what is jupiters gravity compared to earth in percent

ane.   a) Look up the mass of the Moon and the radius of the Moon in the book, and compute the density of the Moon, in gm/cm³.

Part one: Data

Looking on folio 178, we see that the mass of the Moon is 7.35 X ten²² kilograms, and the radius of the Moon is 1738 kilometers.

Part 2: Equation

We must use the density formula: density = mass / book

Part 3: Unit Conversion

Nothing is in the correct units! Nosotros must convert the mass into grams:

Yard_Moon = vii.35X 10²² kg X 1000 gm / kg = 7.35 X 10²⁵ grams

Nosotros must convert the radius into centimeters:

R_Moon = 1738 km X (1000m / km) X (100cm / one thousand) = one.738 X 10⁸ cm

Part four: Computation

So V = (4/3)(pi)R^three = (4/iii)(3.xiv)(1.738 X ten^eight cm)³

Five = 2.20 X ten²⁵ cm³

And Density = M / V = 7.35 10 10²⁵ gm / two.20 10 10²⁵ cm³

density = 3.34 gm/cmⁱⁱⁱ

Part 5: The Answer

The density of the Moon in three.34 grams per cubic centimeter, in good agreement with the value in the volume.

b)   Based on that average density, would you say the moon is made mostly of ice (density = 0.9 gm/cm³), rock (density = 3.0 gm/cm³), or iron (density = ix.0 gm/cm³)?

The average density of the Moon is closest to the value for the density of rock. Thus, information technology is possible for usa to come up to the conclusion that the Moon is made mostly of rock, with niggling h2o or iron.

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ii.   In tardily Baronial of 2003, Mars was at its closest point to Earth in nearly sixty,000 years! This was due to the coincidence that Mars and World lined upwards with the Sunday when the Earth was shut to its farthest betoken from the Lord's day (called aphelion) and Mars was close to its closest approach to the Sun (chosen aphelion).

a) When Mars is at perihelion and Earth is at aphelion, how far apart are the two planets, in kilometers? How many miles is that, if there are approximately 1.six kilometers in a mile?

Reply:  Mars is at a distance of 206,600,000 km from the Sunday at perihelion (Chapter 10, p. 251).  At aphelion, Globe is at a altitude of 152,100,000 km from the Sun.  This is a difference of 54,500,000 km, or 34,000,000 miles.

b) What is the angular diameter of Mars when the Earth and Mars are separated by this altitude, in seconds of arc? This is about how large Mars appeared to be in August 2003.

Function one: Data

Actual diameter of Mars = 3394 km x 2 = 6788 kjm

Distance at closest approach = 54,500,000 km

Part 2: Equation

We use the formula for Angular Diameter:

Angular Diameter = 206265 (Actual Bore / Distance)

Part 3: Unit Conversion

Both Bodily Size and Distance are in kilometers.  No unit of measurement conversions are needed.

Function 4: Computation

Angular Diameter = 206265 (6788 km / 54,500,000 km)

Angular Diameter = 25.7 seconds of arc

Part v: The Answer

So Mars has an angular diameter of 25.7 seconds of arc when it it at its closest to Earth

c) Mars is about 200 one thousand thousand kilometers from Earth on average. What is the boilerplate athwart bore of Mars? How many times smaller is this than the Baronial 2003 effigy?

Part 1: Data

Actual diameter of Mars = 3394 km x 2 = 6788 kjm

Boilerplate altitude = 200,000,000 km

Part two: Equation

We once more utilize the formula for Angular Diameter:

Angular Diameter = 206265 (Actual Diameter / Distance)

Part three: Unit Conversion

Both Actual Size and Distance are in kilometers.  No unit conversions are needed.

Part 4: Computation

Athwart Diameter = 206265 (6788 km / 200,000,000 km)

Angular Diameter = vii seconds of arc

Role five: The Answer

And then Mars has an angular diameter of merely 7 seconds of arc at its boilerplate altitude from Earth.  This is 3.67 times smaller than its angular size at closest approach.

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3.   a)   Jupiter is about five times farther abroad from the Sun than the World is, and has about 300 times the mass of the World. Compare the gravitational force between Jupiter and the Sunday to the gravitational force between the Earth and the Sun.

Role i: Data

Masses: Thousand_Jup = 300 M_Ear

distances from the Sun: R_{Sun Jup} = five R_{Sun Ear}

Part two: Equation

We want to compare the gravitational forcefulness exerted past the Sunday on Jupiter to the gravitational strength exerted by the Sun on Earth. Since when we compare we split, we want to compute

F_{Sun Jup} / F_{Sunday Ear}

Outset, nosotros write out the relevant formulas

F_{Sun Jup} = G K_{Lord's day} M_Jup / (R_{Sun Jup})^two

F_{Sun Ear} = G M_Sun M_Ear / (R_{Sun Ear})^two

Now we perform the divisions. See the gravity handout for details:

F_{Sun Jup} / F_{Sun Ear} = Yard M_Sun M_Jup (R_{Sun Ear})ⁱⁱ / K M_Sun One thousand_Ear (R_{Lord's day Jup})^two

Note how, happily, both G and the mass of the Sun drop out! Nosotros are left with

F_{Sun Jup} / F_{Lord's day Ear} = M_Jup (R_{Sun Ear})ⁱⁱ / One thousand_Ear (R_{Dominicus Jup})²

Part 3: Unit Conversion

No unit of measurement conversions are needed!

Part 4: Computation

We substitute from the data higher up. M_Jup becomes 300 M_Ear and R_{Sunday Jup} becomes 5 R_{Sunday Ear}

F_{Sun Jup} / F_{Lord's day Ear} = (300 M_Ear) (R_{Sun Ear})² / M_Ear (5 R_{Lord's day Ear})²

Do the squaring first:

F_{Sunday Jup} / F_{Lord's day Ear} = (300) (Yard_Ear) (R_{Dominicus Ear})² / M_Ear (25) (R_{Dominicus Ear})ⁱⁱ

Note that the 5 is squared to 25! The mass of the World and the distance between the World and Sun both drop out and we are left with merely numbers:

F_{Dominicus Jup} / F_{Dominicus Ear} = (300) / (25) = 12

Nosotros become rid of the fraction by multiplying both sides by F_{Sun Ear}:

F_{Sun Jup} = 12 F_{Sun Ear}

Part 5: The Respond

The gravitational strength betwixt the Sunday and Jupiter is 12 times greater than the gravitational force between the Sunday and Earth. Earth may exist closer to the Sun than Jupiter, merely Jupiter's mass more than makes up for information technology's astringent distance.

b)   Perform the aforementioned ciphering for Saturn which is ten times farther away from the Sun than World, and 100 times more massive than the Earth.

Part 1: Data

Masses: K_Sat = 100 Grand_Ear

distances from the Sun: R_{Sunday Sat} = 10 R_{Lord's day Ear}

Office 2: Equation

We desire to compare the gravitational forcefulness exerted past the Sun on Saturn to the gravitational force exerted by the Sun on Earth. Since when we compare we divide, we want to compute

F_{Sunday Sat} / F_{Sunday Ear}

Commencement, we write out the relevant formulas

F_{Lord's day Sat} = Thousand One thousand_Sun M_Sabbatum / (R_{Sun Saturday})²

F_{Sun Ear} = One thousand M_Sun M_Ear / (R_{Sun Ear})²

Now we perform the divisions. See the gravity handout for details:

F_{Lord's day Sat} / F_{Sun Ear} = 1000 Chiliad_Sun M_Sat (R_{Sun Ear})ⁱⁱ / G Grand_Sun Yard_Ear (R_{Lord's day Saturday})²

Annotation how, happily, both G and the mass of the Sun drop out! We are left with

F_{Sun Sabbatum} / F_{Sunday Ear} = M_Sat (R_{Sun Ear})^two / K_Ear (R_{Sun Sat})ⁱⁱ

Part 3: Unit of measurement Conversion

No unit of measurement conversions are needed!

Part 4: Computation

We substitute from the information to a higher place. Thousand_Sabbatum becomes 100 M_Ear and R_{Sunday Sat} becomes ten R_{Lord's day Ear}

F_{Sun Saturday} / F_{Lord's day Ear} = (100 M_Ear) (R_{Sun Ear})² / M_Ear (10 R_{Dominicus Ear})²

Do the squaring first:

F_{Sun Sat} / F_{Dominicus Ear} = (100) (Grand_Ear) (R_{Dominicus Ear})² / M_Ear (100) (R_{Sun Ear})ⁱⁱ

Note that the 10 is squared to 100! The mass of the Globe and the altitude between the Earth and Sun both drop out and nosotros are left with just numbers:

F_{Lord's day Saturday} / F_{Sun Ear} = (100) / (100) = ane

We become rid of the fraction by multiplying both sides past F_{Sun Ear}:

F_{Sun Sat} = 1 X F_{Lord's day Ear}

Role five: The Respond

Amazingly, The gravitational force between the Sun and Saturn is the same as than the gravitational force betwixt the Sun and Globe. Globe may be closer to the Dominicus than Saturn, but Saturn'southward mass exactly makes up for it's astringent distance.

Updated viii/sixteen/99

By James E. Heath

Copyright Ó 1999 Austin Community Higher

maffeiwaidelve.blogspot.com

Source: https://www.austincc.edu/jheath/Solar/Ans/brookfield.htm