Question

Imagine if astronomers have discovered a new planet next to Jupiter and named it Planet X. The average distance of Jupiter from the sun is about 5 AU and it has an orbital period of 12 years. Astronomers are not sure about how far Planet X is, but they do know that it had an orbital period of about 10 years. What is the average distance of Planet X from the sun in AU?

Answer 1

95

Step-by-step explanation:

because x × au= 69 +26

which means planet x is destroyed

Answer 2

The average distance of Planet X from the Sun is approximately 36.3 AU.

Step-by-step explanation:

The average distance of a planet from the Sun can be determined using its orbital period and the relationship between orbital period and distance in the solar system. According to the information given, Jupiter has an orbital period of 12 years and an average distance from the Sun of 5 AU (astronomical units). Planet X has an orbital period of 10 years, so we can use this relationship to find its average distance from the Sun.

Using the formula T2 = k * R3, where T is the orbital period in years and R is the distance from the Sun in AU, we can solve for the distance of Planet X.

Plugging in the known values for Jupiter (T = 12 years, R = 5 AU) and Planet X (T = 10 years), we can find the distance of Planet X:

102 = k * R3

100 = k * R3

R3 = 100/k

Since the value of k is the same for all planets in the solar system, we can set up a ratio to find the distance of Planet X:

RX3/53 = 102/122

RX3/125 = 100/144

RX3 = 125/144 * 100

RX3 = 52083.33

RX ≈ 36.3 AU

Therefore, the average distance of Planet X from the Sun is approximately 36.3 AU.