Question

Two Jupiter-size planets are released from rest 1.40×1011m m apart. What are their speeds as they crash together?

Answer 1

Hold on is the 1011 10^11 or just 1011???

Answer 2

10^11

Answer 3

M₁ = mass of planet #1
M₂ = mass of planet #2
M = total mass
R₁ = radius of planet #1
R₂ = radius of planet #2
d₁ = initial distance between planet centers
d₂ = final distance between planet centers
a = semimajor axis of plunge orbit
v₁ = relative speed of approach at distance d₁
v₂ = relative speed of approach at distance d₂

M₁ = M₂ = 1.8986e27 kilograms
M = M₁ + M₂ = 3.7972e27 kg
G = 6.6742e-11 m³ kg⁻¹ sec⁻²
GM = 2.5343e17 m³ sec⁻²
d₁ = 1.4e11 meters
a = d₁/2 = 7e10 meters
R₁ = R₂ = 7.1492e7 meters
d₂ = R₁ + R₂ = 1.42984e8 meters
v₁ = 0
v₂ = √[GM(2/d₂−1/a)]
v₂ = 59508.4 m/s
The time to fall is 1337.7 days
:)) Does this help of is it just confzzing???? :))

Answer 4

The top is what the variables mean and the bottom is the math!!! ;))

Answer 5

Or think of it like this (I have reasoning in this one!
F = GMm/r^2 where M = m = mass of Jupiter = 1.8987 × 10^27 kilograms

r = 1.40 x 10^11 kilometers = 1.40 x 10^14 meters (so the answer will come out in Newtons)

G = 6.67 × 10−11 N · m2/kg^2
mass^2 = 3.598609 x10^54 kg2
r^2 = 1.96 x 10^28 meters ^2

F= ((6.67 × 10−11 N · m2/kg2)(1.8987 × 10^27 kilograms)^2)/(1.40 x 10^14 meters )^2

acceleration = 0 m^2/sec^2, velocity = 0 m/sec,since the planets were released at REST, which means both velocity and acceleration = 0. All acceleration is due to the mass and gravitational acceleration due to the mass of the two planets

m^2 = 3.60506169 x 10^54 kg^2
r^2 = 1.96 x 10^28 m^2

F = 1.226824565 x 10^16 Newtons

Divide by the mass x G to get the acceleration. If you want the velocity, you have to integrate the acceleration according the basic formula y = x + v + a where x and y = coordinates on a two dimensional plane, v = velocity a = acceleration. First derivative =dy /dx = x^0 + v, second derivative = d^2y/dx^2 = a. This is basic second semester calculus, and physics is applied math lol.

Answer 6

Do you understand?????

Answer 7

I understand what you are saying. I've been stuck on this problem for a while and just tried the answer. Unfortunately, it's not right :/

Answer 8

No its right........ I already had this quesion on one of my previous assensments and I got it correct.... :\

Answer 9

Hold on what did you put in for your answer?

Answer 10

59508m/s

Answer 11

Did you read my answer or just skip to the bottom?????? Because that not correct.....

Answer 12

Divide by the mass x G to get the acceleration. If you want the velocity, you have to integrate the acceleration according the basic formula y = x + v + a where x and y = coordinates on a two dimensional plane, v = velocity a = acceleration. First derivative =dy /dx = x^0 + v, second derivative = d^2y/dx^2 = a.

Answer 13

I think you took a pre answer hold on........ well just keep in mind the process... :))

Answer 14

I read the whole thing and thought I understood it. It made sense for the most part. Your determination of the a value did not make sense to m though. I have been trying to solve it with only using conservation of energy.

Answer 15

Ok see I solve things differently, and usually it takes longer but it works for me, yeah know , well im glas your read the whole thing! Most people don't and it is soo annoying!! :))

Answer 16

I'm pretty sure it'll be on my final so I need to make sure that I know it :P

Answer 17

Oh well good luck! I don't have to take those yet see im in 7th grade, but if I wanted to I could skip ALL of high school!!!!! :)) So happy I just found out this morning! :))

Answer 18

Thanks :) NowI just need to figure out how to get the right answer. Or at least get it and work backwards

Answer 19

Ok well I need to go, I have homework, do you want a website that I use all the time for calc help????

Answer 20

For calcules three:
http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx
For calcules 2:
http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx
For calcules 1:
http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

Answer 21

These are sooo great! They explain things soo well!!!!! :))
There also the reason I did not fail calc 1 and 2!

Answer 22

thanks :)