# Weight on [Planet] Question

Neptune has a masss 17.2 times larger than that of Earth and a radius 3.88 times larger. A person weighing 176 lb on the Earth would weigh how much on Neptune?

Earth's mass is 6x10^24; Earth's radius is 6.4x10^6. Neptune's mass is 1.032x10^26; Neptune's radius is 24832000. 176 lbs is 80 kgs.

Weight (or Force) = G$\frac{Mplanet\bullet Mperson}{r2}$

G (universal) = 6.7x10^-11
Mperson for Earth = 80 kgs
Mplanet for Earth = 6x10^24 kgs
r for Earth = 6.4x10^6

Mperson for Neptune = ?
Mplanet for Neptune = 1.032x10^26
r for Neptune = 24832000

Every time I try to solve for the mass of the person on Neptune, I keep getting around 70 kgs, which is 154 lbs. The correct answer according to my online homework system is 201.084048 lbs.

First, I solve for Force on Earth. I plug all four values into the equation to get 785.15625 Newtons.

Second, I then plug the answer above into the Force value to solve for Mperson on Neptune. To isolate Mperson I multiply both sides of the equation by r^2, divide both sides of the equation by G, and divide both sides of the equation by Mplanet. The answer I get is 70.02 kgs, which is 154.05 lbs. That is not the correct answer.

I know that all I really need to do is divide 3.88^2 by 17.2, then multiply that value by 176, but I want to find out what I'm doing wrong. I don't want to use any shortcuts until I actually understand the long process.

Thanks!

## Answers and Replies

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Dick
Science Advisor
Homework Helper
Neptune has a masss 17.2 times larger than that of Earth and a radius 3.88 times larger. A person weighing 176 lb on the Earth would weigh how much on Neptune?

Earth's mass is 6x10^24; Earth's radius is 6.4x10^6. Neptune's mass is 1.032x10^26; Neptune's radius is 24832000. 176 lbs is 80 kgs.

Weight (or Force) = G$\frac{Mplanet\bullet Mperson}{r2}$

G (universal) = 6.7x10^-11
Mperson for Earth = 80 kgs
Mplanet for Earth = 6x10^24 kgs
r for Earth = 6.4x10^6

Mperson for Neptune = ?
Mplanet for Neptune = 1.032x10^26
r for Neptune = 24832000

Every time I try to solve for the mass of the person on Neptune, I keep getting around 70 kgs, which is 154 lbs. The correct answer according to my online homework system is 201.084048 lbs.

First, I solve for Force on Earth. I plug all four values into the equation to get 785.15625 Newtons.

Second, I then plug the answer above into the Force value to solve for Mperson on Neptune. To isolate Mperson I multiply both sides of the equation by r^2, divide both sides of the equation by G, and divide both sides of the equation by Mplanet. The answer I get is 70.02 kgs, which is 154.05 lbs. That is not the correct answer.

I know that all I really need to do is divide 3.88^2 by 17.2, then multiply that value by 176, but I want to find out what I'm doing wrong. I don't want to use any shortcuts until I actually understand the long process.

Thanks!
You are going the long way around. Mperson on Earth=Mperson on Neptune and it's about 80kg. You don't need to solve for a different mass on Neptune. Mass doesn't change. Only the weight changes.

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You are going the long way around. Mperson on Earth=Mperson on Neptune and it's about 80kg. You don't need to solve for a different mass on Neptune. Mass doesn't change. Only the weight changes.
Okay, I see what you're saying. I made a note in my notebook regarding universality of mass too, haha. I can't believe I skipped past that.

So if I plug the value for Mplanet of Neptune, Mperson, r^2 of Neptune, and G, then I will get around 897.06 N. I just convert this into pounds right?

Dick
Science Advisor
Homework Helper
Okay, I see what you're saying. I made a note in my notebook regarding universality of mass too, haha. I can't believe I skipped past that.

So if I plug the value for Mplanet of Neptune, Mperson, r^2 of Neptune, and G, then I will get around 897.06 N. I just convert this into pounds right?
Sure, but as you said, just using ratios is the easy way to do it.

Sure, but as you said, just using ratios is the easy way to do it.
Thank you!