Monday, December 14, 2015

Answers to Planet Volumes



Answers to Planet Volumes

This answer sheet has the answer to Planet Volume Questions: 

Page with complete questions on Planet Volumes:

http://www.dailymathproblem.com/p/planet-volumes-this-post-uses-data-on.html

What are the volumes of the planets and the sun based on the assumption that all of the planets and the sun are perfect spheres?


Sun and Planet Volumes
Radius km
Volume cubic km
Sun
695000
1.41E+18
Mercury
2440
6.08E+10
Venus
6052
9.29E+11
Earth
6378
1.09E+12
Mars
3397
1.64E+11
Jupiter
71492
1.53E+15
Saturn
60268
9.17E+14
Uranus
25559
6.99E+13
Neptune
24766
6.36E+13
Pluto
1150
6.37E+09



Calculation for earth

=(4/3) *3.14 *6.3783 x 109


Note the (4/3) x 3.14 .6.3783 is 1086.8

1086.8 x 109 is 1.087  x 1012


In the problems below I round this to 1.09 x 1012   

The volume is in cubic kilometers.

Calculate the volume of each planet as a percent of the volume of Jupiter.

The volume of each planet was divided by the volume of Jupiter the largest planet.   



Planet volumes as a percent of Jupiter
Radius km
Volume cubic km
Volume Planet over Volume Jupiter
Mercury
2440
6.08E+10
0.00%
Venus
6052
9.29E+11
0.06%
Earth
6378
1.09E+12
0.07%
Mars
3397
1.64E+11
0.01%
Saturn
60268
9.17E+14
59.91%
Uranus
25559
6.99E+13
4.57%
Neptune
24766
6.36E+13
4.16%
Pluto
1150
6.37E+09
0.00%



Calculation for Earth as a fraction of Jupiter: 


1.09x 1012  / 1.53 x 1015


(1.09)/1.53 = 7.1 x10-1


1012/ 1015 is 10-3


Multiplying terms gets us

7.1 x 10-4



How many planets might potentially fit inside an area of space the size of the volume of Jupiter?

They should all fit.  Note the sum of each planet as a fraction of Jupiter for the eight other planets is around 0.68 or 68%. Note that volume of Saturn is around 60 percent of Jupiter.  The next highest volume planet, Neptune, is less than 5 percent of Jupiter.

How many planets the size of Jupiter might fit inside an area the size of the sun?

Take the ratio of the volume of the Sun to the volume of Jupiter

=1.41 x 1018/ 1.53 x 1015

This comes out to around 921.

How many planets the size of the earth might fit inside an area the size of the sun?

Take the ratio of the volume of the Sun to the volume of the Earth.


1.41 x 1018 / 1.09 x 1012

This simplifies to 1.29 x 106 or around 1,290,000 earths.

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