Question

In: Physics

Calculate the temperature of a planet. A star has a surface temperature of 4000K and a...

Calculate the temperature of a planet. A star has a surface temperature of 4000K and a radius of R = 8 × 108 m It has a rocky, airless planet orbiting it at a distance of 1.0×1011 meters. The planet has a radius of 5.0 × 106 m. We will estimate 1 for all objects. (a) What is the total power output of the star?

(b) What is the power incident on each square meter at distance to the planet (i.e. on an imaginary sphere).

(c) How much power is absorbed by the planet? (Assume the planet is black. Use the fact that the planet looks like a disk.)

(d) In equilibrium, Pin = Pout. How much power does the planet radiate per square meter of surface area of the planet?

(e) What is the temperature of the planet? (Should humans try to live there?)

Solutions

Expert Solution

what does this statement mean - "We will estimate 1 for all objects'' ????E

(a) Area of star = 4*pi*r²

Area = 4 *pi*8e8²

Area = 8.042e18 m²

The flux is given as

W = T⁴

where = 5.6704e-8 ( stefan boltzmann constant)

W = 5.6704e-8 (4000)⁴

W = 1.45e7 W/m²

Therefore, total power output is

P = W* Area

P = 1.1674e26 W

---------------------------------------------------------------------------------------------

(b) Area radiated by star power

A = 4 *pi*1e11²

A = 1.257e23 m²

Therefore,

power incident on each square meter = 1.1674e26 W / 1.257e23 m²

power incident on each square meter = 928.98 W/m²

---------------------------------------------------------------------------------------------------------

A = pi*r²

A = pi*5e6²

A = 7.854e13 m²

Therefore, power abosrbed = 928.98 W/m² * 7.854e13 m²

power abosrbed = 7.296e16 W

-------------------------------------------------------------------------------------------

(d) P_in = P_out = 7.296e16 W

P_out = T⁴A

T⁴ = P_out / A

T⁴ = 7.296e16 / 5.6704e-8 * 4 *pi *(5000000)²

T⁴ = 4.0956e9 K

T = 252.97 K

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

If the surface temperature of a blue star is 25000 K, at what wavelength would it...

If the surface temperature of a blue star is 25000 K, at what wavelength would it emit most of its light and which part of the electromagnetic spectrum would that light be? Calculate the surface temperature of an X-ray star which emits at 1nm peak wavelength?

(a) The star Antaresemits radiation with a peak wavelength of 792nm. What is its surface temperature...

(a) The star Antaresemits radiation with a peak wavelength of 792nm. What is its surface temperature (in K)? (Assume the star behaves like a blackbody.) (b) The star Denebemits radiation with a peak wavelength of 340nm. What is its surface temperature (in K)? (Assume the star behaves like a blackbody.) (c) X-rays are scattered from a target at an angle of 55.8°with the direction of the incident beam. Find the wavelength shift of the scattered x-rays in nm.

even though a Jovian planet is close to its star, its interior temperature is cool. explain...

even though a Jovian planet is close to its star, its interior temperature is cool. explain what this tells me about the planet's mass.

A composite series wall has an inside surface temperature of 1600F and outside surface temperature of...

A composite series wall has an inside surface temperature of 1600F and outside surface temperature of 500F. If it consists of 3.5 in. of mineral wool, 0.05 in. of plaster on the outside, and 0.75 in. of cork board on the inside, determine the heat loss in a 120 square foot of wall.

Calculate the surface redshift due to gravity for both the white dwarf and neutron star.

A planet has the same density as Earth but has a surface gravitational acceleration of nine...

A planet has the same density as Earth but has a surface gravitational acceleration of nine times that of the Earth (a person would instantly black out if placed on the surface). What is the escape velocity from the planet? If the planet was in an orbit of 1 AU from a 1 M⊙ star, what is the maximum distance that a moon could orbit the planet?

A mystery planet and its moon are found revolving around a nearby star. The star is...

A mystery planet and its moon are found revolving around a nearby star. The star is a K3 Main Sequence star with a mass of approximately 0.8 M☉ and a radius of 0.78 R☉. The planet is believed to be terrestrial (Earth-like, and therefore of a similar density) and has an observed orbital period of 243 days. The moon orbits the planet every 13.2 hours with an average orbital radius of 19,600 km. Using this information, find: (a)the orbital radius...

For a relatively weak gravitational field, such as that of a planet or an ordinary star,...

For a relatively weak gravitational field, such as that of a planet or an ordinary star, the following formula tells us the fractional amount of gravitational time dilation at a distance r from the center of an object of mass Mobject: 1c2×GMobjectr (G=6.67×10?11m3/(kg×s2); c=3×108m/s.) For example, while 1 hour passes in deep space far from the object, the amount of time that passes at a distance r is 1 hour minus 1 hour multiplied by the factor above. (This formula...

A planet has an eccentricity of 0.664 and orbits a star of mass 8.72×10^30 kg with...

A planet has an eccentricity of 0.664 and orbits a star of mass 8.72×10^30 kg with a period of 5.72 years. Give Answers in Meters 1. What is the semi-major axis of the planet's orbit? 2. What is the average velocity of the planet in its orbit? 3. What is the distance of closest approach to its parent start (perihelion)? 4. What is the farthest distance the planet travels away from its parent start (aphelion)?

Calculate Debye Length and the electron plasma frequency in the neutron star environment of temperature Te...

Calculate Debye Length and the electron plasma frequency in the neutron star environment of temperature Te = 300 keV, the electron density is 1017 cm-3, and magnetic field B = 1012 T.

Subjects