Calculating the Size of an Arbitrary Planet

Using the circumference formula, we can calculate the circumference of the planet by setting up a proportion. Since we traveled 10 degrees in 1 hour, and there are 360 degrees in a full circle, we can set up the proportion: 10/360 = 1000/C, where C is the circumference of the planet. Solving for C, we get a circumference of approximately 35,714 km. Therefore, the planet has a circumference of about 35,714 km.
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Maximil
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Homework Statement


You land on an unknown planet. The first night you note that its celestial pole is 40 degrees above the northern horizon at your current position. Your flight module is able to go 1000 km/hour. You fly an hour due south, and note that the celestial pole is now 30 degrees above the horizon. How big is the planet?

Homework Equations


Circle Circumference Formula

The Attempt at a Solution


What I started off with was that we traveled 10 degrees in 1 hour, right? That means 10 degrees of the planet as a "circle" is 1000km. Using this, we can calculate the circumference as 1000km * 36, right? Am I on the right track? Thank you.
 
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Hi Maximil, Welcome to Physics Forums!

Yes, it looks like you're on the right track.
 
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What is the formula for calculating the size of an arbitrary planet?

The formula for calculating the size of an arbitrary planet is: R = √(GM/4πρ) where R is the radius of the planet, G is the gravitational constant, M is the planet's mass, and ρ is the average density of the planet.

What units should be used for the input variables in the formula?

The units for the input variables in the formula should be consistent. For example, if the mass is given in kilograms, then the density should be in kilograms per cubic meter and the gravitational constant should be in units of meters cubed per kilogram per second squared (m^3/kg/s^2).

Can this formula be used for any type of planet?

Yes, this formula can be used for any type of planet as long as the input variables are accurate. However, this formula does not take into account any irregular shapes or variations in density within the planet.

What other methods can be used to calculate the size of a planet?

Other methods for calculating the size of a planet include using spacecraft imaging and radar measurements, as well as using the transit method or radial velocity method to observe the planet's orbit around its host star.

How accurate is this formula in determining the size of a planet?

This formula is generally accurate for estimating the size of a planet. However, as mentioned before, it does not take into account any irregularities or variations in density. Therefore, the accuracy may vary depending on the specific characteristics of the planet being studied.

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