 times the radius of Y"

Answer 6

You don't need to know the actual mass of Planet Y or X; and you don't need to know the actual radius of either planet.

Answer 7

So you know that the mass of planet Y=M. You also note that the mass of Planet X =1.31M. You also know that radius of planet X = 0.903r

Answer 8

Now we can set up a ratio:\[\frac{ v _{X} }{ v _{Y} }=\frac{ \sqrt{\frac{ 2GM _{X} }{ r _{X} }} }{ \sqrt{\frac{ 2GM _{Y} }{ r _{Y}}} }=\sqrt{\frac{ r _{Y}M _{X} }{ r _{X}M _{Y} }}\]

Answer 9

Let's say that Mx=aMy and rx=bry. If we put that in my equation we get:\[\frac{ v _{X} }{ v _{Y} }=\sqrt{\frac{ r _{Y}aM _{Y} }{ br _{Y} M _{Y}}}=\sqrt{\frac{ a }{ b }}\]

Answer 10

That means that vX is given by the following:\[v _{X}=v _{Y}\sqrt{\frac{ a }{ b }}\]

Answer 11

Do you see how to solve the problem now?

Answer 12

Let me try and see this one second...

Answer 13

vx=1983.0sqrt(...) I am confused as to what a and b would be

Answer 14

it wouldn't be 1.31 and .903 would it?

Answer 15

You see where I typed that Mx=aMy? That's the same as saying the mass of Planet X is 1.31 times the mass of Planet Y. In other words, Mx=1.31My.

Answer 16

Yes, those would be a and b.

Answer 17

I'm out of here, but if you get an answer that looks like 2388.4m/s, you've done things correctly.

Answer 18

Okay, thank you for your help!

Answer 19

I got it! Thank you!