For each planet in a solar system, its year is the time it takes the planet to revolve around the center star. The formula Upper E equals 0.2 x Super

[TSschmigel]

For each planet in a solar system, its year is the time it takes the planet to revolve around the center star. The formula
E = 0.2 x ^ 3 divided by 2

models the number of Earth days in a planet's year, E, where x is the average distance of the planet from the center star, in millions of kilometers. There are approximately
87.8

Earth days in the year of
Planet Upper A
.
What is the average distance of
Planet Upper A from the center star?

 

[MarkFL]

Can you solve the given formula for x?

 

[blamocur]

For each planet in a solar system, its year is the time it takes the planet to revolve around the center star. The formula
E = 0.2 x ^ 3 divided by 2

models the number of Earth days in a planet's year, E, where x is the average distance of the planet from the center star, in millions of kilometers.

For Earth [imath]x\approx 150[/imath], but the resulting [imath]E[/imath] seems to be much, much larger than 365.

 

[Dr.Peterson]

For Earth [imath]x\approx 150[/imath], but the resulting [imath]E[/imath] seems to be much, much larger than 365.

For each planet in a solar system, its year is the time it takes the planet to revolve around the center star. The formula
E = 0.2 x ^ 3 divided by 2

models the number of Earth days in a planet's year, E, where x is the average distance of the planet from the center star, in millions of kilometers. There are approximately
87.8

Earth days in the year of
Planet Upper A
.
What is the average distance of
Planet Upper A from the center star?

The constants presumably depend on the star.

 

[The Highlander]

Or maybe time is just a construct and it appears to fly by much more quickly for us old codgers? ?

 

[Mr. Bland]

If I understand the problem correctly, the orbital period of a planet is given by this formula:

[imath]E=\frac{x^3}{10}[/imath]​

Where [imath]E[/imath] is the number of Earth days in the planet's year and and [imath]x[/imath] is the distance of the planet from its star in units of 1000 Km.

For Planet A, [imath]E=87.8[/imath]:

[imath]87.8=\frac{x^3}{10}[/imath]​

The problem asks to solve for [imath]x[/imath], the distance of Planet A from the star in 1000 Km units.

 

[Dr.Peterson]

For each planet in a solar system, its year is the time it takes the planet to revolve around the center star. The formula
E = 0.2 x ^ 3 divided by 2

models the number of Earth days in a planet's year, E, where x is the average distance of the planet from the center star, in millions of kilometers. There are approximately
87.8

Earth days in the year of
Planet Upper A
.
What is the average distance of
Planet Upper A from the center star?

I've seen this problem in many places (with different numbers), including at least once here; but it is not always pasted as poorly as this. (I'm especially curious about how the "Upper", meaning "upper case" got into it.)

The actual equation should be written as

E = 0.2 x^(3/2)​

That is, [math]E=0.2x^{\frac{3}{2}}[/math]
What we need to see is some work, so we can know what help you need. You are given a value for E; how can you solve for x?

Note: In addition, I find that some versions specify that this is for our solar system, and in fact it does work for Earth, when understood correctly.

 

[The Highlander]

If I understand the problem correctly, the orbital period of a planet is given by this formula:

[imath]E=\frac{x^3}{10}[/imath]​

Where [imath]E[/imath] is the number of Earth days in the planet's year and and [imath]x[/imath] is the distance of the planet from its star in units of 1000 Km.

For Planet A, [imath]E=87.8[/imath]:

[imath]87.8=\frac{x^3}{10}[/imath]​

I believe your interpretation of the formula the OP is trying to write is not correct.

The correct version of it should be: \(\displaystyle E=0.2x^\frac{3}{2}\)

which would correspond to \(\displaystyle E^2=0.04x^3\) (in accordance with Kepler's 3^rd Law)

and

The problem asks to solve for [imath]x[/imath], the distance of Planet A from the star in 1000 Km units.

No, the distance would be in millions of km (10⁶ or 1,000,000 km units) not "1000 Km units"
(Note too that its "km" not "Km")

For Earth [imath]x\approx 150[/imath], but the resulting [imath]E[/imath] seems to be much, much larger than 365.

You'll be much happier using my formula (367.42 days). ??

 

[The Highlander]

The constants presumably depend on the star.

Very true but the formula (as we have just re-written it) is (approximately) correct for our solar system. ("Planet (Upper?) A" is clearly meant to be Mercury.)
Substituting 0.2043 for 0.2 gives much more accurate results (using our "correct" distance from the Sun)

 

[Dr.Peterson]

Very true but the formula (as we have just re-written it) is (approximately) correct for our solar system. ("Planet (Upper?) A" is clearly meant to be Mercury.)

... as I already said.

I found textbooks containing similar problems, specifying "our solar system" and actual planets, such as

​

and

​

But I also find versions like these that say "a solar system", but still use the specific formula (and actual planets without giving their names):

​

​

I find it interesting when problems get passed around and changed, often for the worse! The fact is, the formula is not applicable to any solar system.

 

[The Highlander]

... as I already said.

Yes, I know but I was too upset to read that far down because your post (with the corrected formula) went up 2 minutes before mine (while I was adding (unnecessary?) extra comments/responses at the end of mine)! ?
That's what I get for being a smart ass, I suppose. ?