How do scientist measure the mass of the planets?

Question

Anna Armstrong · Accepted Answer

The mass of a planet can be determined using Kepler's 3rd law and by gravitational effects.

Sending a spacecraft to a planet and measuring the acceleration caused by gravity as it passes by is the most accurate method of determining the mass of that planet. Alternatively, the orbit of the moon can be used to determine the mass of the planet if it has one. In order to determine the distance from Earth to the Sun, we must first determine the planet's distance from Earth. For Venus, this is accomplished by timing the return of radar signals bounced off the planet and measuring the resulting time. Once we know Venus's distance from Earth at its closest point, we can use Kepler's third law to calculate the distance to any other planet. To calculate the mass of the planet we need the distance of the planet form Earth #R#. We then need to measure the orbital period #T# of the moon and the largest angular separation #theta# of the planet and the moon as the moon orbits the planet. We can now calculate the radius of the moon's orbit #r=R theta#. We now use Newton's form of Kepler's third law: #T^2=(4 pi^2)/(G(M+m))r^3# Where #G# is the gravitational constant, #M# is the mass of the planet and #m# is the mass of the moon. Rearranging the equation gives: #M+m=(4 pi^2 r^3)/(GT^2)# We now have calculated the combined mass of the planet and the moon. If the moon is small compared to the planet then we can ignore the moon's mass and set #m=0#. This is true of most moons in the solar system. If the moon is relatively large such as the Earth's Moon and Pluto and Charon, then we need to find the centre of mass which the planet and the moon are orbiting around. The distance #d# from the centre of the planet to the centre of mass of the planet and moon can be used to calculate the ratio of that planet and moon masses and hence the planet''s mass. #Md=m(r-d)# The planet's mass is thus given as: #M=(4 pi^2 r^2(r-d))/(GT^2)#

Audrey Arnold · Answer

undefined By observing the orbit of moons or artificial satellites around a planet, scientists can determine the mass of the planet. This is done by using Newton's law of universal gravitation, which relates the gravitational force between two objects to their masses and the distance between them.

Parker Albertson · Answer

undefined Scientists measure the mass of planets using various methods, including:

1. Orbital Dynamics: By observing the gravitational interactions between planets and their moons, satellites, or other celestial bodies, scientists can calculate the mass of a planet. This method relies on Newton's law of universal gravitation and Kepler's laws of planetary motion.

2. Astrometry: Astrometric observations involve precisely measuring the positions and movements of celestial objects over time. By tracking the orbit of a planet around its star, scientists can infer the planet's mass based on its gravitational influence on the star's motion.

3. Radial Velocity: This method involves observing the slight wobble or Doppler shift in a star's spectral lines caused by the gravitational pull of an orbiting planet. By analyzing these changes in the star's velocity, scientists can determine the mass of the planet.

4. Transit Photometry: When a planet passes in front of its star from our perspective on Earth (transit), it causes a slight decrease in the star's brightness. By studying these periodic changes in brightness, scientists can estimate the size and mass of the planet.

5. Gravitational Microlensing: In rare cases, the gravitational field of a planet can bend and magnify the light of a background star, acting as a gravitational lens. By analyzing the duration and shape of this lensing event, scientists can deduce the mass of the planet responsible for the lensing.

Overall, scientists employ a combination of observational techniques and theoretical models to accurately measure the mass of planets in our solar system and beyond. Each method has its strengths and limitations, but together they provide valuable insights into the composition and dynamics of planetary systems.