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

Click For Summary

Homework Help Overview

The discussion revolves around calculating the mass and orbital distance of a planetary body within the context of a planetary simulation model. Participants are exploring basic astrophysical concepts related to mass, density, and orbital mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand how to calculate mass from volume and density, and subsequently how to determine the orbital distance of a satellite. Other participants provide insights into the relationship between mass, density, and orbital mechanics, while also raising questions about the equations for orbital speed.

Discussion Status

Participants are actively engaging with the problem, with some providing equations and insights into gravitational forces and centripetal acceleration. There is a collaborative atmosphere, with guidance being shared without reaching a definitive conclusion.

Contextual Notes

There is an emphasis on the foundational nature of the questions, with participants acknowledging the elementary level of the concepts being discussed. The original poster expresses a lack of formal physics training, which influences the nature of the inquiries.

revolv
Messages
4
Reaction score
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
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
 
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:
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
 
Thanks a bunch, Andrew. That is exactly wahat I needed.

-B.
 

Similar threads

Replies
18
Views
3K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 84 ·
3
Replies
84
Views
7K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
17
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 23 ·
Replies
23
Views
2K
  • · Replies 12 ·
Replies
12
Views
4K