Discovering the Radius of a Planet with a Man, a Parachute, and a Satellite

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In summary, a man jumped out of a plane with a parachute at 1000m above a spherical planet (point A). He saw a satellite rise at the eastern horizon and standing 2m above the surface of the planet at the equator (point B), the satellite reappeared 1.5 minutes later. The satellite's position at this point was at a 90 degree angle from the zenith, corresponding to the middle of the planet. The difference in angle between the radius of the small planet plus 2 and the radius plus 1000 was 1.35 degrees. It takes 100 minutes for the satellite to alter its position by 90 degrees. From this information, we can determine the radius of the planet.
  • #1
johnW
a man jumps out of a plane w/ a parachute at 1000m above a spherical planet (point A). He sees a satellite rise at the eatern horizon. Standing 2 m above surface of the planet (equator)(point B), the satellite re-appears 1.5 minutes after he saw it at 1000 m above sea level. From this point, the satellites position is exactly corresponding to a 90 degree angle from the zenith, ie, point B = middle of the planet. The difference in angle between radius of small planet+2 and radius+1000 is 1.35 degrees. Similary, 90 degree altering of position for satellite takes 100 minutes.
What is the radius of the planet?
 
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  • #2
This sounds like a homework problem to me... Perhaps it should be moved to the Homework help section?
 

Related to Discovering the Radius of a Planet with a Man, a Parachute, and a Satellite

1. How can a man, a parachute, and a satellite be used to discover the radius of a planet?

By measuring the time it takes for the man to fall to the surface of the planet with the parachute, and comparing it to the time it takes for the satellite to orbit the planet, we can calculate the radius of the planet using the equation for centripetal force.

2. What is the equation for calculating the radius of a planet using this method?

The equation is: r = (g * t^2) / (4π^2), where r is the radius of the planet, g is the acceleration due to gravity, and t is the time it takes for the man to fall or for the satellite to orbit.

3. How accurate is this method for determining the radius of a planet?

This method can provide a relatively accurate estimate of the planet's radius, but it may be affected by external factors such as air resistance and the satellite's orbit. It is best used as a rough estimate rather than a precise measurement.

4. Can this method be used for any planet in our solar system?

Yes, this method can be used for any planet in our solar system as long as we have accurate measurements of the planet's gravitational acceleration and the time it takes for the man to fall or for the satellite to orbit.

5. Are there any limitations to using this method for discovering the radius of a planet?

Yes, this method is limited by the accuracy of our measurements and the external factors that may affect the results. It is also not suitable for planets with very dense atmospheres or no atmosphere at all.

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