1.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).
2.IF a particular galaxys has a total mass of 10 to the 52 grams and the average star in that galaxy has a mass of 10 to the 38 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.
3.A particular spiral galaxy can be approximated by a thin disk-like volume 88 Thousand Light Years in radius and 5 Hundred Light Years thick. If this Galaxy contains 1,050 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.
4.Given that the acceleration of gravity at the Earth's surface is about 980 cm per sec per sec, the centripetal acceleration [v squared over r] of an artificial satellite in a circular orbit with a radius 2.7 times that of the Earth's radius would be about _____ cm per sec per sec. (Hint: F = m a, and the force of gravity gets weaker as the square of the distance, so how much weaker is gravity at 2.7 times the Earth's Radius than it is at the surface of the Earth?)
Update: 5.If a certain force accelerates an object of mass 29 Kg at 59 m/s/s, what acceleration in m/s/s would the same force produce on another object of mass 29? Enter answer to at least one decimal place to the right of the decimal point.
6.If the distance between the Earth and the Sun were increased by a factor of 5.26, by what factor would the strength of the force between them change? [Hint: Use Newton's Law of Universal Gravitation, and give your answer to 2 decimal places only]
Update 2: 7.The term "void ratio" means the ratio of the volume of empty space to volume of occupied space. It is a measure of how empty a volume is. Within stellar systems, the average separation between planets is roughly 10 to the 15 cm and the average planetary radius is typically 10 to the 15 cm. The void ratio for this stellar system is roughly 10 to what power:
Update 3: 7.The term "void ratio" means the ratio of the volume of empty space to volume of occupied space. It is a measure of how empty a volume is. Within stellar systems, the average separation between planets is roughly 10 to the 15 cm and the average planetary radius is typically 10 to the 15 cm. The void ratio for this stellar system is roughly 10 to what power
1. To calculate the time it takes for a signal to reach Earth from the spacecraft, we need to find the distance traveled by the signal and divide it by the speed of light.
Given:
- Distance between spacecraft and Earth = 3.3 AU
- 1 AU = 149.9 Million Km
- Speed of light = 299,800 Km/s
First, convert the distance from AU to Km:
Distance = 3.3 AU * 149.9 Million Km/AU
Next, divide the distance by the speed of light:
Time = Distance / Speed of light
Finally, round the answer to the nearest whole second to get the desired result.
2. To calculate the number of stars in the galaxy, we need to divide the total mass of the galaxy by the mass of an average star.
Given:
- Total mass of the galaxy = 10^52 grams
- Mass of an average star = 10^38 grams
To find the number of stars, we divide the total mass by the mass of an average star:
Number of stars = Total mass of the galaxy / Mass of an average star
To make the answer more manageable, we can express it using scientific notation by determining the exponent.
3. To estimate the average distance between stars in the galaxy, we need to calculate the average volume per star and then estimate the approximate linear dimension across that volume.
Given:
- Radius of the galaxy = 88 Thousand Light Years
- Thickness of the galaxy = 5 Hundred Light Years
- Number of stars in the galaxy = 1,050 Billion
First, calculate the volume of the galaxy:
Volume = π * (Radius^2) * Thickness
Next, calculate the average volume per star:
Average volume per star = Volume / Number of stars
To estimate the approximate linear dimension across the volume, we need to calculate the cube root of the average volume per star.
Finally, we can use this approximate linear dimension to estimate the average distance between stars.
4. To calculate the centripetal acceleration of the artificial satellite in a circular orbit, we need to determine the gravitational force acting on it and divide it by its mass.
Given:
- Acceleration of gravity at the Earth's surface = 980 cm/s^2
- Radius of the satellite's orbit = 2.7 * Radius of the Earth
- Centripetal acceleration formula: v^2 / r, where v is the velocity and r is the radius
First, calculate the gravitational force acting on the satellite using the formula:
Force of Gravity = (Mass of the satellite) * (Acceleration of gravity)
Next, calculate the centripetal acceleration using the formula:
Centripetal acceleration = Force of Gravity / (Mass of the satellite)
5. To calculate the acceleration produced by the force on another object with the same mass, we can use Newton's second law of motion, which states that force is equal to mass times acceleration.
Given:
- Mass of the first object = 29 Kg
- Acceleration of the first object = 59 m/s^2
- Mass of the second object = 29 Kg
Since the mass of the two objects is the same, the force applied will be the same. Therefore, the acceleration on the second object will also be 59 m/s^2.
6. To calculate the factor by which the strength of the force between the Earth and the Sun would change if their distance is increased, we can use Newton's law of universal gravitation.
Given:
- Initial distance between the Earth and the Sun = 1 AU
- Increase in distance = factor of 5.26
According to Newton's law of universal gravitation, the force between two objects is inversely proportional to the square of the distance between them.
Therefore, if the distance is increased by a factor of 5.26, the strength of the force will decrease by the square of that factor.
7. To determine the void ratio of the stellar system, we need to calculate the volume of empty space and the volume of occupied space. Then, take the ratio of the two volumes.
Given:
- Average separation between planets = 10^15 cm
- Average planetary radius = 10^15 cm
To calculate the volume of empty space, we can assume that each planet can be approximated by a sphere. The volume of empty space is the space between the planets.
To calculate the volume of occupied space, we can assume that the occupied space is the space occupied by the planets themselves.
Finally, to find the void ratio, we divide the volume of empty space by the volume of occupied space and express the answer as a power of 10.