Solving for the Day on Planet X - Help!

In summary, the conversation discusses the concept of planetary motion and how it relates to the rotation of Planet X. It is noted that Planet X rotates around an axis through its north and south poles and is perfectly spherical. An astronaut's weight is also compared at different points on Planet X, indicating a difference in gravitational acceleration. The conversation then discusses how to calculate the day length on Planet X, with different approaches being suggested. The final solution involves calculating the radius and mass of the planet and using the formula T=mrw^2 to find the day length.
  • #1
dudgey
5
0
Help! Planetary motion

Please help!
Planet X rotates in the same manner as the earth, around an axis through its north and south poles, and is perfectly spherical. An astronaut who weighs 946 N on the Earth weighs 920 N at the north pole of Planet X and only 854 N at its equator. The distance from the north pole to the equator is 1.889×104 km , measured along the surface of Planet X.

How long is the day on Planet X? Take free fall acceleration on Earth to be 9.80 m/s^2

I'm totally stuck and I've being trying to do this for about an hour in many different ways. The equation T^2=(4*pi^2*r^3)/G*M doesn't seem to work. I don't know what I'm doing wrong, and I don't understand what to do with the two different weights at the pole and equator. :(
 
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  • #2
With the distance given you can calculate the radius of planet X.
Calculate the mass of the astronaut on the earth. Using this mass, you will find the gravitational acceleration of planet X. Then apply the formula T+mg'=mrw^2. Work out the w and eventually you will find T
 
  • #3
That's a different approach than what I was trying. How would I find w though from that information? There's something I'm missing on this question. I can do all the others that go along with it, just not this one. so frustrating...
 
  • #4
sorry. I need to clarify something. the former T and the latter T in my post is different one. The latter T means the time. The former T is given by the question. So you just need to put in everything to get the w.
 

1. What is planetary motion?

Planetary motion refers to the movement of planets, moons, and other celestial bodies in our solar system and beyond. This includes their rotations on their axes and their orbits around the sun.

2. What causes planetary motion?

The force of gravity is responsible for the motion of planets. The sun's gravitational pull keeps the planets in their orbits, while the planets' own gravity holds their moons in orbit around them.

3. How did scientists help plan the understanding of planetary motion?

Scientists such as Isaac Newton and Johannes Kepler used mathematics and observations to develop the laws of planetary motion, which helped us understand how and why planets move the way they do.

4. Can planetary motion be predicted?

Yes, planetary motion can be predicted using mathematical models and computer simulations. These predictions are based on the laws of gravity and the known positions and velocities of the planets.

5. Why is understanding planetary motion important?

Understanding planetary motion helps us gain a deeper understanding of our universe and how the solar system works. It also has practical applications, such as predicting the positions of planets for space missions and understanding the effects of gravitational forces on spacecraft.

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