Need help with a problem involving planets and moons.

In summary, the equations for the x and y positions of the moon at time t are x(t) = 2100*cos(pi*t) + sin(2*pi*t) and y(t) = 2100*sin(pi*t) + cos(2*pi*t) respectively, assuming the motion is counter-clockwise.
  • #1
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Homework Statement


While a planet P rotates in a circle about its sun, a moon M rotates in a circle about the planet, and both motions are in a plane. Let's call the distance between M and P one { lunar unit}. Suppose the distance of P from the sun is 2100 lunar units; the planet makes one revolution about the sun every 2 years, and the moon makes one rotation about the planet every 0.25 years. Choosing coordinates centered at the sun, so that, at time t=0 the planet is at (2100, 0), and the moon is at (2100, 1), then the location of the moon at time t, where t is measured in years, is (x(t), y(t)).

Find equations for x(t) and y(t)

Homework Equations


Parametric equations of a circle:
x = rcos(t)
y = rsin(t)

The Attempt at a Solution


Seems like a fairly straightforward problem, except that it doesn't indicate whether the planets rotate counter-clockwise or clockwise. I've emailed my professor asking to clear up that point, but in the meantime, I'm assuming they both rotate clockwise.

My professor says counter-clockwise. I'm adjusting the equations to make it that way.

Using some intuition, I got the equations:
x(t) = 2100*cos(-pi*t) + sin(-2*pi*t)

y(t) = 2100*sin(-pi*t) + cos(-2*pi*t)

in other words, x(t) = x-position of the planet + x-position of the moon. Same for y(t)

I'm fairly sure these equations describe the motion of the moon correctly, but apparently, they are not the correct answers (it's an online submission process).

Any thoughts?
 
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  • #2
Since your professor has clarified that the motion is counter-clockwise, the equations should be:x(t) = 2100*cos(pi*t) + sin(2*pi*t)y(t) = 2100*sin(pi*t) + cos(2*pi*t)
 

Related to Need help with a problem involving planets and moons.

What is the difference between a planet and a moon?

A planet is a celestial body that orbits a star, has enough mass to form a spherical shape due to its own gravity, and has cleared its neighboring region of other objects. A moon, on the other hand, is a natural satellite that orbits a planet.

How many planets are in our solar system?

There are eight planets in our solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.

What are some characteristics of the planets in our solar system?

The eight planets in our solar system have varying sizes, compositions, and distances from the sun. For example, Jupiter is the largest planet and is made mostly of gas, while Mercury is the smallest planet and has a rocky surface.

Can moons have their own moons?

Yes, moons can have their own moons, also known as submoons or moonlets. However, they are much smaller and less common compared to planets having moons.

What is the significance of studying planets and moons?

Studying planets and moons can help us understand the formation and evolution of our solar system, as well as provide insights into the possibility of life beyond Earth. It also helps us understand the physical and chemical processes that shape these celestial bodies and how they may impact our planet.

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