Question

MEDAL:If the moon was made of gold would it be heavier than the earth?(formulas and steps pls no direct answers)

Answer 1

heavier? In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity. Now the space is a place where gravity is zero. So how are you going to find the weight of the moon even if you know its mass.

Answer 2

you have to find the mass of a moon made of gold.
do you know the volume of the moon?

Answer 3

i have the volume of the moon (21.9 billion cubic kilometers) or (2190000 cubic centimeters)

Answer 4

Then use the formula
mass = density * volume

Answer 5

okaay one moment

Answer 6

In other words
$$ \rm mass ~of~ gold~ moon= density~ of~ gold * volume~ of~ moon$$

Answer 7

42310800 cm ^3

Answer 8

and the earth is: 1.08 x 1012

Answer 9

We need to have same units to make a good comparison.

Answer 10

soz i ment 1.08 x 1012^12 cubic km soo 1.09296 × 1018^18 cubic cm

Answer 11

That looks right, I will check on paper. Give me one minute.

Answer 12

ok

Answer 13

I got a different answer.

Answer 14

21.9 billion cubic kilometers = 21.9 * 10^9 km^3

Answer 15

what is that in cm?

Answer 16

density of gold = 19.32 g /cm^3

21.9 billion cubic kilometers = 21.9 * (10^9) (km^3) = 2.19 × 10^25 cm^3

mass of gold moon = 19.32 g/cm^3 × 2.19 × 10^25 cm^3

Answer 17

hmm im not seeing this i used a calculator for my calculations can you give me a step by step of how yoiu got this?

Answer 18

Do you agree that $$ \large \rm 21.9 ~billion ~km^3= 21.9 \times 10^9 ~km^3 $$

Answer 19

since
1 thousand = 1 x 10^3
1 million = 1 x 10^6
1 billion = 1 x 10^9
1 trillion = 1 x 10^12

Answer 20

okay
so i got no it would not is that what you have?

Answer 21

\[\large \rm 21.9 ~billion ~km^3
\\ \large = 21.9 \times 10^9 ~km^3
\\ \large = 21.9 \times 10^9 ~ ( 1 \times 10^3 ~m ) ^3
\\ \large = 21.9 \times 10^9 ~ ( 1 \times 10^3 \times 10^2 ~cm ) ^3
\\ \large = 21.9 \times 10^9 ~ ( 10^5 cm ) ^3
\\ \large = 21.9 \times 10^9 ~ 10^{5\times 3} ~cm^3
\\ \large = 21.9 \times 10^9 ~ 10^{15}~ cm^3
\\ \large = 21.9 \times 10^{24} ~cm^3
\\ \large = 2.19 \times 10^{25} ~cm^3
\]
multiply this by the density of gold, 19.32 g/cm^3
4.23*10^26 g is the mass of the gold moon

the mass of earth is
5.27 x 10^27 g

so earth has more mass than a gold moon

Answer 22

And you are correct - just read what you typed.

Answer 23

ok thx

Answer 24

@random231
makes an interesting point

Answer 25

The question would be better to ask which object has more mass. Not which is heavier, since you can't weigh earth on earth.
However you can imagine weighing earth and the solid gold moon on a planet much bigger than earth or the gold moon. The earth will come out 'heavier' on such a planet.
\[ \rm Weight = mass \times gravity ~constant \]