How do I calculate the mass and orbital distance of a planetary body?

In summary, the conversation is about a programmer seeking help with calculating the mass and orbital distance of a planetary body for a simulation model. The equations for calculating mass and orbital speed are discussed, with the force of gravity being a key factor. The universal gravitation constant and an example for determining orbital speed are also mentioned. The programmer expresses their gratitude for the help provided.
  • #1
revolv
4
0
Hey everyone. I am working on a planetary simulation model and am having a bit of trouble with the math. Given the volume and density of a particular planetary body, how do I calculate the mass? Once I have the mass, how do I calculate the orbital distance of a satellite body to said panetary body? I'm sure this is somewhat elementary astrophysics but, in the immortal edited words of Dr. McCoy, I'm a programmer, not a physicist! Thanks in advance for any help.
 
Physics news on Phys.org
  • #2
revolv said:
Hey everyone. I am working on a planetary simulation model and am having a bit of trouble with the math. Given the volume and density of a particular planetary body, how do I calculate the mass? Once I have the mass, how do I calculate the orbital distance of a satellite body to said panetary body? I'm sure this is somewhat elementary astrophysics but, in the immortal edited words of Dr. McCoy, I'm a programmer, not a physicist! Thanks in advance for any help.

Density is mass/volume:[itex] \rho = m/V[/itex] so [itex]m = \rho V[/itex]

The orbital radius of a satellite (distance from satellite to centre of the planet) will depend on the speed of the satellite. A satellite can orbit at any distance.

AM
 
  • #3
Thanks for the info, Andrew. It is very much appreciated. One other question if I may. If i know the distance, what is the equation for determining the orbital speed? Or, from a education standpoint, where can i find said equation?
 
Last edited:
  • #4
revolv said:
Thanks for the info. It is very much appreciated. One other question if I may. If i know the distance, what is the equation for determining the orbital speed? Or, from a education standpoint, where can i find said equation?
The force of gravity provides the centripetal acceleration, so:

[tex]mv^2/r = GMm/r^2[/tex] so:

[tex]v = \sqrt{GM/r}[/tex] where G is the universal gravitation constant and M is the mass of the planet

G = 6.67 x 10-11 m3/kg sec2

Example: The mass of the Earth is M = 5.98 x 1024kg

The radius of the Earth at the equator is about 6,378,000 m. So, at a distance of 1000 km above the earth, the orbital speed would be:

[tex]v = \sqrt{6.67e-11*5.98e24/7.378e6} = 7.35 x 10^3 m/sec[/tex]

This works out to about 26,500 km/hr.

AM
 
  • #5
Thanks a bunch, Andrew. That is exactly wahat I needed.

-B.
 

1. What is the Mass of stellar bodies?

The mass of stellar bodies refers to the amount of matter contained within a celestial object, such as a star or planet. It is typically measured in units of solar masses, which is equivalent to the mass of our Sun.

2. How is the Mass of stellar bodies measured?

The mass of stellar bodies is measured using various techniques, including radial velocity measurements, astrometry, and gravitational lensing. These methods involve observing the effects of a star's mass on its surrounding environment to determine its mass.

3. What is the average mass of a star?

The average mass of a star is about 1 solar mass, or 2 x 10^30 kilograms. However, there is a wide range of stellar masses, with some stars being much larger or smaller than average.

4. How does the Mass of stellar bodies affect their lifespan?

The mass of a star directly impacts its lifespan. Higher mass stars have a shorter lifespan, as they burn through their fuel at a faster rate. Lower mass stars, on the other hand, have a longer lifespan as they consume their fuel more slowly.

5. Can the Mass of stellar bodies change over time?

Yes, the mass of stellar bodies can change over time through various processes such as mass loss due to stellar winds, accretion of material from a companion star, or merging with other stars. However, these changes are usually small and do not significantly affect the overall mass of the star.

Similar threads

  • Introductory Physics Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Special and General Relativity
Replies
23
Views
1K
  • Classical Physics
3
Replies
84
Views
4K
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
17
Views
2K
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
2K
Back
Top