# What size would a planet have to be such that I could throw a tennis ball into orbit?

If I was affixed to the surface of some solid spherical body in space (so as to ignore effects like me floating away), would it be possible for me to throw a tennis ball so that it went into orbit around the body?

I imagine the average density would be an important variable since I can only throw a tennis ball so hard.

I think, if the density was right, there would be some radius R of this spherical body such that I could throw a tennis ball and it would go into orbit around this sphere.

For the average peson, what would the density and radius be of a sphere such that you could toss a tennis ball and it would go into orbit around this sphere?

• Need to know how much atmosphere you have to push through and if there are limits to your speed you can throw. Also, how high in orbit, like geosync orbit? You ask for hard science, but the problem is you said "I", so a human, a human needs Earth or Earth like, which means a human can never do this on Earth. So the size of the planet is "small enough that the person suffocates and dies but large enough to generate some gravity" Dec 18, 2018 at 21:14
• You can not, it'll fall back down or fly away, unless orbit height = your height, but then it'll only fly once and hit you on the back of your head. Otherwise you need two impulses to get an orbit. Would calculations for orbit radius equal to the planet radius + 1.8m satisfy your needs? Dec 18, 2018 at 21:53
• Obligatory XKCD: xkcd.com/681. Note though as Mołot said, it is referencing escape velocities. If you are ok though with throwing it from a tower or something and having it orbit really low to the ground, check out the stats for Phobos. Dec 18, 2018 at 22:02
• Hardest question at the moment - how fast you can throw a tennis ball... Can someone tell me speed of an average man's throw for a that ball? Dec 18, 2018 at 22:19
• This would probably fit better on Physics.SE. The boring answer is "yes absolutely, for any speed of throw," though you may be sad at the physics definition of being in orbit. (As Mołot said, you'll hit the back of your own head) The longer answer is "Take a look at wikipedia's page on Orbital speed" The longer-longer answers involving specifics are the kinds of things that Physics.SE is good at providing. They might explore interesting questions like eliptical orbits rather than merely circular ones. Dec 18, 2018 at 22:21

## 1 Answer

When the hardest part to give my petty answer is finding out how fast an average person can throw a tennis ball, people serve them mostly. If you throw it is probably somewhere in 80-120 km/h range. Fastballs of pro's in baseball are 150-170 km/h, serves in tennis are close to the same number only in miles per hour.

There is an infinite number of orbits = orbit velocities your tennis ball can go at, from circle to elliptical ones, till you hit escape velocity and then you have a chance at murdering some innocent alien few million years in the future.

• Circular orbit velocity: ; ;

• Escape velocity: or ;

G - gravitational constant ; M - mass of both objects or mass of the planet in our case; R - distance between centers of gravity; g - gravitational acceleration aka. surface gravity.

Table with some fast calculations

So 30-50 km radius for my speeds of 80-120 km per hour. Density used is what you would expect of a nonmetallic asteroid, but a rocky one at least.

Of course, you could make a tennis ball orbit any asteroid with smaller values, just don't throw it too fast or it will escape. You can even let the tennis ball orbit you if you are okay to wait for something around the magnitude of 1-3 months for a revolution or way more if the radius is bigger.

You can increase it by using a hollowed/altered asteroid, you can play with new mass and radius. How big you could build it before it collapses? That is a big question of itself. Just find what asteroid fulfills requirements of your story and then tweak it for this stunt.

• This is a bounty-worthy answer. Dec 19, 2018 at 11:55