Math part 2

The distance between two masses increases by 13.7. The resulting gravitational force between the two masses is now only _____ of what it originally was. (Carry out your answer to 4 decimal places, for example: 0.0123.)

0.0053

Find the product of the significant figure numbers: 6.601×104 × 8.291×10−7 Note the negative exponent and carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

0.0547

The distance between two masses changes by 2.7. The resulting gravitational force, carried out to 3 decimal places, is then _____ what it originally was.

0.137

The distance between two masses increases by 2.6. The resulting gravitational force between the two masses is now only _____ of what it originally was. (Carry out your answer to 4 decimal places, for example: 0.0123.)

0.1479

Find the quotient of the significant figure numbers: 8.01×105 ÷ 3.71×106 Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

0.2159

Find the product of the significant figure numbers: 4.03×106 × 5.597×10−8 Note the negative exponent and carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

0.2256

The distance between two masses changes by 2.1. The resulting gravitational force, carried out to 3 decimal places, is then _____ what it originally was.

0.227

If the distance between the two masses increases by 5.3 and mass one increases by 1.9 while mass two increases by 5.7, then the resulting gravitational force then between the masses would be ______ times the original force.

0.39

The distance between two masses changes by 1.6. The resulting gravitational force, carried out to 3 decimal places, is then _____ what it originally was.

0.391

An asteroid orbits the Sun every 9.43 years and in its orbit, reaches its farthest distance from the Sun at 8.5 AU. What would its perihelion be? Round your answer to 3 decimal places in normal decimal format in units of AU.

0.427

The astronomical unit (AU), which is the average distance between the Earth and the , is equal to km. (Note: use the 10^# or E# for the exponential, where # is the tens power being raised and return your mantissa to 4 significant figures, please.)

1.496 x 10^8 Correct Answer 1.496x10^8 Correct Answer 149.6 x 10^6 Correct Answer 149.6x10^6 Correct Answer 149.6 million Correct Answer 149.6E6 Correct Answer 1.496E8 Correct Answer 1.49589e8 Correct Answer 1.496E+8 Correct Answer 1.49589e+8 Correct Answer 149,600,000 Correct Answer 149600000

Find the quotient of the significant figure numbers: 8.48×106 ÷ 5.59×106 Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

1.517

The distance between two masses changes by 0.8. The resulting gravitational force, carried out to 3 decimal places, is then _____ what it originally was.

1.563

Planet A has 5.2 times the mass of planet B and its radius is 1.5 times that of B's. A's escape velocity is then __________ times that of planet B. Report your answer in normal decimal notation to 3 significant figures.

1.862

Planet A has 4.8 times the mass of planet B and its radius is 1.3 times that of B's. A's escape velocity is then __________ times that of planet B. Report your answer in normal decimal notation to 3 significant figures.

1.922

A comet orbits the Sun every 15.9 years and reaches its closest distance to the Sun at 1.81 AU in its orbit. What would its aphelion be? Round your answer to 3 decimal places in normal decimal format in units of AU.

10.836

The average orbital velocity of an asteroid is 34.543 km/s. What is the semi-major axis of its orbit in kilometers? Round your answer to 4 significant figures in scientific notation.

111,200,000

A comet's perihelion occurs at 2.93 AU and its aphelion is at 43.28 AU. What is the period of its orbit? (Round your answer to 4 significant figures in units of years.)

111.1

Suppose a new Oort comet was found revolving around the Sun with a semi-major axis of 508.6 AU. The period of this comet, calculated out to 4 significant figures in units of years, would be:

11470

A comet's perihelion occurs at 1.11 AU and its aphelion is at 46.4 AU. What is the period of its orbit? (Round your answer to 4 significant figures in units of years.)

115.8

A comet's perihelion occurs at 1.15 AU and its aphelion is at 46.44 AU. What is the period of its orbit? (Round your answer to 4 significant figures in units of years.)

116.1

In units of km, what is the distance of a moon that has a physical diameter of 6,564 km and appears to have an angular diameter of 10.63 arcsec? Please round with your answer to 4 significant figures in exponential form, as in #.###e##.

127,400,000

The average orbital velocity of an asteroid is 30.665 km/s. What is the semi-major axis of its orbit in kilometers? Round your answer to 4 significant figures in scientific notation.

141,100,000

Find the product of the significant figure numbers: 2.284×105 × 6.927×107. Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

15,820,000,000,000

Find the quotient of the significant figure numbers: 6.06×108 ÷ 3.74×104 Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

16,200

In units of km, what is the distance of a moon that has a physical diameter of 6,245 km and appears to have an angular diameter of 7.79 arcsec? Please round with your answer to 4 significant figures in exponential form, as in #.###e##.

165,400,000

Find the product of the significant figure numbers: 8.336×106 × 2.1×106. Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

17,510,000,000,000

Find the quotient of the significant figure numbers: 8.84×105 ÷ 5.19×103 Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

170.3

In units of km, what is the distance of a moon that has a physical diameter of 9,150 km and appears to have an angular diameter of 10.38 arcsec? Please round with your answer to 4 significant figures in exponential form, as in #.###e##.

181,800,000

Find the product of the significant figure numbers: 6.88×107 × 2.654×10−6 Note the negative exponent and carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2) You Answered

182.6

Planet A has 2 times the mass of planet B and its radius is 0.5 times that of B's. A's escape velocity is then __________ times that of planet B. Report your answer in normal decimal notation to 3 significant figures.

2

An asteroid orbits the Sun every 15.31 years and in its orbit, reaches its farthest distance from the Sun at 10.3 AU. What would its perihelion be? Round your answer to 3 decimal places in normal decimal format in units of AU.

2.032

Planet A has 6.6 times the mass of planet B and its radius is 1.5 times that of B's. A's escape velocity is then __________ times that of planet B. Report your answer in normal decimal notation to 3 significant figures

2.098

An asteroid orbits the Sun every 10.27 years and in its orbit, reaches its farthest distance from the Sun at 7.3 AU. What would its perihelion be? Round your answer to 3 decimal places in normal decimal format in units of AU.

2.15

Planet A has 6.5 times the mass of planet B and its radius is 1 times that of B's. A's escape velocity is then __________ times that of planet B. Report your answer in normal decimal notation to 3 significant figures.

2.55

An asteroid orbits the Sun every 5.44 years. Its average appearance at opposition is only 0.137 arcsecs across. What is its physical diameter in km? Round your answer to 4 significant figures in normal decimal format.

208

An asteroid orbits the Sun every 6.38 years. Its average appearance at opposition is only 0.119 arcsecs across. What is its physical diameter in km? Round your answer to 4 significant figures in normal decimal format.

210.6

The law of gravitational attraction is F=G\frac{m_1m_2}{r_{12}^2}F = G m 1 m 2 r 12 2. If the distance between the two masses decreases by the factor of 0.14 from what it was before and mass 1 increases by 1.6 while mass 2 increases by 2.7, then the gravitational force between the two objects would be ______ times the original force. (Note: calculate your answer to 2 decimal places.)

220.41

If an asteroid has a semi-major axis of 38.4 AU, then its orbital period in years carried out to 4 significant figures would be:

238

Mars is famous for being a place that we could visit and move to one day. Its average orbital radius is 1.524 AU, but it has a rather large orbital eccentricity of ε = 0.093. The difference that its eccentricity makes is that at perihelion it is only rperih = a − aε = (1.524 AU) − (1.524 AU)×(0.093) = 1.3823 AU away from the Sun. The planet reaches this perihelion position in its orbit at the same ecliptic angle as when Earth is in the month of August. Hence, when we see Mars in its opposition to the Sun during the month of August, we are as close to the red planet as we can be for the next 15 years, for that is how long these particular oppositions take to come around. The next near August opposition after the one that occurred in 2018 will be 2033, which is a possible targeted year for a visitation by astronauts. The August opposition before then happened was in 2003. This event was particularly celebrated because the planetary line up was so perfect, that the two planet's closeness would not be matched again for the next 60,000 years! Mars's physical radius is 3,397 km. At that 2003 solar opposition, how big did Mars appear to measure across its angular diameter in arcsec in the sky then?

24.5

A moon that is 7.901 ×108 km away is measured have an angular diameter of 6.702 arcsec. What is the moon's physical diameter in units of km? Please round your answer to 4 significant figures and in normal decimal format.

25,670

The law of gravitational attraction is: F=G\frac{m_1m_2}{r_{12}^2}F = G m 1 m 2 r 12 2. If the distance between the two masses increases by 1.4 and mass one increases by 5.8 while mass two increases by 8.7, then the resulting gravitational force then between the masses would be ______ times the original force. (Note: calculate your answer to 2 decimal places.)

25.74

In units of km, what is the distance of a moon that has a physical diameter of 1,410 km and appears to have an angular diameter of 10.31 arcsec? Please round with your answer to 4 significant figures in exponential form, as in #.###e##.

28,210,000

A dwarf planet's orbital distance from the Sun varies from 35.83 AUs to 50.14 AUs. In units of years, what is the period of its orbit? (Round your answer to 4 significant figures.)

281.8

An asteroid orbits the Sun every 13.76 years and in its orbit, reaches its farthest distance from the Sun at 8.3 AU. What would its perihelion be? Round your answer to 3 decimal places in normal decimal format in units of AU.

3.185

Planet A has 4.3 times the mass of planet B and its radius is 0.4 times that of B's. A's escape velocity is then __________ times that of planet B. Report your answer in normal decimal notation to 3 significant figures.

3.279

A dwarf planet's orbital distance from the Sun varies from 40.38 AUs to 51.96 AUs. In units of years, what is the period of its orbit? (Round your answer to 4 significant figures.)

313.7

A dwarf planet's orbital distance from the Sun varies from 41.27 AUs to 51.43 AUs. In units of years, what is the period of its orbit? (Round your answer to 4 significant figures.)

315.6

A dwarf planet's orbital distance from the Sun varies from 43.86 AUs to 49.73 AUs. In units of years, what is the period of its orbit? (Round your answer to 4 significant figures.)

320.1

The law of gravitational attraction is F=G\frac{m_1m_2}{r_{12}^2}F = G m 1 m 2 r 12 2. If the distance between the two masses decreases by the factor of 0.41 from what it was before and mass 1 increases by 2.4 while mass 2 increases by 2.7, then the gravitational force between the two objects would be ______ times the original force. (Note: calculate your answer to 2 decimal places.)

38.55

If an asteroid had an orbital period of 9.5 years around the Sun, its semi-major axis in AU carried out to 3 decimal places will be:

4.486

Find the sum of the significant figure numbers: 2.57×106 + 3.622×106. Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

6,192,000

An asteroid orbits the Sun every 15.92 years and in its orbit, reaches its farthest distance from the Sun at 6.5 AU. What would its perihelion be? Round your answer to 3 decimal places in normal decimal format in units of AU.

6.157

The distance between two masses changes by 0.4. The resulting gravitational force, carried out to 3 decimal places, is then _____ what it originally was.

6.25

If an asteroid had an orbital period of 15.8 years around the Sun, its semi-major axis in AU carried out to 3 decimal places will be:

6.297

A comet's perihelion occurs at 1.03 AU and its aphelion is at 43.42 AU. What is the comet's average orbital velocity? Round your answer to 4 significant figures in units of km/s.

6.318

If an asteroid had an orbital period of 17.1 years around the Sun, its semi-major axis in AU carried out to 3 decimal places will be:

6.637

There are arc seconds in an arc minute, arc minutes in an arc degree, and there are arc degrees in a circle.

60 360

After the Sun and the Moon, Venus is the brightest object that we can see in the sky. Two factors that this so is that it has a very bright white cloud cover and, at the orbital radius of 0.7233 AU, it is inside our orbit around the Sun, so it reflects a lot of light. Other reasons that helps is its size (radius = 6,052 km) and that, besides our Moon, Venus is the object that comes closer to the Earth than any other. At solar inferior conjunction, Venus lies directly between the Sun and us. How big would its angular diameter measure in arcsec in the sky then?

60.3

The distance between two masses decreases to 0.32 times what it was before. The then resulting gravitational force will grow to _____ times of what it originally was.

9.766

The distance between two masses decreases to 0.32 times what it was before. The then resulting gravitational force will grow to _____ times of what it originally was. (Carry out your answer to 4 significant figures, for example: 12.34.)

9.766

A comet orbits the Sun every 11.89 years and reaches its closest distance to the Sun at 0.42 AU in its orbit. What would its aphelion be? Round your answer to 3 decimal places in normal decimal format in units of AU.

9.99

Find the sum of the significant figure numbers: 3.403×106 + 9.048×107. Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in:

93,880,000

A moon that is 5.238 ×108 km away is measured have an angular diameter of 7.893 arcsec. What is the moon's physical diameter in units of km? Please round your answer to 4 significant figures and in normal decimal format.

A moon that is 5.238 ×108 km away is measured have an angular diameter of 7.893 arcsec. What is the moon's physical diameter in units of km? Please round your answer to 4 significant figures and in normal decimal format.

Find the quotient of the significant figure numbers: 9.2×106 ÷ 2.44×103 Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in:

Find the quotient of the significant figure numbers: 9.2×106 ÷ 2.44×103 Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in:

Newton's law of universal gravitation asserts that all objects in the universe attract each other with a/an that is proportional to the product of the two and inversely proportional to the square of their

force mass distance

The distances between two celestial bodies is shown below in the image. From the top image to the bottom, measure their respective distances and then calculate the resulting gravitational force between the two bodies. Has it ("increased", "decreased" or "stayed constant")? If different, then by the factor of . (And if so, round your answer to 1 decimal point.)

increased 11

The distances between two celestial bodies is shown below in the image. From the top image to the bottom, measure their respective distances and then calculate the resulting gravitational force between the two bodies. Has it ("increased", "decreased" or "stayed constant")? If different, then by the factor of . (And if so, round your answer to 1 decimal point.)

increased 11

The distances between two celestial bodies is shown below in the image. From the top image to the bottom, measure their respective distances and then calculate the resulting gravitational force between the two bodies. Has it ("increased", "decreased" or "stayed constant")? If different, then by the factor of . (If so, round your answer to 3 decimal places.)

increased 2.04

The distances between two celestial bodies is shown below in the image. From the top image to the bottom, measure their respective distances and then calculate the resulting gravitational force between the two bodies. Has it ("increased", "decreased" or "stayed constant")? If different, then by the factor of

increased 4

The Earth's rotational axis is tilted 23.5 degrees with respect to the plane of its ____

orbit

The Earth's rotational axis is tilted 23.5 degrees with respect to the plane of its _________.

orbit

In Kepler's model of the solar system, the planets move in orbits and thus they move with a speed.

oval changing

There are arc seconds in an arc minute, arc minutes in an arc degree, and there are arc degrees in a circle.

sixty sixty 360

Find the product of the significant figure numbers: 9.315×104 × 3.722×10−8 Note the negative exponent and carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

0.0035

If an asteroid had an orbital period of 0.8 years around the Sun, its semi-major axis in AU carried out to 3 decimal places will be:

0.862

The law of gravitational attraction is F=G\frac{m_1m_2}{r_{12}^2}F = G m 1 m 2 r 12 2. If the distance between the two masses decreases by the factor of 0.08 from what it was before and mass 1 increases by 2.3 while mass 2 increases by 2.9, then the gravitational force between the two objects would be ______ times the original force. (Note: calculate your answer to 2 decimal places.)

1,042.19

A moon that is 6.875 ×107 km away is measured have an angular diameter of 4.447 arcsec. What is the moon's physical diameter in units of km? Please round your answer to 4 significant figures and in normal decimal format.

1,482

Find the product of the significant figure numbers: 5.366×107 × 3.19×107. Carry out your calculations to 4 significant figures in the mantissa (the decimal part of the number) and express your answer in exponential form, as in: #.###e(-)##. Examples: 2.071e4 or 9.227e-2)

1,712,000,000,000,000

The Moon orbits the Earth at the average distance of 384,400 km. Assuming its orbit is circular, at what speed (in km/s) does the Moon orbit the Earth? (Calculate your answer to 4 significant figures. Note, you'll need to recall the time of a sidereal month and the length of a solar day.)

1.022 and 1.024

Jupiter's mean radius is 69,911 km (or 69,911 × 103 m = 6.9911 × 107 m), and, of course, its diameter is twice its radius at 139,822 km (or 1.39822 × 108 m). When Jupiter appears at opposition from the Sun, we are at the closest position to it in our orbit and it is only 628.7 Gm (or 628.7 × 109 m = 6.287 × 1011 m) away from us. In arcsec, how big would its angular diameter then appear in the sky rounded to three significant figures?

45.87

Planet A has 95.16 times the mass of planet B and its radius is 4.57 times that of B's. If planet B's escape velocity is 11.186 km/s, then planet A's escape velocity is _____________ km/s.

51.044

A comet's perihelion occurs at 0.79 AU and its aphelion is at 28 AU. What is the period of its orbit? (Round your answer to 4 significant figures in units of years.)

54.62

Given an object with a diameter of 1,000 km, what is the Distance of that object if it appears to have a parallax angle of: 1° across: 1' across: 1" across: . Round your answers to 4 significant figures in normal decimal notation that is expressed in units of km.

57290 3.438E6 2.063E8

Given an object with a diameter of 1,000 km, what is the Distance of that object if it appears to have a parallax angle of:

57300 3.438E6 2.063E8

If an asteroid has a semi-major axis of 15.4 AU, then its orbital period in years carried out to 4 significant figures would be:

60.43

In units of km, what is the distance of a moon that has a physical diameter of 1,365 km and appears to have an angular diameter of 4.05 arcsec? Please round with your answer to 4 significant figures in exponential form, as in #.###e##.

69,520,000

A comet's perihelion occurs at 2.46 AU and its aphelion is at 29.52 AU. What is the comet's average orbital velocity? Round your answer to 4 significant figures in units of km/s.

7.449

A comet's perihelion occurs at 2.11 AU and its aphelion is at 29.1 AU. What is the comet's average orbital velocity? Round your answer to 4 significant figures in units of km/s.

7.54

The astronomical unit (AU), which is the average distance between the Earth and the , is equal to km. (Note: use the 10^# or E# for the exponential, where # is the tens power being raised and return your mantissa to 4 significant figures, please.)

Sun 1.496 x 10^8

Kepler's third law establishes that the of the average distance (in AU) from a planet to the Sun, equals the of the period (in years) of the planet's revolution around the Sun.

cube square

Kepler's third law establishes that the of the average distance (in AU) from a planet to the Sun, equals the of the period (in years) of the planet's revolution around the Sun.

cube , square