Can I have some help

De acuerdo con la tercera ley de movimiento planetario de Kepler, la masa de un planeta es directamente proporcional al cubo de

Sunny_sXe [5.5K]

Answer:

La masa del Sol es $2.509\times 10^{31}$ kilogramos.

Step-by-step explanation:

Tras una lectura cuidadosa al enunciado, tenemos que la Tercera Ley de Kepler queda descrita por la siguiente relación:

$M \propto \frac{r^{3}}{T^{2}}$

$M = k\cdot \frac{r^{3}}{T^{2}}$ (Eq. 1)

Donde:

$r$ - Distancia entre los centros del planeta y el satélite, medido en kilómetros.

$T$ - Período oribital del satélite, medido en días.

$k$ - Constante de proporcionalidad, medida en kilogramo-días cuadrados por kilómetro cúbico.

$M$ - Masa del planeta, medida en kilogramos.

Podemos obtener la masa del Sol mediante la siguiente relación:

$\frac{M_{S}}{M_{E}} = \frac{\frac{r_{E}^{3}}{T_{E}^{2}} }{\frac{r_{M}^{3}}{T_{M}^{2}} }$

$\frac{M_{S}}{M_{E}} = \left(\frac{T_{M}}{T_{E}} \right)^{2}\cdot \left(\frac{r_{E}}{r_{M}} \right)^{3}$ (Eq. 2)

Donde:

$T_{M}$ , $T_{E}$ - Períodos orbitales de la Luna y la Tierra, medidos en días.

$r_{E}$ , $r_{M}$ - Distancias entre la Tierra y el Sol, así como entre la Luna y la Tierra, medidas en kilómetros.

$M_{S}$ , $M_{E}$ - Masas del Sol y la Tierra, medidos en kilogramos.

Si $M_{E} = 75.97\times 10^{24}\,kg$ , $T_{E} = 365.3\,d$ , $T_{M} = 27.3\,d$ , $r_{M} = 3.84\times 10^{5}\,km$ y $r_{E} = 1.496\times 10^{8}\,km$ , entonces tenemos que la masa del Sol es:

$M_{S} = \left(\frac{T_{M}}{T_{E}} \right)^{2}\cdot \left(\frac{r_{E}}{r_{M}} \right)^{3}\cdot M_{E}$

$M_{S} = \left(\frac{27.3\,d}{365.3\,d} \right)^{2}\cdot \left(\frac{1.496\times 10^{8}\,km}{3.84\times 10^{5}\,km} \right)^{3}\cdot (75.97\times 10^{24}\,kg)$

$M_{S} = 2.509\times 10^{31}\,kg$

La masa del Sol es $2.509\times 10^{31}$ kilogramos.

7 0

3 years ago

Sam delivers 167 newspapers every morning, he receives 5 cents per paper seven day a week, what is his weekly pay

steposvetlana [31]

Answer:

$58,45 or 5845 cents

Step-by-step explanation:

Weekly pay = 167 * 0.05 * 7 = $58.45 or 5845 cents

4 0

4 years ago

Read 2 more answers

The product of 3 consecutive even integers is equal to the cube of the first plus the square of the second plus twice the square

algol [13]

Answer:

6, 8 and 10 and -2, 0, 2

There are two roots x = -2 and 6,

but the since I don't believe 0 is an even number the answer is 6, 8 and 10

I was incorrect according to G0ggle zero is an even number so another answer is -2, 0, 2

Step-by-step explanation:

read the question and convert the English to mathematics

x, y and z even consecutive number

y = x+2

z = y+2 = x+4

and

xyz = x³ + y² + 2z² substitiute x terms in for y and z

x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solve for x by graphing on DEMOS

x = -2, 6 solved algebraically below

x = -2 y=0 z=2

x = 6 y=8 z=10

Checked both answers

xyz = x³ + y² + 2z²

-2(0)2 = -8 + 0 + 8 when x = -2

0 = 0

and

6(8)(10) = 6³ + 8² +2(10)² when x = 6

480 = 216+64+200

= 480

x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solved algebraically

(x²+2x)(x+4) = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + 3x² + 20x + 36

3x² - 12x - 36 = 0 factor out the 3

3[x² - 4x - 12] = 0

3(x+2)(x-6) = 0 x = -2 and -12

6 0

3 years ago

Plz hurry I really need the answer… like now

Dvinal [7]

Answer:

2700 square feet

Step-by-step explanation:

5+4=9x300=2700

3 0

2 years ago

1.what is the slope of the line passing through the points (1,-5) and (4,1)?

hoa [83]

Answer:

C. 2

Step-by-step explanation:

Slope = (y2-y1) / (x2-x1) , (x1,y1) = (1,-5) , (x2,y2)=(4,1)

= (1-(-5)) / (4-1)

= (1+5) / 3

= 6/3

= 2

3 0

3 years ago