IF a particular galaxys has a total mass of 10 to the 56 grams and the average star in that galaxy has a mass of 10 to the 35 grams, approximately how many stars are there in that galaxy? Give your answer to the nearest whole power of 10 by entering the exponent only.

A certain spacecraft is 3.3 AU (Astronomical Units) from Earth. How long in seconds does it take for a signal to reach the Earth after it is transmitted from the spacecraft? Hint: An AU is about 149.9 Million Km, and light moves at 299,800 Km/s. {Indicate your answer to the nearest whole second).

If a hypothetical planet in our Solar System had a sidereal period of 11.1 Earth years and a circular orbit, how far from the Sun in Astronomical Units would it be? Enter your answer to the nearest 0.01 AU.

A particular spiral galaxy can be approximated by a thin disk-like volume 35 Thousand Light Years in radius and 8 Hundred Light Years thick. If this Galaxy contains 790 Billion stars, estimate the average distance between the stars in this galaxy. Hint: calculate the average volume per star in cubic Light Years, and then estimate the approximate linear dimension across such a volume. (Indicate your answer to one decimal place.)

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1. 10^56/10^35 =

2. d = 3.3AU * 1.499*10^8km/AU =

2. Continued.

d = V*t, V = 3*10^5 km/s, t = ?.

To determine the number of stars in the galaxy, divide the total mass of the galaxy by the average mass of each star:

Number of stars = Total mass of galaxy / Average mass of each star

Number of stars = 10^56 grams / 10^35 grams

Number of stars = 10^(56 - 35)

Number of stars = 10^21

Therefore, there are approximately 10^21 stars in the galaxy.

To calculate the time it takes for a signal to reach Earth from the spacecraft, first convert the distance from AU to kilometers:

Distance = 3.3 AU * 149.9 million km/AU

Distance ≈ 494.67 million km

Divide the distance by the speed of light to get the time:

Time = Distance / Speed of light

Time ≈ 494.67 million km / 299,800 km/s

Time ≈ 1650 seconds

Therefore, it takes approximately 1650 seconds for the signal to reach Earth.

To determine the distance of the hypothetical planet from the Sun, we can use Kepler's Third Law of planetary motion. The formula is:

T^2 = (4π^2 * r^3) / (G * M)

where T is the period of revolution in years, r is the distance from the Sun in AU, G is the gravitational constant, and M is the mass of the Sun.

Rearranging the equation, we get:

r = (T^2 * (G * M) / (4π^2))^(1/3)

Plugging in the given values:

r = (11.1^2 * (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 1.989 × 10^30 kg) / (4π^2))^(1/3)

r ≈ 11.56 AU

Therefore, the hypothetical planet would be approximately 11.56 AU from the Sun.

To estimate the average distance between stars in the galaxy, we need to calculate the volume of the galaxy first:

Volume = π * (radius^2) * thickness

Volume = π * (35,000 light years)^2 * (800 light years)

Volume ≈ 2.2 × 10^14 cubic light years

Next, we divide this volume by the number of stars to get the average volume per star:

Average volume per star = Volume / Number of stars

Average volume per star = 2.2 × 10^14 cubic light years / 790 billion

Average volume per star ≈ 278.48 cubic light years

Lastly, we estimate the approximate linear dimension across this volume using the formula for the volume of a sphere:

Volume of sphere = (4/3) * π * (radius^3)

Solving for the radius:

Radius ≈ (∛(3 * Average volume per star / (4π)))^(1/3)

Radius ≈ (∛(3 * 278.48 / (4π)))^(1/3)

Radius ≈ 2.5 light years

Therefore, the average distance between stars in this galaxy is estimated to be approximately 2.5 light years.

Sure! Let's go through each question one by one and break down the steps to find the answers.

1. Number of Stars in a Galaxy:
To find the number of stars in the galaxy, we can divide the total mass of the galaxy by the average mass of each star.

Given:
Total mass of the galaxy = 10^56 grams
Average mass of each star = 10^35 grams

To calculate the number of stars:
Number of stars = Total mass of the galaxy / Average mass of each star

Number of stars ≈ 10^56 / 10^35
Number of stars ≈ 10^(56-35)
Number of stars ≈ 10^21

So, there are approximately 10^21 stars in that galaxy.

2. Signal Transmission Time from a Spacecraft:
To calculate the time it takes for a signal to reach Earth from the spacecraft, we need to find the distance between them and divide it by the speed of light.

Given:
Distance from spacecraft to Earth = 3.3 AU
1 AU = 149.9 million km
Speed of light = 299,800 km/s

To calculate the transmission time:
Convert the AU distance to kilometers:
Distance in km = 3.3 AU * 149.9 million km/AU

Now, divide the converted distance by the speed of light:
Time = Distance in km / Speed of light

Time ≈ (3.3 * 149.9 million) km / 299,800 km/s
Time ≈ 495.67 million km / 299,800 km/s
Time ≈ 1651.72 seconds

So, it takes approximately 1652 seconds for the signal to reach Earth from the spacecraft.

3. Distance of a Hypothetical Planet from the Sun:
To find the distance of the hypothetical planet from the Sun, we need to use its sidereal period (orbital period in Earth years).

Given:
Sidereal period of the planet = 11.1 Earth years

To calculate the distance from the Sun:
We can use Kepler's Third Law, which states:

(Average distance from the Sun)³ = (Sidereal period)²

Let's convert the Earth years to sidereal years:
Sidereal period = 11.1 * 365.25 days (sidereal year has 365.25 days)

Now, solve for the distance from the Sun:
(Average distance from the Sun)³ = (11.1 * 365.25)²

Taking the cube root of both sides:
Average distance from the Sun = cuberoot ((11.1 * 365.25)²)

Average distance from the Sun ≈ 19.45 AU

So, the hypothetical planet would be approximately 19.45 AU away from the Sun.

4. Average Distance between Stars in a Spiral Galaxy:
To estimate the average distance between stars in the galaxy, we need to calculate the average volume per star and then estimate the linear dimension across such a volume.

Given:
Radius of the galaxy = 35 thousand light years
Thickness of the galaxy = 8 hundred light years
Number of stars in the galaxy = 790 billion

To calculate the average distance between stars:
Calculate the volume of the galaxy:
Volume = π * (radius)² * (thickness)

Average volume per star = Volume / Number of stars

Now, estimate the linear dimension across the average volume per star:
Average distance between stars = (Average volume per star)^(1/3)

Calculating step by step:
Volume = π * (35,000 light years)² * (800 light years)
Volume = 2.96 * 10^14 cubic light years

Average volume per star = 2.96 * 10^14 cubic light years / 790 billion
Average volume per star = 3.75 * 10^5 cubic light years

Average distance between stars = (3.75 * 10^5)^(1/3)
Average distance between stars ≈ 71.4 light years

Therefore, the average distance between stars in this galaxy is estimated to be approximately 71.4 light years.

I hope this helps! Let me know if you have any further questions.