answered question
answers (3)
>For any planet with a moon, the planet's mass can be approximated by GmM/r² = mv²/r = mr?² = mr(2p/P)², where G is the gravitational constant, m the mass of the moon, M the mass of the planet, r the distance between planet and moon, and P the period of the moon. The mass of the moon cancels out, leaving
M = r³(2p/P)²/G
The masses of moonless planets have to be determined by Perturbation Theory, the effect of one planet's orbit on the orbits of other planets.
The diameter of another celestial object can be estimated by multiplying the angle subtended by the object by its distance from us. A closer estimate is obtained by
d/2 = Dsin(a/2)
where d is the diameter, D is distance to the object, and a is the subtended angle.
M = r³(2p/P)²/G
The masses of moonless planets have to be determined by Perturbation Theory, the effect of one planet's orbit on the orbits of other planets.
The diameter of another celestial object can be estimated by multiplying the angle subtended by the object by its distance from us. A closer estimate is obtained by
d/2 = Dsin(a/2)
where d is the diameter, D is distance to the object, and a is the subtended angle.
| Asker's rating: |
voted helpful: nativenerd
We start by determining the mass of the Earth. Issac Newton's Law of Universal Gravitation tells us that the force of attraction between two objects is proportional the product of their masses divided by the square of the distance between their centers of mass. To obtain a reasonable approximation, we assume their geographical centers are their centers of mass.
Because we know the radius of the Earth, we can use the Law of Universal Gravitation to calculate the mass of the Earth in terms of the gravitational force on an object (its weight) at the Earth's surface, using the radius of the Earth as the distance. We also need the Constant of Proportionality in the Law of Universal Gravitation, G. This value was experimentally determined by Henry Cavendish in the 18th century to be the extemely small force of 6.67 x 10-11 Newtons between two objects weighing one kilogram each and separated by one meter. Cavendish determined this constant by accurately measuring the horizontal force between metal spheres in an experiment sometimes referred to as "weighing the earth."
Knowing the mass and radius of the Earth and the distance of the Earth from the sun, we can calculate the mass of the sun (right), again by using the law of universal gravitation. The gravitational attraction between the Earth and the sun is G times the sun's mass times the Earth's mass, divided by the distance between the Earth and the sun squared. This attraction must be equal to the centripetal force needed to keep the earth in its (almost circular) orbit around the sun. The centripetal force is the Earth's mass times the square of its speed divided by its distance from the sun. By astronomically determining the distance to the sun, we can calculate the earth's speed around the sun and hence the sun's mass.
Once we have the sun's mass, we can similarly determine the mass of any planet by astronomically determining the planet's orbital radius and period, calculating the required centripetal force and equating this force to the force predicted by the law of universal gravitation using the sun's mass.
Because we know the radius of the Earth, we can use the Law of Universal Gravitation to calculate the mass of the Earth in terms of the gravitational force on an object (its weight) at the Earth's surface, using the radius of the Earth as the distance. We also need the Constant of Proportionality in the Law of Universal Gravitation, G. This value was experimentally determined by Henry Cavendish in the 18th century to be the extemely small force of 6.67 x 10-11 Newtons between two objects weighing one kilogram each and separated by one meter. Cavendish determined this constant by accurately measuring the horizontal force between metal spheres in an experiment sometimes referred to as "weighing the earth."
Knowing the mass and radius of the Earth and the distance of the Earth from the sun, we can calculate the mass of the sun (right), again by using the law of universal gravitation. The gravitational attraction between the Earth and the sun is G times the sun's mass times the Earth's mass, divided by the distance between the Earth and the sun squared. This attraction must be equal to the centripetal force needed to keep the earth in its (almost circular) orbit around the sun. The centripetal force is the Earth's mass times the square of its speed divided by its distance from the sun. By astronomically determining the distance to the sun, we can calculate the earth's speed around the sun and hence the sun's mass.
Once we have the sun's mass, we can similarly determine the mass of any planet by astronomically determining the planet's orbital radius and period, calculating the required centripetal force and equating this force to the force predicted by the law of universal gravitation using the sun's mass.
voted helpful: nativenerd
These guys have mentioned how to find the mass of planets that we can "see". I'm going to take it a bit further and go into planet hunting...measuring the suspected planets in other solar systems or even galaxies.
There are 3 main ways to find and measure these planets: Astrometry, Doppler spectroscopy, Photometry. There is a good simple explaination here:
http://www.howstuffworks.com/planet-hunting2.htm
"Astrometry - As a planet tugs on a star with its gravitational pull, it causes the star to wobble in its path across the sky. By making careful, precise measurements of the star's position in the sky, we can detect this extremely slight wobble. When we know the period of the wobble, we can calculate the period of the planet's orbit, the distance or radius of the planet's orbit and the mass of the planet. " The Universal Law of Gravitation is then used for the details.
"Doppler Spectroscopy - As a planet orbits a star, it periodically pulls the star closer to and farther away from Earth (our observation point). This motion has an effect on the spectrum of light coming from the star. " They then watch the spectrums of light for changes. It will shift red when planet is moving away, and shift to the blue when it's moving towards us. They can also guestimate the size by how big the shifts are.
"Photometry - If the orbit of an extrasolar planet is in a straight line of sight with Earth, the planet will pass directly between the star it's orbiting and Earth. When the planet passes in front of the star, it blocks some portion of the star's light, and the star gets slightly dimmer (by about 2 to 5 percent). The planet eclipses the star. As the planet passes behind the star, the star's normal brightness returns. By constantly measuring the star's light intensity over time, we can detect changes in its brightness that might indicate the presence of a planet or planets. "
There are 3 main ways to find and measure these planets: Astrometry, Doppler spectroscopy, Photometry. There is a good simple explaination here:
http://www.howstuffworks.com/planet-hunting2.htm
"Astrometry - As a planet tugs on a star with its gravitational pull, it causes the star to wobble in its path across the sky. By making careful, precise measurements of the star's position in the sky, we can detect this extremely slight wobble. When we know the period of the wobble, we can calculate the period of the planet's orbit, the distance or radius of the planet's orbit and the mass of the planet. " The Universal Law of Gravitation is then used for the details.
"Doppler Spectroscopy - As a planet orbits a star, it periodically pulls the star closer to and farther away from Earth (our observation point). This motion has an effect on the spectrum of light coming from the star. " They then watch the spectrums of light for changes. It will shift red when planet is moving away, and shift to the blue when it's moving towards us. They can also guestimate the size by how big the shifts are.
"Photometry - If the orbit of an extrasolar planet is in a straight line of sight with Earth, the planet will pass directly between the star it's orbiting and Earth. When the planet passes in front of the star, it blocks some portion of the star's light, and the star gets slightly dimmer (by about 2 to 5 percent). The planet eclipses the star. As the planet passes behind the star, the star's normal brightness returns. By constantly measuring the star's light intensity over time, we can detect changes in its brightness that might indicate the presence of a planet or planets. "
Related questions
140 characters left
ask any question
